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Rationalisation of the ODE solvers library
This commit is contained in:
Henry
@ -29,7 +29,6 @@ Description
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#include "IOmanip.H"
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#include "IOmanip.H"
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#include "ODESystem.H"
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#include "ODESystem.H"
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#include "ODESolver.H"
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#include "ODESolver.H"
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#include "RK.H"
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using namespace Foam;
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using namespace Foam;
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@ -137,11 +136,10 @@ int main(int argc, char *argv[])
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scalarField y(yStart);
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scalarField y(yStart);
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scalarField dydx(dyStart);
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scalarField dydx(dyStart);
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scalarField yScale(ode.nEqns(), 1.0);
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scalar hEst = 0.6;
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scalar hEst = 0.6;
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scalar hDid, hNext;
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scalar hDid, hNext;
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odeSolver->solve(ode, x, y, dydx, eps, yScale, hEst, hDid, hNext);
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odeSolver->solve(ode, x, y, dydx, eps, hEst, hDid, hNext);
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Info<< scientific << setw(13) << eps;
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Info<< scientific << setw(13) << eps;
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Info<< fixed << setw(11) << hEst;
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Info<< fixed << setw(11) << hEst;
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@ -1,19 +1,11 @@
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ODE = ODE
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ODESolvers/ODESolver/ODESolver.C
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ODESolvers = ODESolvers
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ODESolvers/ODESolver/ODESolverNew.C
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ODESolversODESolver = ODESolvers/ODESolver
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ODESolversKRR4 = ODESolvers/KRR4
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ODESolversRK = ODESolvers/RK
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ODESolversSIBS = ODESolvers/SIBS
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$(ODESolversODESolver)/ODESolver.C
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ODESolvers/adaptiveSolver/adaptiveSolver.C
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$(ODESolversODESolver)/ODESolverNew.C
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ODESolvers/RKCK5/RKCK5.C
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ODESolvers/KRR4/KRR4.C
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$(ODESolversRK)/RK.C
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ODESolvers/SIBS/SIBS.C
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ODESolvers/SIBS/SIMPR.C
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$(ODESolversKRR4)/KRR4.C
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ODESolvers/SIBS/polyExtrapolate.C
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$(ODESolversSIBS)/SIBS.C
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$(ODESolversSIBS)/SIMPR.C
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$(ODESolversSIBS)/polyExtrapolate.C
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LIB = $(FOAM_LIBBIN)/libODE
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LIB = $(FOAM_LIBBIN)/libODE
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@ -2,7 +2,7 @@
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========= |
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========= |
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\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
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\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
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\\ / O peration |
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\\ / O peration |
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\\ / A nd | Copyright (C) 2011-2012 OpenFOAM Foundation
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\\ / A nd | Copyright (C) 2011-2013 OpenFOAM Foundation
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\\/ M anipulation |
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\\/ M anipulation |
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-------------------------------------------------------------------------------
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-------------------------------------------------------------------------------
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License
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License
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@ -31,13 +31,8 @@ License
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namespace Foam
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namespace Foam
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{
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{
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defineTypeNameAndDebug(KRR4, 0);
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defineTypeNameAndDebug(KRR4, 0);
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addToRunTimeSelectionTable(ODESolver, KRR4, ODE);
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addToRunTimeSelectionTable(ODESolver, KRR4, ODE);
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const scalar
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KRR4::safety = 0.9, KRR4::grow = 1.5, KRR4::pgrow = -0.25,
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KRR4::shrink = 0.5, KRR4::pshrink = (-1.0/3.0), KRR4::errcon = 0.1296;
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const scalar
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const scalar
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KRR4::gamma = 1.0/2.0,
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KRR4::gamma = 1.0/2.0,
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KRR4::a21 = 2.0, KRR4::a31 = 48.0/25.0, KRR4::a32 = 6.0/25.0,
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KRR4::a21 = 2.0, KRR4::a31 = 48.0/25.0, KRR4::a32 = 6.0/25.0,
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@ -58,166 +53,112 @@ const scalar
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Foam::KRR4::KRR4(const ODESystem& ode)
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Foam::KRR4::KRR4(const ODESystem& ode)
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:
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:
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ODESolver(ode),
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ODESolver(ode),
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yTemp_(n_, 0.0),
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adaptiveSolver(ode),
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dydxTemp_(n_, 0.0),
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g1_(n_),
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g1_(n_, 0.0),
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g2_(n_),
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g2_(n_, 0.0),
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g3_(n_),
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g3_(n_, 0.0),
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g4_(n_),
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g4_(n_, 0.0),
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err_(n_),
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yErr_(n_, 0.0),
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dfdx_(n_),
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dfdx_(n_, 0.0),
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dfdy_(n_, n_),
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dfdy_(n_, n_, 0.0),
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a_(n_, n_),
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a_(n_, n_, 0.0),
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pivotIndices_(n_)
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pivotIndices_(n_, 0.0)
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{}
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{}
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// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
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// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
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void Foam::KRR4::solve
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Foam::scalar Foam::KRR4::solve
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(
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(
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const ODESystem& ode,
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const ODESystem& ode,
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const scalar x0,
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const scalarField& y0,
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const scalarField& dydx0,
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const scalar dx,
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scalarField& y,
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const scalar eps
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) const
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{
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ode.jacobian(x0, y0, dfdx_, dfdy_);
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for (register label i=0; i<n_; i++)
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{
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for (register label j=0; j<n_; j++)
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{
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a_[i][j] = -dfdy_[i][j];
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}
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a_[i][i] += 1.0/(gamma*dx);
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}
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LUDecompose(a_, pivotIndices_);
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forAll(g1_, i)
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{
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g1_[i] = dydx0[i] + dx*c1X*dfdx_[i];
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}
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LUBacksubstitute(a_, pivotIndices_, g1_);
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forAll(y, i)
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{
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y[i] = y0[i] + a21*g1_[i];
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}
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ode.derivatives(x0 + a2X*dx, y, dydx_);
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forAll(g2_, i)
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{
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g2_[i] = dydx_[i] + dx*c2X*dfdx_[i] + c21*g1_[i]/dx;
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}
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LUBacksubstitute(a_, pivotIndices_, g2_);
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forAll(y, i)
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{
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y[i] = y0[i] + a31*g1_[i] + a32*g2_[i];
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}
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ode.derivatives(x0 + a3X*dx, y, dydx_);
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forAll(g3_, i)
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{
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g3_[i] = dydx0[i] + dx*c3X*dfdx_[i] + (c31*g1_[i] + c32*g2_[i])/dx;
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}
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LUBacksubstitute(a_, pivotIndices_, g3_);
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forAll(g4_, i)
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{
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g4_[i] = dydx_[i] + dx*c4X*dfdx_[i]
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+ (c41*g1_[i] + c42*g2_[i] + c43*g3_[i])/dx;
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}
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LUBacksubstitute(a_, pivotIndices_, g4_);
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forAll(y, i)
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{
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y[i] = y0[i] + b1*g1_[i] + b2*g2_[i] + b3*g3_[i] + b4*g4_[i];
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err_[i] = e1*g1_[i] + e2*g2_[i] + e3*g3_[i] + e4*g4_[i];
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}
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return normalizeError(eps, y0, y, err_);
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}
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void Foam::KRR4::solve
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(
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const ODESystem& odes,
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scalar& x,
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scalar& x,
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scalarField& y,
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scalarField& y,
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scalarField& dydx,
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scalarField& dydx,
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const scalar eps,
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const scalar eps,
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const scalarField& yScale,
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const scalar dxTry,
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const scalar hTry,
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scalar& dxDid,
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scalar& hDid,
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scalar& dxNext
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scalar& hNext
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) const
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) const
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{
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{
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scalar xTemp = x;
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adaptiveSolver::solve(odes, x, y, dydx, eps, dxTry, dxDid, dxNext);
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yTemp_ = y;
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dydxTemp_ = dydx;
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ode.jacobian(xTemp, yTemp_, dfdx_, dfdy_);
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scalar h = hTry;
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for (register label jtry=0; jtry<maxtry; jtry++)
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{
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for (register label i=0; i<n_; i++)
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{
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for (register label j=0; j<n_; j++)
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{
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a_[i][j] = -dfdy_[i][j];
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}
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a_[i][i] += 1.0/(gamma*h);
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}
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LUDecompose(a_, pivotIndices_);
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for (register label i=0; i<n_; i++)
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{
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g1_[i] = dydxTemp_[i] + h*c1X*dfdx_[i];
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}
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LUBacksubstitute(a_, pivotIndices_, g1_);
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for (register label i=0; i<n_; i++)
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{
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y[i] = yTemp_[i] + a21*g1_[i];
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}
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x = xTemp + a2X*h;
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ode.derivatives(x, y, dydx_);
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for (register label i=0; i<n_; i++)
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{
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g2_[i] = dydx_[i] + h*c2X*dfdx_[i] + c21*g1_[i]/h;
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}
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LUBacksubstitute(a_, pivotIndices_, g2_);
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for (register label i=0; i<n_; i++)
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{
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y[i] = yTemp_[i] + a31*g1_[i] + a32*g2_[i];
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}
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x = xTemp + a3X*h;
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ode.derivatives(x, y, dydx_);
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for (register label i=0; i<n_; i++)
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{
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g3_[i] = dydx[i] + h*c3X*dfdx_[i] + (c31*g1_[i] + c32*g2_[i])/h;
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}
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LUBacksubstitute(a_, pivotIndices_, g3_);
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for (register label i=0; i<n_; i++)
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{
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g4_[i] = dydx_[i] + h*c4X*dfdx_[i]
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+ (c41*g1_[i] + c42*g2_[i] + c43*g3_[i])/h;
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}
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LUBacksubstitute(a_, pivotIndices_, g4_);
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for (register label i=0; i<n_; i++)
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{
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y[i] = yTemp_[i] + b1*g1_[i] + b2*g2_[i] + b3*g3_[i] + b4*g4_[i];
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yErr_[i] = e1*g1_[i] + e2*g2_[i] + e3*g3_[i] + e4*g4_[i];
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}
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x = xTemp + h;
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if (x == xTemp)
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{
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FatalErrorIn
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(
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"void Foam::KRR4::solve"
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"("
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"const ODESystem&, "
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"scalar&, "
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"scalarField&, "
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"scalarField&, "
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"const scalar, "
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"const scalarField&, "
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"const scalar, "
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"scalar&, "
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"scalar&"
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||||||
") const"
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) << "solver stalled: step size = 0"
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<< exit(FatalError);
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}
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scalar maxErr = 0.0;
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for (register label i=0; i<n_; i++)
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{
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maxErr = max(maxErr, mag(yErr_[i]/yScale[i]));
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}
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maxErr /= eps;
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if (maxErr <= 1.0)
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{
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hDid = h;
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hNext = (maxErr > errcon ? safety*h*pow(maxErr, pgrow) : grow*h);
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return;
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}
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else
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{
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hNext = safety*h*pow(maxErr, pshrink);
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h = (h >= 0.0 ? max(hNext, shrink*h) : min(hNext, shrink*h));
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}
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}
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FatalErrorIn
|
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(
|
|
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"void Foam::KRR4::solve"
|
|
||||||
"("
|
|
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"const ODESystem&, "
|
|
||||||
"scalar&, "
|
|
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"scalarField&, "
|
|
||||||
"scalarField&, "
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|
||||||
"const scalar, "
|
|
||||||
"const scalarField&, "
|
|
||||||
"const scalar, "
|
|
||||||
"scalar&, "
|
|
||||||
"scalar&"
|
|
||||||
") const"
|
|
||||||
) << "Maximum number of solver iterations exceeded"
|
|
||||||
<< exit(FatalError);
|
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
||||||
|
|||||||
@ -2,7 +2,7 @@
|
|||||||
========= |
|
========= |
|
||||||
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
|
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
|
||||||
\\ / O peration |
|
\\ / O peration |
|
||||||
\\ / A nd | Copyright (C) 2011 OpenFOAM Foundation
|
\\ / A nd | Copyright (C) 2011-2013 OpenFOAM Foundation
|
||||||
\\/ M anipulation |
|
\\/ M anipulation |
|
||||||
-------------------------------------------------------------------------------
|
-------------------------------------------------------------------------------
|
||||||
License
|
License
|
||||||
@ -25,11 +25,26 @@ Class
|
|||||||
Foam::KRR4
|
Foam::KRR4
|
||||||
|
|
||||||
Description
|
Description
|
||||||
Foam::KRR4
|
4th Order Kaps Rentrop Rosenbrock stiff ODE solver
|
||||||
|
|
||||||
|
References:
|
||||||
|
\verbatim
|
||||||
|
"Generalized Runge-Kutta methods of order four with stepsize control
|
||||||
|
for stiff ordinary differential equations"
|
||||||
|
Kaps, P.,
|
||||||
|
Rentrop, P.,
|
||||||
|
Numerische Thematic, vol. 33, 1979, pp. 55–68.
|
||||||
|
\endverbatim
|
||||||
|
|
||||||
|
Constants from:
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||||||
|
\verbatim
|
||||||
|
"Implementation of Rosenbrock Methods"
|
||||||
|
Shampine, L. F.,
|
||||||
|
ACM Transactions on Mathematical Software, vol. 8, 1982, pp. 93–113.
|
||||||
|
\endverbatim
|
||||||
|
|
||||||
SourceFiles
|
SourceFiles
|
||||||
KRR4CK.C
|
KRR4.C
|
||||||
KRR4QS.C
|
|
||||||
|
|
||||||
\*---------------------------------------------------------------------------*/
|
\*---------------------------------------------------------------------------*/
|
||||||
|
|
||||||
@ -37,6 +52,7 @@ SourceFiles
|
|||||||
#define KRR4_H
|
#define KRR4_H
|
||||||
|
|
||||||
#include "ODESolver.H"
|
#include "ODESolver.H"
|
||||||
|
#include "adaptiveSolver.H"
|
||||||
|
|
||||||
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
|
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
|
||||||
|
|
||||||
@ -49,26 +65,21 @@ namespace Foam
|
|||||||
|
|
||||||
class KRR4
|
class KRR4
|
||||||
:
|
:
|
||||||
public ODESolver
|
public ODESolver,
|
||||||
|
public adaptiveSolver
|
||||||
{
|
{
|
||||||
// Private data
|
// Private data
|
||||||
|
|
||||||
mutable scalarField yTemp_;
|
|
||||||
mutable scalarField dydxTemp_;
|
|
||||||
mutable scalarField g1_;
|
mutable scalarField g1_;
|
||||||
mutable scalarField g2_;
|
mutable scalarField g2_;
|
||||||
mutable scalarField g3_;
|
mutable scalarField g3_;
|
||||||
mutable scalarField g4_;
|
mutable scalarField g4_;
|
||||||
mutable scalarField yErr_;
|
mutable scalarField err_;
|
||||||
mutable scalarField dfdx_;
|
mutable scalarField dfdx_;
|
||||||
mutable scalarSquareMatrix dfdy_;
|
mutable scalarSquareMatrix dfdy_;
|
||||||
mutable scalarSquareMatrix a_;
|
mutable scalarSquareMatrix a_;
|
||||||
mutable labelList pivotIndices_;
|
mutable labelList pivotIndices_;
|
||||||
|
|
||||||
static const int maxtry = 40;
|
|
||||||
|
|
||||||
static const scalar safety, grow, pgrow, shrink, pshrink, errcon;
|
|
||||||
|
|
||||||
static const scalar
|
static const scalar
|
||||||
gamma,
|
gamma,
|
||||||
a21, a31, a32,
|
a21, a31, a32,
|
||||||
@ -93,6 +104,19 @@ public:
|
|||||||
|
|
||||||
// Member Functions
|
// Member Functions
|
||||||
|
|
||||||
|
//- Solve a single step dx and return the error
|
||||||
|
scalar solve
|
||||||
|
(
|
||||||
|
const ODESystem& ode,
|
||||||
|
const scalar x0,
|
||||||
|
const scalarField& y0,
|
||||||
|
const scalarField& dydx0,
|
||||||
|
const scalar dx,
|
||||||
|
scalarField& y,
|
||||||
|
const scalar eps
|
||||||
|
) const;
|
||||||
|
|
||||||
|
//- Solve the ODE system and the update the state
|
||||||
void solve
|
void solve
|
||||||
(
|
(
|
||||||
const ODESystem& ode,
|
const ODESystem& ode,
|
||||||
@ -100,10 +124,9 @@ public:
|
|||||||
scalarField& y,
|
scalarField& y,
|
||||||
scalarField& dydx,
|
scalarField& dydx,
|
||||||
const scalar eps,
|
const scalar eps,
|
||||||
const scalarField& yScale,
|
const scalar dxTry,
|
||||||
const scalar hTry,
|
scalar& dxDid,
|
||||||
scalar& hDid,
|
scalar& dxNext
|
||||||
scalar& hNext
|
|
||||||
) const;
|
) const;
|
||||||
};
|
};
|
||||||
|
|
||||||
|
|||||||
@ -39,7 +39,6 @@ namespace Foam
|
|||||||
Foam::ODESolver::ODESolver(const ODESystem& ode)
|
Foam::ODESolver::ODESolver(const ODESystem& ode)
|
||||||
:
|
:
|
||||||
n_(ode.nEqns()),
|
n_(ode.nEqns()),
|
||||||
yScale_(n_),
|
|
||||||
dydx_(n_)
|
dydx_(n_)
|
||||||
{}
|
{}
|
||||||
|
|
||||||
@ -67,11 +66,6 @@ void Foam::ODESolver::solve
|
|||||||
{
|
{
|
||||||
ode.derivatives(x, y, dydx_);
|
ode.derivatives(x, y, dydx_);
|
||||||
|
|
||||||
for (label i=0; i<n_; i++)
|
|
||||||
{
|
|
||||||
yScale_[i] = mag(y[i]) + mag(dydx_[i]*h) + SMALL;
|
|
||||||
}
|
|
||||||
|
|
||||||
if ((x + h - xEnd)*(x + h - xStart) > 0.0)
|
if ((x + h - xEnd)*(x + h - xStart) > 0.0)
|
||||||
{
|
{
|
||||||
h = xEnd - x;
|
h = xEnd - x;
|
||||||
@ -80,7 +74,7 @@ void Foam::ODESolver::solve
|
|||||||
|
|
||||||
hNext = 0;
|
hNext = 0;
|
||||||
scalar hDid;
|
scalar hDid;
|
||||||
solve(ode, x, y, dydx_, eps, yScale_, h, hDid, hNext);
|
solve(ode, x, y, dydx_, eps, h, hDid, hNext);
|
||||||
|
|
||||||
if ((x - xEnd)*(xEnd - xStart) >= 0.0)
|
if ((x - xEnd)*(xEnd - xStart) >= 0.0)
|
||||||
{
|
{
|
||||||
|
|||||||
@ -56,7 +56,6 @@ protected:
|
|||||||
// Private data
|
// Private data
|
||||||
|
|
||||||
label n_;
|
label n_;
|
||||||
mutable scalarField yScale_;
|
|
||||||
mutable scalarField dydx_;
|
mutable scalarField dydx_;
|
||||||
|
|
||||||
|
|
||||||
@ -117,7 +116,6 @@ public:
|
|||||||
scalarField& y,
|
scalarField& y,
|
||||||
scalarField& dydx,
|
scalarField& dydx,
|
||||||
const scalar eps,
|
const scalar eps,
|
||||||
const scalarField& yScale,
|
|
||||||
const scalar hTry,
|
const scalar hTry,
|
||||||
scalar& hDid,
|
scalar& hDid,
|
||||||
scalar& hNext
|
scalar& hNext
|
||||||
|
|||||||
@ -1,204 +0,0 @@
|
|||||||
/*---------------------------------------------------------------------------*\
|
|
||||||
========= |
|
|
||||||
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
|
|
||||||
\\ / O peration |
|
|
||||||
\\ / A nd | Copyright (C) 2011-2012 OpenFOAM Foundation
|
|
||||||
\\/ M anipulation |
|
|
||||||
-------------------------------------------------------------------------------
|
|
||||||
License
|
|
||||||
This file is part of OpenFOAM.
|
|
||||||
|
|
||||||
OpenFOAM is free software: you can redistribute it and/or modify it
|
|
||||||
under the terms of the GNU General Public License as published by
|
|
||||||
the Free Software Foundation, either version 3 of the License, or
|
|
||||||
(at your option) any later version.
|
|
||||||
|
|
||||||
OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
|
|
||||||
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
|
|
||||||
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
|
|
||||||
for more details.
|
|
||||||
|
|
||||||
You should have received a copy of the GNU General Public License
|
|
||||||
along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
|
|
||||||
|
|
||||||
\*---------------------------------------------------------------------------*/
|
|
||||||
|
|
||||||
#include "RK.H"
|
|
||||||
#include "addToRunTimeSelectionTable.H"
|
|
||||||
|
|
||||||
// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
|
|
||||||
|
|
||||||
namespace Foam
|
|
||||||
{
|
|
||||||
defineTypeNameAndDebug(RK, 0);
|
|
||||||
addToRunTimeSelectionTable(ODESolver, RK, ODE);
|
|
||||||
|
|
||||||
const scalar
|
|
||||||
RK::safety=0.9, RK::pGrow=-0.2, RK::pShrink=-0.25, RK::errCon=1.89e-4;
|
|
||||||
|
|
||||||
const scalar
|
|
||||||
RK::a2 = 0.2, RK::a3 = 0.3, RK::a4 = 0.6, RK::a5 = 1.0, RK::a6 = 0.875,
|
|
||||||
RK::b21 = 0.2, RK::b31 = 3.0/40.0, RK::b32 = 9.0/40.0,
|
|
||||||
RK::b41 = 0.3, RK::b42 = -0.9, RK::b43 = 1.2,
|
|
||||||
RK::b51 = -11.0/54.0, RK::b52 = 2.5, RK::b53 = -70.0/27.0,
|
|
||||||
RK::b54 = 35.0/27.0,
|
|
||||||
RK::b61 = 1631.0/55296.0, RK::b62 = 175.0/512.0, RK::b63 = 575.0/13824.0,
|
|
||||||
RK::b64 = 44275.0/110592.0, RK::b65 = 253.0/4096.0,
|
|
||||||
RK::c1 = 37.0/378.0, RK::c3 = 250.0/621.0,
|
|
||||||
RK::c4 = 125.0/594.0, RK::c6 = 512.0/1771.0,
|
|
||||||
RK::dc1 = RK::c1 - 2825.0/27648.0, RK::dc3 = RK::c3 - 18575.0/48384.0,
|
|
||||||
RK::dc4 = RK::c4 - 13525.0/55296.0, RK::dc5 = -277.00/14336.0,
|
|
||||||
RK::dc6 = RK::c6 - 0.25;
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
// * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
|
|
||||||
|
|
||||||
Foam::RK::RK(const ODESystem& ode)
|
|
||||||
:
|
|
||||||
ODESolver(ode),
|
|
||||||
yTemp_(n_, 0.0),
|
|
||||||
ak2_(n_, 0.0),
|
|
||||||
ak3_(n_, 0.0),
|
|
||||||
ak4_(n_, 0.0),
|
|
||||||
ak5_(n_, 0.0),
|
|
||||||
ak6_(n_, 0.0),
|
|
||||||
yErr_(n_, 0.0),
|
|
||||||
yTemp2_(n_, 0.0)
|
|
||||||
{}
|
|
||||||
|
|
||||||
|
|
||||||
// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
|
|
||||||
|
|
||||||
void Foam::RK::solve
|
|
||||||
(
|
|
||||||
const ODESystem& ode,
|
|
||||||
const scalar x,
|
|
||||||
const scalarField& y,
|
|
||||||
const scalarField& dydx,
|
|
||||||
const scalar h,
|
|
||||||
scalarField& yout,
|
|
||||||
scalarField& yerr
|
|
||||||
) const
|
|
||||||
{
|
|
||||||
forAll(yTemp_, i)
|
|
||||||
{
|
|
||||||
yTemp_[i] = y[i] + b21*h*dydx[i];
|
|
||||||
}
|
|
||||||
|
|
||||||
ode.derivatives(x + a2*h, yTemp_, ak2_);
|
|
||||||
|
|
||||||
forAll(yTemp_, i)
|
|
||||||
{
|
|
||||||
yTemp_[i] = y[i] + h*(b31*dydx[i] + b32*ak2_[i]);
|
|
||||||
}
|
|
||||||
|
|
||||||
ode.derivatives(x + a3*h, yTemp_, ak3_);
|
|
||||||
|
|
||||||
forAll(yTemp_, i)
|
|
||||||
{
|
|
||||||
yTemp_[i] = y[i] + h*(b41*dydx[i] + b42*ak2_[i] + b43*ak3_[i]);
|
|
||||||
}
|
|
||||||
|
|
||||||
ode.derivatives(x + a4*h, yTemp_, ak4_);
|
|
||||||
|
|
||||||
forAll(yTemp_, i)
|
|
||||||
{
|
|
||||||
yTemp_[i] = y[i]
|
|
||||||
+ h*(b51*dydx[i] + b52*ak2_[i] + b53*ak3_[i] + b54*ak4_[i]);
|
|
||||||
}
|
|
||||||
|
|
||||||
ode.derivatives(x + a5*h, yTemp_, ak5_);
|
|
||||||
|
|
||||||
forAll(yTemp_, i)
|
|
||||||
{
|
|
||||||
yTemp_[i] = y[i]
|
|
||||||
+ h*
|
|
||||||
(
|
|
||||||
b61*dydx[i] + b62*ak2_[i] + b63*ak3_[i]
|
|
||||||
+ b64*ak4_[i] + b65*ak5_[i]
|
|
||||||
);
|
|
||||||
}
|
|
||||||
|
|
||||||
ode.derivatives(x + a6*h, yTemp_, ak6_);
|
|
||||||
|
|
||||||
forAll(yout, i)
|
|
||||||
{
|
|
||||||
yout[i] = y[i]
|
|
||||||
+ h*(c1*dydx[i] + c3*ak3_[i] + c4*ak4_[i] + c6*ak6_[i]);
|
|
||||||
}
|
|
||||||
|
|
||||||
forAll(yerr, i)
|
|
||||||
{
|
|
||||||
yerr[i] =
|
|
||||||
h*
|
|
||||||
(
|
|
||||||
dc1*dydx[i] + dc3*ak3_[i] + dc4*ak4_[i]
|
|
||||||
+ dc5*ak5_[i] + dc6*ak6_[i]
|
|
||||||
);
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
void Foam::RK::solve
|
|
||||||
(
|
|
||||||
const ODESystem& ode,
|
|
||||||
scalar& x,
|
|
||||||
scalarField& y,
|
|
||||||
scalarField& dydx,
|
|
||||||
const scalar eps,
|
|
||||||
const scalarField& yScale,
|
|
||||||
const scalar hTry,
|
|
||||||
scalar& hDid,
|
|
||||||
scalar& hNext
|
|
||||||
) const
|
|
||||||
{
|
|
||||||
scalar h = hTry;
|
|
||||||
scalar maxErr = 0.0;
|
|
||||||
|
|
||||||
for (;;)
|
|
||||||
{
|
|
||||||
solve(ode, x, y, dydx, h, yTemp2_, yErr_);
|
|
||||||
|
|
||||||
maxErr = 0.0;
|
|
||||||
for (register label i=0; i<n_; i++)
|
|
||||||
{
|
|
||||||
maxErr = max(maxErr, mag(yErr_[i]/yScale[i]));
|
|
||||||
}
|
|
||||||
maxErr /= eps;
|
|
||||||
|
|
||||||
if (maxErr <= 1.0)
|
|
||||||
{
|
|
||||||
break;
|
|
||||||
}
|
|
||||||
|
|
||||||
{
|
|
||||||
scalar hTemp = safety*h*pow(maxErr, pShrink);
|
|
||||||
h = (h >= 0.0 ? max(hTemp, 0.1*h) : min(hTemp, 0.1*h));
|
|
||||||
}
|
|
||||||
|
|
||||||
if (h < VSMALL)
|
|
||||||
{
|
|
||||||
FatalErrorIn("RK::solve")
|
|
||||||
<< "stepsize underflow"
|
|
||||||
<< exit(FatalError);
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
hDid = h;
|
|
||||||
|
|
||||||
x += h;
|
|
||||||
y = yTemp2_;
|
|
||||||
|
|
||||||
if (maxErr > errCon)
|
|
||||||
{
|
|
||||||
hNext = safety*h*pow(maxErr, pGrow);
|
|
||||||
}
|
|
||||||
else
|
|
||||||
{
|
|
||||||
hNext = 5.0*h;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
// ************************************************************************* //
|
|
||||||
155
src/ODE/ODESolvers/RKCK5/RKCK5.C
Normal file
155
src/ODE/ODESolvers/RKCK5/RKCK5.C
Normal file
@ -0,0 +1,155 @@
|
|||||||
|
/*---------------------------------------------------------------------------*\
|
||||||
|
========= |
|
||||||
|
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
|
||||||
|
\\ / O peration |
|
||||||
|
\\ / A nd | Copyright (C) 2011-2013 OpenFOAM Foundation
|
||||||
|
\\/ M anipulation |
|
||||||
|
-------------------------------------------------------------------------------
|
||||||
|
License
|
||||||
|
This file is part of OpenFOAM.
|
||||||
|
|
||||||
|
OpenFOAM is free software: you can redistribute it and/or modify it
|
||||||
|
under the terms of the GNU General Public License as published by
|
||||||
|
the Free Software Foundation, either version 3 of the License, or
|
||||||
|
(at your option) any later version.
|
||||||
|
|
||||||
|
OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
|
||||||
|
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
|
||||||
|
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
|
||||||
|
for more details.
|
||||||
|
|
||||||
|
You should have received a copy of the GNU General Public License
|
||||||
|
along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
|
||||||
|
|
||||||
|
\*---------------------------------------------------------------------------*/
|
||||||
|
|
||||||
|
#include "RKCK5.H"
|
||||||
|
#include "addToRunTimeSelectionTable.H"
|
||||||
|
|
||||||
|
// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
|
||||||
|
|
||||||
|
namespace Foam
|
||||||
|
{
|
||||||
|
defineTypeNameAndDebug(RKCK5, 0);
|
||||||
|
addToRunTimeSelectionTable(ODESolver, RKCK5, ODE);
|
||||||
|
|
||||||
|
const scalar
|
||||||
|
RKCK5::a2 = 0.2, RKCK5::a3 = 0.3, RKCK5::a4 = 0.6, RKCK5::a5 = 1.0,
|
||||||
|
RKCK5::a6 = 0.875,
|
||||||
|
RKCK5::b21 = 0.2, RKCK5::b31 = 3.0/40.0, RKCK5::b32 = 9.0/40.0,
|
||||||
|
RKCK5::b41 = 0.3, RKCK5::b42 = -0.9, RKCK5::b43 = 1.2,
|
||||||
|
RKCK5::b51 = -11.0/54.0, RKCK5::b52 = 2.5, RKCK5::b53 = -70.0/27.0,
|
||||||
|
RKCK5::b54 = 35.0/27.0,
|
||||||
|
RKCK5::b61 = 1631.0/55296.0, RKCK5::b62 = 175.0/512.0,
|
||||||
|
RKCK5::b63 = 575.0/13824.0, RKCK5::b64 = 44275.0/110592.0,
|
||||||
|
RKCK5::b65 = 253.0/4096.0,
|
||||||
|
RKCK5::c1 = 37.0/378.0, RKCK5::c3 = 250.0/621.0,
|
||||||
|
RKCK5::c4 = 125.0/594.0, RKCK5::c6 = 512.0/1771.0,
|
||||||
|
RKCK5::dc1 = RKCK5::c1 - 2825.0/27648.0,
|
||||||
|
RKCK5::dc3 = RKCK5::c3 - 18575.0/48384.0,
|
||||||
|
RKCK5::dc4 = RKCK5::c4 - 13525.0/55296.0, RKCK5::dc5 = -277.00/14336.0,
|
||||||
|
RKCK5::dc6 = RKCK5::c6 - 0.25;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
// * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
|
||||||
|
|
||||||
|
Foam::RKCK5::RKCK5(const ODESystem& ode)
|
||||||
|
:
|
||||||
|
ODESolver(ode),
|
||||||
|
adaptiveSolver(ode),
|
||||||
|
yTemp_(n_),
|
||||||
|
k2_(n_),
|
||||||
|
k3_(n_),
|
||||||
|
k4_(n_),
|
||||||
|
k5_(n_),
|
||||||
|
k6_(n_),
|
||||||
|
err_(n_)
|
||||||
|
{}
|
||||||
|
|
||||||
|
|
||||||
|
// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
|
||||||
|
|
||||||
|
Foam::scalar Foam::RKCK5::solve
|
||||||
|
(
|
||||||
|
const ODESystem& odes,
|
||||||
|
const scalar x0,
|
||||||
|
const scalarField& y0,
|
||||||
|
const scalarField& dydx0,
|
||||||
|
const scalar dx,
|
||||||
|
scalarField& y,
|
||||||
|
const scalar eps
|
||||||
|
) const
|
||||||
|
{
|
||||||
|
forAll(yTemp_, i)
|
||||||
|
{
|
||||||
|
yTemp_[i] = y0[i] + b21*dx*dydx0[i];
|
||||||
|
}
|
||||||
|
|
||||||
|
odes.derivatives(x0 + a2*dx, yTemp_, k2_);
|
||||||
|
|
||||||
|
forAll(yTemp_, i)
|
||||||
|
{
|
||||||
|
yTemp_[i] = y0[i] + dx*(b31*dydx0[i] + b32*k2_[i]);
|
||||||
|
}
|
||||||
|
|
||||||
|
odes.derivatives(x0 + a3*dx, yTemp_, k3_);
|
||||||
|
|
||||||
|
forAll(yTemp_, i)
|
||||||
|
{
|
||||||
|
yTemp_[i] = y0[i] + dx*(b41*dydx0[i] + b42*k2_[i] + b43*k3_[i]);
|
||||||
|
}
|
||||||
|
|
||||||
|
odes.derivatives(x0 + a4*dx, yTemp_, k4_);
|
||||||
|
|
||||||
|
forAll(yTemp_, i)
|
||||||
|
{
|
||||||
|
yTemp_[i] = y0[i]
|
||||||
|
+ dx*(b51*dydx0[i] + b52*k2_[i] + b53*k3_[i] + b54*k4_[i]);
|
||||||
|
}
|
||||||
|
|
||||||
|
odes.derivatives(x0 + a5*dx, yTemp_, k5_);
|
||||||
|
|
||||||
|
forAll(yTemp_, i)
|
||||||
|
{
|
||||||
|
yTemp_[i] = y0[i]
|
||||||
|
+ dx
|
||||||
|
*(b61*dydx0[i] + b62*k2_[i] + b63*k3_[i] + b64*k4_[i] + b65*k5_[i]);
|
||||||
|
}
|
||||||
|
|
||||||
|
odes.derivatives(x0 + a6*dx, yTemp_, k6_);
|
||||||
|
|
||||||
|
forAll(y, i)
|
||||||
|
{
|
||||||
|
y[i] = y0[i]
|
||||||
|
+ dx*(c1*dydx0[i] + c3*k3_[i] + c4*k4_[i] + c6*k6_[i]);
|
||||||
|
}
|
||||||
|
|
||||||
|
forAll(err_, i)
|
||||||
|
{
|
||||||
|
err_[i] =
|
||||||
|
dx
|
||||||
|
*(dc1*dydx0[i] + dc3*k3_[i] + dc4*k4_[i] + dc5*k5_[i] + dc6*k6_[i]);
|
||||||
|
}
|
||||||
|
|
||||||
|
return normalizeError(eps, y0, y, err_);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
void Foam::RKCK5::solve
|
||||||
|
(
|
||||||
|
const ODESystem& odes,
|
||||||
|
scalar& x,
|
||||||
|
scalarField& y,
|
||||||
|
scalarField& dydx,
|
||||||
|
const scalar eps,
|
||||||
|
const scalar dxTry,
|
||||||
|
scalar& dxDid,
|
||||||
|
scalar& dxNext
|
||||||
|
) const
|
||||||
|
{
|
||||||
|
adaptiveSolver::solve(odes, x, y, dydx, eps, dxTry, dxDid, dxNext);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
// ************************************************************************* //
|
||||||
@ -2,7 +2,7 @@
|
|||||||
========= |
|
========= |
|
||||||
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
|
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
|
||||||
\\ / O peration |
|
\\ / O peration |
|
||||||
\\ / A nd | Copyright (C) 2011 OpenFOAM Foundation
|
\\ / A nd | Copyright (C) 2011-2013 OpenFOAM Foundation
|
||||||
\\/ M anipulation |
|
\\/ M anipulation |
|
||||||
-------------------------------------------------------------------------------
|
-------------------------------------------------------------------------------
|
||||||
License
|
License
|
||||||
@ -22,21 +22,30 @@ License
|
|||||||
along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
|
along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
|
||||||
|
|
||||||
Class
|
Class
|
||||||
Foam::RK
|
Foam::RKCK5
|
||||||
|
|
||||||
Description
|
Description
|
||||||
Runge-Kutta ODE solver
|
5th Order Cash-Karp Runge-Kutta ODE solver
|
||||||
|
|
||||||
|
References:
|
||||||
|
\verbatim
|
||||||
|
"A variable order Runge-Kutta method for initial value problems
|
||||||
|
with rapidly varying right-hand sides"
|
||||||
|
Cash, J.R.,
|
||||||
|
Karp, A.H.
|
||||||
|
ACM Transactions on Mathematical Software, vol. 16, 1990, pp. 201–222.
|
||||||
|
\endverbatim
|
||||||
|
|
||||||
SourceFiles
|
SourceFiles
|
||||||
RKCK.C
|
RKCK5.C
|
||||||
RKQS.C
|
|
||||||
|
|
||||||
\*---------------------------------------------------------------------------*/
|
\*---------------------------------------------------------------------------*/
|
||||||
|
|
||||||
#ifndef RK_H
|
#ifndef RKCK5_H
|
||||||
#define RK_H
|
#define RKCK5_H
|
||||||
|
|
||||||
#include "ODESolver.H"
|
#include "ODESolver.H"
|
||||||
|
#include "adaptiveSolver.H"
|
||||||
|
|
||||||
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
|
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
|
||||||
|
|
||||||
@ -44,16 +53,17 @@ namespace Foam
|
|||||||
{
|
{
|
||||||
|
|
||||||
/*---------------------------------------------------------------------------*\
|
/*---------------------------------------------------------------------------*\
|
||||||
Class RK Declaration
|
Class RKCK5 Declaration
|
||||||
\*---------------------------------------------------------------------------*/
|
\*---------------------------------------------------------------------------*/
|
||||||
|
|
||||||
class RK
|
class RKCK5
|
||||||
:
|
:
|
||||||
public ODESolver
|
public ODESolver,
|
||||||
|
public adaptiveSolver
|
||||||
{
|
{
|
||||||
// Private data
|
// Private data
|
||||||
static const scalar safety, pGrow, pShrink, errCon;
|
|
||||||
|
|
||||||
|
//- RKCK Constants
|
||||||
static const scalar
|
static const scalar
|
||||||
a2, a3, a4, a5, a6,
|
a2, a3, a4, a5, a6,
|
||||||
b21, b31, b32, b41, b42, b43,
|
b21, b31, b32, b41, b42, b43,
|
||||||
@ -61,43 +71,45 @@ class RK
|
|||||||
c1, c3, c4, c6,
|
c1, c3, c4, c6,
|
||||||
dc1, dc3, dc4, dc5, dc6;
|
dc1, dc3, dc4, dc5, dc6;
|
||||||
|
|
||||||
|
// Temporary fields
|
||||||
mutable scalarField yTemp_;
|
mutable scalarField yTemp_;
|
||||||
mutable scalarField ak2_;
|
mutable scalarField k2_;
|
||||||
mutable scalarField ak3_;
|
mutable scalarField k3_;
|
||||||
mutable scalarField ak4_;
|
mutable scalarField k4_;
|
||||||
mutable scalarField ak5_;
|
mutable scalarField k5_;
|
||||||
mutable scalarField ak6_;
|
mutable scalarField k6_;
|
||||||
|
|
||||||
|
//- Error-estimate field
|
||||||
|
mutable scalarField err_;
|
||||||
|
|
||||||
mutable scalarField yErr_;
|
|
||||||
mutable scalarField yTemp2_;
|
|
||||||
|
|
||||||
public:
|
public:
|
||||||
|
|
||||||
//- Runtime type information
|
//- Runtime type information
|
||||||
TypeName("RK");
|
TypeName("RKCK5");
|
||||||
|
|
||||||
|
|
||||||
// Constructors
|
// Constructors
|
||||||
|
|
||||||
//- Construct from ODE
|
//- Construct from ODE
|
||||||
RK(const ODESystem& ode);
|
RKCK5(const ODESystem& ode);
|
||||||
|
|
||||||
|
|
||||||
// Member Functions
|
// Member Functions
|
||||||
|
|
||||||
void solve
|
//- Solve a single step dx and return the error
|
||||||
|
scalar solve
|
||||||
(
|
(
|
||||||
const ODESystem& ode,
|
const ODESystem& ode,
|
||||||
const scalar x,
|
const scalar x0,
|
||||||
const scalarField& y,
|
const scalarField& y0,
|
||||||
const scalarField& dydx,
|
const scalarField& dydx0,
|
||||||
const scalar h,
|
const scalar dx,
|
||||||
scalarField& yout,
|
scalarField& y,
|
||||||
scalarField& yerr
|
const scalar eps
|
||||||
) const;
|
) const;
|
||||||
|
|
||||||
|
//- Solve the ODE system and the update the state
|
||||||
void solve
|
void solve
|
||||||
(
|
(
|
||||||
const ODESystem& ode,
|
const ODESystem& ode,
|
||||||
@ -105,10 +117,9 @@ public:
|
|||||||
scalarField& y,
|
scalarField& y,
|
||||||
scalarField& dydx,
|
scalarField& dydx,
|
||||||
const scalar eps,
|
const scalar eps,
|
||||||
const scalarField& yScale,
|
const scalar dxTry,
|
||||||
const scalar hTry,
|
scalar& dxDid,
|
||||||
scalar& hDid,
|
scalar& dxNext
|
||||||
scalar& hNext
|
|
||||||
) const;
|
) const;
|
||||||
};
|
};
|
||||||
|
|
||||||
@ -75,7 +75,6 @@ void Foam::SIBS::solve
|
|||||||
scalarField& y,
|
scalarField& y,
|
||||||
scalarField& dydx,
|
scalarField& dydx,
|
||||||
const scalar eps,
|
const scalar eps,
|
||||||
const scalarField& yScale,
|
|
||||||
const scalar hTry,
|
const scalar hTry,
|
||||||
scalar& hDid,
|
scalar& hDid,
|
||||||
scalar& hNext
|
scalar& hNext
|
||||||
@ -164,7 +163,11 @@ void Foam::SIBS::solve
|
|||||||
maxErr = SMALL;
|
maxErr = SMALL;
|
||||||
for (register label i=0; i<n_; i++)
|
for (register label i=0; i<n_; i++)
|
||||||
{
|
{
|
||||||
maxErr = max(maxErr, mag(yErr_[i]/yScale[i]));
|
maxErr = max
|
||||||
|
(
|
||||||
|
maxErr,
|
||||||
|
mag(yErr_[i])/(mag(yTemp_[i]) + SMALL)
|
||||||
|
);
|
||||||
}
|
}
|
||||||
maxErr /= eps;
|
maxErr /= eps;
|
||||||
km = k - 1;
|
km = k - 1;
|
||||||
|
|||||||
@ -122,7 +122,6 @@ public:
|
|||||||
scalarField& y,
|
scalarField& y,
|
||||||
scalarField& dydx,
|
scalarField& dydx,
|
||||||
const scalar eps,
|
const scalar eps,
|
||||||
const scalarField& yScale,
|
|
||||||
const scalar hTry,
|
const scalar hTry,
|
||||||
scalar& hDid,
|
scalar& hDid,
|
||||||
scalar& hNext
|
scalar& hNext
|
||||||
|
|||||||
123
src/ODE/ODESolvers/adaptiveSolver/adaptiveSolver.C
Normal file
123
src/ODE/ODESolvers/adaptiveSolver/adaptiveSolver.C
Normal file
@ -0,0 +1,123 @@
|
|||||||
|
/*---------------------------------------------------------------------------*\
|
||||||
|
========= |
|
||||||
|
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
|
||||||
|
\\ / O peration |
|
||||||
|
\\ / A nd | Copyright (C) 2011-2013 OpenFOAM Foundation
|
||||||
|
\\/ M anipulation |
|
||||||
|
-------------------------------------------------------------------------------
|
||||||
|
License
|
||||||
|
This file is part of OpenFOAM.
|
||||||
|
|
||||||
|
OpenFOAM is free software: you can redistribute it and/or modify it
|
||||||
|
under the terms of the GNU General Public License as published by
|
||||||
|
the Free Software Foundation, either version 3 of the License, or
|
||||||
|
(at your option) any later version.
|
||||||
|
|
||||||
|
OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
|
||||||
|
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
|
||||||
|
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
|
||||||
|
for more details.
|
||||||
|
|
||||||
|
You should have received a copy of the GNU General Public License
|
||||||
|
along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
|
||||||
|
|
||||||
|
\*---------------------------------------------------------------------------*/
|
||||||
|
|
||||||
|
#include "adaptiveSolver.H"
|
||||||
|
#include "addToRunTimeSelectionTable.H"
|
||||||
|
|
||||||
|
// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
|
||||||
|
|
||||||
|
namespace Foam
|
||||||
|
{
|
||||||
|
|
||||||
|
const scalar
|
||||||
|
adaptiveSolver::safeScale=0.9,
|
||||||
|
adaptiveSolver::alphaInc=0.2,
|
||||||
|
adaptiveSolver::alphaDec=0.25,
|
||||||
|
adaptiveSolver::minScale=0.2,
|
||||||
|
adaptiveSolver::maxScale=10;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
// * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
|
||||||
|
|
||||||
|
Foam::adaptiveSolver::adaptiveSolver(const ODESystem& ode)
|
||||||
|
:
|
||||||
|
yTemp_(ode.nEqns())
|
||||||
|
{}
|
||||||
|
|
||||||
|
|
||||||
|
// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
|
||||||
|
|
||||||
|
Foam::scalar Foam::adaptiveSolver::normalizeError
|
||||||
|
(
|
||||||
|
const scalar eps,
|
||||||
|
const scalarField& y0,
|
||||||
|
const scalarField& y,
|
||||||
|
const scalarField& err
|
||||||
|
) const
|
||||||
|
{
|
||||||
|
scalar epsAbs = 1e-10;
|
||||||
|
scalar epsRel = eps;
|
||||||
|
|
||||||
|
// Calculate the maximum error
|
||||||
|
scalar maxErr = 0.0;
|
||||||
|
forAll(err, i)
|
||||||
|
{
|
||||||
|
scalar eps = epsAbs + epsRel*max(mag(y0[i]), mag(y[i]));
|
||||||
|
maxErr = max(maxErr, mag(err[i])/eps);
|
||||||
|
}
|
||||||
|
|
||||||
|
return maxErr;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
void Foam::adaptiveSolver::solve
|
||||||
|
(
|
||||||
|
const ODESystem& odes,
|
||||||
|
scalar& x,
|
||||||
|
scalarField& y,
|
||||||
|
scalarField& dydx,
|
||||||
|
const scalar eps,
|
||||||
|
const scalar dxTry,
|
||||||
|
scalar& dxDid,
|
||||||
|
scalar& dxNext
|
||||||
|
) const
|
||||||
|
{
|
||||||
|
scalar dx = dxTry;
|
||||||
|
scalar err = 0.0;
|
||||||
|
|
||||||
|
// Loop over solver and adjust step-size as necessary
|
||||||
|
// to achieve desired error
|
||||||
|
do
|
||||||
|
{
|
||||||
|
// Solve step and provide error estimate
|
||||||
|
err = solve(odes, x, y, dydx, dx, yTemp_, eps);
|
||||||
|
|
||||||
|
// If error is large reduce dx
|
||||||
|
if (err > 1)
|
||||||
|
{
|
||||||
|
scalar scale = max(safeScale*pow(err, -alphaDec), minScale);
|
||||||
|
dx *= scale;
|
||||||
|
|
||||||
|
if (dx < VSMALL)
|
||||||
|
{
|
||||||
|
FatalErrorIn("adaptiveSolver::solve")
|
||||||
|
<< "stepsize underflow"
|
||||||
|
<< exit(FatalError);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
} while (err > 1);
|
||||||
|
|
||||||
|
// Update the state
|
||||||
|
dxDid = dx;
|
||||||
|
x += dx;
|
||||||
|
y = yTemp_;
|
||||||
|
|
||||||
|
// If the error is small increase the step-size
|
||||||
|
dxNext = min(max(safeScale*pow(err, -alphaInc), minScale), maxScale)*dx;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
// ************************************************************************* //
|
||||||
127
src/ODE/ODESolvers/adaptiveSolver/adaptiveSolver.H
Normal file
127
src/ODE/ODESolvers/adaptiveSolver/adaptiveSolver.H
Normal file
@ -0,0 +1,127 @@
|
|||||||
|
/*---------------------------------------------------------------------------*\
|
||||||
|
========= |
|
||||||
|
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
|
||||||
|
\\ / O peration |
|
||||||
|
\\ / A nd | Copyright (C) 2011 OpenFOAM Foundation
|
||||||
|
\\/ M anipulation |
|
||||||
|
-------------------------------------------------------------------------------
|
||||||
|
License
|
||||||
|
This file is part of OpenFOAM.
|
||||||
|
|
||||||
|
OpenFOAM is free software: you can redistribute it and/or modify it
|
||||||
|
under the terms of the GNU General Public License as published by
|
||||||
|
the Free Software Foundation, either version 3 of the License, or
|
||||||
|
(at your option) any later version.
|
||||||
|
|
||||||
|
OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
|
||||||
|
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
|
||||||
|
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
|
||||||
|
for more details.
|
||||||
|
|
||||||
|
You should have received a copy of the GNU General Public License
|
||||||
|
along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
|
||||||
|
|
||||||
|
Class
|
||||||
|
Foam::adaptiveSolver
|
||||||
|
|
||||||
|
Description
|
||||||
|
5th Order Cash-Karp Runge-Kutta ODE solver
|
||||||
|
|
||||||
|
References:
|
||||||
|
\verbatim
|
||||||
|
"A variable order Runge-Kutta method for initial value problems
|
||||||
|
with rapidly varying right-hand sides"
|
||||||
|
Cash, J.R.,
|
||||||
|
Karp, A.H.
|
||||||
|
ACM Transactions on Mathematical Software, vol. 16, 1990, pp. 201–222.
|
||||||
|
\endverbatim
|
||||||
|
|
||||||
|
SourceFiles
|
||||||
|
adaptiveSolver.C
|
||||||
|
|
||||||
|
\*---------------------------------------------------------------------------*/
|
||||||
|
|
||||||
|
#ifndef adaptiveSolver_H
|
||||||
|
#define adaptiveSolver_H
|
||||||
|
|
||||||
|
#include "ODESolver.H"
|
||||||
|
|
||||||
|
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
|
||||||
|
|
||||||
|
namespace Foam
|
||||||
|
{
|
||||||
|
|
||||||
|
/*---------------------------------------------------------------------------*\
|
||||||
|
Class adaptiveSolver Declaration
|
||||||
|
\*---------------------------------------------------------------------------*/
|
||||||
|
|
||||||
|
class adaptiveSolver
|
||||||
|
{
|
||||||
|
// Private data
|
||||||
|
|
||||||
|
//- Step-size adjustment controls
|
||||||
|
static const scalar safeScale, alphaInc, alphaDec, minScale, maxScale;
|
||||||
|
|
||||||
|
mutable scalarField yTemp_;
|
||||||
|
|
||||||
|
|
||||||
|
public:
|
||||||
|
|
||||||
|
// Constructors
|
||||||
|
|
||||||
|
//- Construct from ODESystem
|
||||||
|
adaptiveSolver(const ODESystem& ode);
|
||||||
|
|
||||||
|
|
||||||
|
//- Destructor
|
||||||
|
virtual ~adaptiveSolver()
|
||||||
|
{}
|
||||||
|
|
||||||
|
|
||||||
|
// Member Functions
|
||||||
|
|
||||||
|
//- Return the nomalized scalar error
|
||||||
|
scalar normalizeError
|
||||||
|
(
|
||||||
|
const scalar eps,
|
||||||
|
const scalarField& y0,
|
||||||
|
const scalarField& y,
|
||||||
|
const scalarField& err
|
||||||
|
) const;
|
||||||
|
|
||||||
|
//- Solve a single step dx and return the error
|
||||||
|
virtual scalar solve
|
||||||
|
(
|
||||||
|
const ODESystem& ode,
|
||||||
|
const scalar x0,
|
||||||
|
const scalarField& y0,
|
||||||
|
const scalarField& dydx0,
|
||||||
|
const scalar dx,
|
||||||
|
scalarField& y,
|
||||||
|
const scalar eps
|
||||||
|
) const = 0;
|
||||||
|
|
||||||
|
//- Solve the ODE system and the update the state
|
||||||
|
void solve
|
||||||
|
(
|
||||||
|
const ODESystem& ode,
|
||||||
|
scalar& x,
|
||||||
|
scalarField& y,
|
||||||
|
scalarField& dydx,
|
||||||
|
const scalar eps,
|
||||||
|
const scalar dxTry,
|
||||||
|
scalar& dxDid,
|
||||||
|
scalar& dxNext
|
||||||
|
) const;
|
||||||
|
};
|
||||||
|
|
||||||
|
|
||||||
|
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
|
||||||
|
|
||||||
|
} // End namespace Foam
|
||||||
|
|
||||||
|
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
|
||||||
|
|
||||||
|
#endif
|
||||||
|
|
||||||
|
// ************************************************************************* //
|
||||||
@ -51,7 +51,7 @@ public:
|
|||||||
|
|
||||||
// Constructors
|
// Constructors
|
||||||
|
|
||||||
//- Construct null8
|
//- Construct null
|
||||||
ODESystem()
|
ODESystem()
|
||||||
{}
|
{}
|
||||||
|
|
||||||
|
|||||||
Reference in New Issue
Block a user