mirror of
https://develop.openfoam.com/Development/openfoam.git
synced 2025-11-28 03:28:01 +00:00
95e9467e84
Capabilities include: - Wave generation - Solitary wave using Boussinesq theory - Cnoidal wave theory - StokesI, StokesII, StokesV wave theory - Active wave absorption at the inflow/outflow boundaries based on shallow water theory Authors: - Javier Lopez Lara (jav.lopez@unican.es) - Gabriel Barajas (barajasg@unican.es) - Inigo Losada (losadai@unican.es)
981 lines
26 KiB
C
981 lines
26 KiB
C
/*---------------------------------------------------------------------------*\
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IH-Cantabria 2015 (http://www.ihcantabria.com/en/)
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IHFOAM 2015 (http://ihfoam.ihcantabria.com/)
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Author(s): Javier Lopez Lara (jav.lopez@unican.es)
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Gabriel Barajas (barajasg@unican.es)
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\*---------------------------------------------------------------------------*/
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#include "waveFun.H"
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#include <math.h>
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#include <stdlib.h>
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#include <stdio.h>
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namespace otherFun
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{
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#define PII 3.1415926535897932384626433832795028
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#define grav 9.81
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double interpolation (double x1, double x2, double y1, double y2, double xInt)
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{
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double yInt = y1 + (y2-y1)/(x2-x1)*(xInt-x1);
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return yInt;
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}
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}
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namespace StokesIFun
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{
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#define PII 3.1415926535897932384626433832795028
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#define G 9.81
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double waveLength (double h, double T)
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{
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double L0 = G*T*T/(2.0*PII);
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double L = L0;
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for(int i=1; i<=100; i++)
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{
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L = L0*tanh(2.0*PII*h/L);
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}
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return L;
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}
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double eta (double H, double Kx, double x, double Ky, double y, double omega, double t, double phase)
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{
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double faseTot = Kx*x + Ky*y - omega*t + phase;
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double sup = H*0.5*cos(faseTot);
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return sup;
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}
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double U (double H, double h, double Kx, double x, double Ky, double y, double omega, double t, double phase, double z)
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{
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double k = sqrt(Kx*Kx + Ky*Ky);
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double faseTot = Kx*x + Ky*y - omega*t + phase;
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double velocity = H*0.5*omega*cos(faseTot)*cosh(k*z)/sinh(k*h);
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return velocity;
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}
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double W (double H, double h, double Kx, double x, double Ky, double y, double omega, double t, double phase, double z)
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{
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double k = sqrt(Kx*Kx + Ky*Ky);
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double faseTot = Kx*x + Ky*y - omega*t + phase;
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double velocity = H*0.5*omega*sin(faseTot)*sinh(k*z)/sinh(k*h);
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return velocity;
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}
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}
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namespace StokesIIFun
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{
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#define PII 3.1415926535897932384626433832795028
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#define G 9.81
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double eta (double H, double h, double Kx, double x, double Ky, double y, double omega, double t, double phase)
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{
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double k = sqrt(Kx*Kx + Ky*Ky);
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double sigma = tanh(k*h);
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double faseTot = Kx*x + Ky*y - omega*t + phase;
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double sup = H*0.5*cos(faseTot) + k*H*H/4.0*(3.0-sigma*sigma)/(4.0*pow(sigma,3))*cos(2.0*faseTot);
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return sup;
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}
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double U (double H, double h, double Kx, double x, double Ky, double y, double omega, double t, double phase, double z)
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{
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double k = sqrt(Kx*Kx + Ky*Ky);
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double faseTot = Kx*x + Ky*y - omega*t + phase;
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double velocity = H*0.5*omega*cos(faseTot)*cosh(k*z)/sinh(k*h) + 3.0/4.0*H*H/4.0*omega*k*cosh(2.0*k*z)/pow(sinh(k*h),4)*cos(2.0*faseTot);
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return velocity;
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}
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double W (double H, double h, double Kx, double x, double Ky, double y, double omega, double t, double phase, double z)
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{
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double k = sqrt(Kx*Kx + Ky*Ky);
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double faseTot = Kx*x + Ky*y - omega*t + phase;
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double velocity = H*0.5*omega*sin(faseTot)*sinh(k*z)/sinh(k*h) + 3.0/4.0*H*H/4.0*omega*k*sinh(2.0*k*z)/pow(sinh(k*h),4)*sin(2.0*faseTot);
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return velocity;
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}
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}
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namespace Elliptic
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{
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#define PII 3.1415926535897932384626433832795028
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#define ITER 25
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void ellipticIntegralsKE (double m, double* K, double* E)
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{
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long double a,aOld,g,gOld,aux,sum;
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if ( m == 0.0 )
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{
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*K = PII/2.;
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*E = PII/2.;
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return;
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}
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a = 1.0L;
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g = sqrt(1.0L - m);
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aux = 1.0L;
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sum = 2.0L - m;
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while (1)
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{
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gOld = g;
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aOld = a;
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a = 0.5L * (gOld + aOld);
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g = gOld * aOld;
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aux += aux;
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sum -= aux * (a * a - g);
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if ( fabs(aOld - gOld) <= (aOld * 1.e-22) )
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{
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break;
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}
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g = sqrt(g);
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}
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*K = (double) (PII/2. / a);
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*E = (double) (PII/4. / a * sum);
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return;
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}
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double JacobiAmp (double u, double m)
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{
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long double a[ITER+1], g[ITER+1], c[ITER+1];
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long double aux, amp;
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int n;
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m = fabsl(m);
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if ( m == 0.0 )
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{
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return u;
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}
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if ( m == 1. )
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{
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return 2. * atan( exp(u) ) - PII/2.;
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}
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a[0] = 1.0L;
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g[0] = sqrtl(1.0L - m);
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c[0] = sqrtl(m);
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aux = 1.0L;
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for (n = 0; n < ITER; n++)
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{
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if ( fabsl(a[n] - g[n]) < (a[n] * 1.e-22) )
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{
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break;
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}
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aux += aux;
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a[n+1] = 0.5L * (a[n] + g[n]);
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g[n+1] = sqrtl(a[n] * g[n]);
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c[n+1] = 0.5L * (a[n] - g[n]);
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}
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amp = aux * a[n] * u;
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for (; n > 0; n--)
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{
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amp = 0.5L * ( amp + asinl( c[n] * sinl(amp) / a[n]) );
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}
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return (double) amp;
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}
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void JacobiSnCnDn (double u, double m, double* Sn, double* Cn, double* Dn)
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{
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double amp = Elliptic::JacobiAmp( u, m );
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*Sn = sin( amp );
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*Cn = cos( amp );
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*Dn = sqrt(1.0 - m * sin( amp ) * sin( amp ));
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return;
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}
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}
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namespace cnoidalFun
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{
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#define PII 3.1415926535897932384626433832795028
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#define G 9.81
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double eta (double H, double m, double kx, double ky, double T, double x, double y, double t)
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{
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double K, E;
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Elliptic::ellipticIntegralsKE(m, &K, &E);
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double uCnoidal = K/PII*(kx*x + ky*y - 2.0*PII*t/T);
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double sn, cn, dn;
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Elliptic::JacobiSnCnDn(uCnoidal, m, &sn, &cn, &dn);
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double etaCnoidal = H*((1.0-E/K)/m - 1.0 + pow(cn,2));
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return etaCnoidal;
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}
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double etaCnoidal1D (double H, double m, double t, double T)
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{
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double K, E;
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Elliptic::ellipticIntegralsKE(m, &K, &E);
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double uCnoidal = -2.0*K*(t/T);
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double sn, cn, dn;
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Elliptic::JacobiSnCnDn(uCnoidal, m, &sn, &cn, &dn);
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double etaCnoidal = H*((1.0-E/K)/m - 1.0 + pow(cn,2));
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return etaCnoidal;
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}
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double etaMeanSq (double H, double m, double T)
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{
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double eta = 0;
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double etaSumSq = 0;
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for(int i=0; i<1000; i++)
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{
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eta = etaCnoidal1D(H, m, i*T/(1000.0), T);
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etaSumSq += eta*eta;
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}
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etaSumSq /= 1000.0;
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return etaSumSq;
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}
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double d1EtaDx (double H, double m, double uCnoidal, double L, double K, double E)
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{
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double dudx = 0;
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dudx = 2.0*K/L;
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double sn, cn, dn;
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Elliptic::JacobiSnCnDn(uCnoidal, m, &sn, &cn, &dn);
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double deriv = -2.0*H*cn*dn*sn*dudx;
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return deriv;
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}
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double d2EtaDx (double H, double m, double uCnoidal, double L, double K, double E)
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{
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double dudxx = 0;
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dudxx = 4.0*K*K/L/L;
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double sn, cn, dn;
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Elliptic::JacobiSnCnDn(uCnoidal, m, &sn, &cn, &dn);
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double deriv = 2.0*H*(dn*dn*sn*sn - cn*cn*dn*dn + m*cn*cn*sn*sn)*dudxx;
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return deriv;
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}
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double d3EtaDx (double H, double m, double uCnoidal, double L, double K, double E)
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{
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double dudxxx = 0;
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dudxxx = 8.0*K*K*K/L/L/L;
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double sn, cn, dn;
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Elliptic::JacobiSnCnDn(uCnoidal, m, &sn, &cn, &dn);
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double deriv = 8.0*H*( cn*sn*dn*dn*dn*(-4.0 -2.0*m) + 4.0*m*cn*sn*sn*sn*dn -2.0*m*cn*cn*cn*sn*dn )*dudxxx;
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return deriv;
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}
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int calculations (double H, double d, double T, double* mOut, double* LOut)
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{
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double mTolerance = 0.0001;
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double mElliptic = 0.5;
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double LElliptic = 0;
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double phaseSpeed = 0;
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double mError = 0.0;
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double mMinError = 999;
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while (mElliptic < 1.0)
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{
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double KElliptic, EElliptic;
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Elliptic::ellipticIntegralsKE(mElliptic, &KElliptic, &EElliptic);
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LElliptic = KElliptic*sqrt(16.0*pow(d,3)*mElliptic/(3.0*H));
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phaseSpeed = sqrt(G*d)*(1.0 - H/d/2.0 + H/d/mElliptic*(1.0-3.0/2.0*EElliptic/KElliptic));
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mError = fabs(T-LElliptic/phaseSpeed);
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if (mError <= mMinError)
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{
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*mOut = mElliptic;
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*LOut = LElliptic;
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mMinError = mError;
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}
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mElliptic += mTolerance;
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}
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return 0;
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}
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double U (double H, double h, double m, double kx, double ky, double T, double x, double y, double t, double z)
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{
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double K, E;
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Elliptic::ellipticIntegralsKE(m, &K, &E);
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double uCnoidal = K/PII*(kx*x + ky*y - 2.0*PII*t/T);
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double k = sqrt(kx*kx + ky*ky);
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double L = 2.0*PII/k;
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double c = L/T;
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double etaCN = eta(H, m, kx, ky, T, x, y, t);
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double etaXX = d2EtaDx(H, m, uCnoidal, L, K, E);
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double etaMS = etaMeanSq(H, m, T);
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double velocity = c*etaCN/h - c*(etaCN*etaCN/h/h + etaMS*etaMS/h/h) + 1.0/2.0*c*h*(1.0/3.0 - z*z/h/h)*etaXX;
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return velocity;
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}
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double W (double H, double h, double m, double kx, double ky, double T, double x, double y, double t, double z)
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{
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double K, E;
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Elliptic::ellipticIntegralsKE(m, &K, &E);
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double uCnoidal = K/PII*(kx*x + ky*y - 2.0*PII*t/T);
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double k = sqrt(kx*kx + ky*ky);
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double L = 2.0*PII/k;
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double c = L/T;
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double etaCN = eta(H, m, kx, ky, T, x, y, t);
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double etaX = d1EtaDx(H, m, uCnoidal, L, K, E);
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double etaXXX = d3EtaDx(H, m, uCnoidal, L, K, E);
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double velocity = -c*z*( etaX/h*(1.0-2.0*etaCN/h) + 1.0/6.0*h*(1.0-z*z/h/h)*etaXXX ) ;
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return velocity;
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}
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}
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namespace stokesVFun
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{
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#define PII 3.1415926535897932384626433832795028
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#define G 9.81
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double A11 (double h, double k)
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{
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double s = sinh(k*h);
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double A = 1.0/s;
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return A;
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}
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double A13 (double h, double k)
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{
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double s = sinh(k*h);
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double c = cosh(k*h);
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double A =
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-pow(c,2)*(5.0*pow(c,2)+1.0)
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/
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(8.0*pow(s,5));
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return A;
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}
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double A15 (double h, double k)
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{
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double s = sinh(k*h);
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double c = cosh(k*h);
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double A =
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-(1184.0*pow(c,10)-1440.0*pow(c,8)-1992.0*pow(c,6)+2641.0*pow(c,4)-249.0*pow(c,2)+18)
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/
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(1536.0*pow(s,11));
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return A;
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}
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double A22 (double h, double k)
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{
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double s = sinh(k*h);
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double A =
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3.0
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/
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(8.0*pow(s,4));
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return A;
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}
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double A24 (double h, double k)
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{
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double s = sinh(k*h);
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double c = cosh(k*h);
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double A =
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(192.0*pow(c,8)-424.0*pow(c,6)-312.0*pow(c,4)+480.0*pow(c,2)-17)
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/
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(768.0*pow(s,10));
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return A;
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}
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double A33 (double h, double k)
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{
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double s = sinh(k*h);
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double c = cosh(k*h);
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double A =
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(13.0-4.0*pow(c,2))
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/
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(64.0*pow(s,7));
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return A;
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}
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double A35 (double h, double k)
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{
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double s = sinh(k*h);
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double c = cosh(k*h);
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double A =
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(512.0*pow(c,12)+4224.0*pow(c,10)-6800.0*pow(c,8)-12808.0*pow(c,6)+16704.0*pow(c,4)-3154.0*pow(c,2)+107.0)
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/
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(4096.0*pow(s,13)*(6.0*pow(c,2)-1.0));
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return A;
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}
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double A44 (double h, double k)
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{
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double s = sinh(k*h);
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double c = cosh(k*h);
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double A =
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(80.0*pow(c,6)-816.0*pow(c,4)+1338.0*pow(c,2)-197.0)
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/
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(1536.0*pow(s,10)*(6.0*pow(c,2)-1.0));
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return A;
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}
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double A55 (double h, double k)
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{
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double s = sinh(k*h);
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double c = cosh(k*h);
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double A =
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-(2880.0*pow(c,10)-72480.0*pow(c,8)+324000.0*pow(c,6)-432000.0*pow(c,4)+163470.0*pow(c,2)-16245.0)
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/
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(61440.0*pow(s,11)*(6.0*pow(c,2)-1.0)*(8.0*pow(c,4)-11.0*pow(c,2)+3.0));
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return A;
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}
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double B22 (double h, double k)
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{
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double s = sinh(k*h);
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double c = cosh(k*h);
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double B =
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(2.0*pow(c,2)+1)*c
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/
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(4.0*pow(s,3));
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return B;
|
|
}
|
|
|
|
double B24 (double h, double k)
|
|
{
|
|
double s = sinh(k*h);
|
|
double c = cosh(k*h);
|
|
|
|
double B =
|
|
(272.0*pow(c,8)-504.0*pow(c,6)-192.0*pow(c,4)+322.0*pow(c,2)+21.0)*c
|
|
/
|
|
(384.0*pow(s,9));
|
|
|
|
return B;
|
|
}
|
|
|
|
double B33 (double h, double k)
|
|
{
|
|
double s = sinh(k*h);
|
|
double c = cosh(k*h);
|
|
|
|
double B =
|
|
(8.0*pow(c,6)+1.0)*3.0
|
|
/
|
|
(64.0*pow(s,6));
|
|
|
|
return B;
|
|
}
|
|
|
|
double B33k (double h, double k) // d B33 / d k
|
|
{
|
|
double s = sinh(k*h);
|
|
double c = cosh(k*h);
|
|
|
|
double sk = h*s;
|
|
double ck = h*c;
|
|
|
|
double B =
|
|
9.0*pow(c,5)*ck/(4.0*pow(s,6))-
|
|
(9.0*(8.0*pow(c,6)+1.0))/(32.0*pow(s,7))*sk;
|
|
|
|
return B;
|
|
}
|
|
|
|
double B35 (double h, double k)
|
|
{
|
|
double s = sinh(k*h);
|
|
double c = cosh(k*h);
|
|
|
|
double B =
|
|
(88128.0*pow(c,14)-208224.0*pow(c,12)+70848.0*pow(c,10)+54000.0*pow(c,8)-21816.0*pow(c,6)+6264.0*pow(c,4)-54.0*pow(c,2)-81)
|
|
/
|
|
(12288.0*pow(s,12)*(6.0*pow(c,2)-1.0));
|
|
|
|
return B;
|
|
}
|
|
|
|
double B35k (double h, double k) // d B35 / d k
|
|
{
|
|
double s = sinh(k*h);
|
|
double c = cosh(k*h);
|
|
|
|
double sk = h*s;
|
|
double ck = h*c;
|
|
|
|
double B =
|
|
(14.0*88128.0*pow(c,13)*ck-12.0*208224.0*pow(c,11)*ck
|
|
+10.0*70848.0*pow(c,9)*ck+8.0*54000.0*pow(c,7)*ck
|
|
-6.0*21816.0*pow(c,5)*ck+4.0*6264.0*pow(c,3)*ck
|
|
-2.0*54.0*c*ck)
|
|
/(12288.0*pow(s,12)*(6.0*pow(c,2)-1.0))
|
|
-(88128.0*pow(c,14)-208224.0*pow(c,12)+70848.0*pow(c,10)+54000.0*pow(c,8)
|
|
-21816.0*pow(c,6)+6264.0*pow(c,4)-54.0*pow(c,2)-81.0)*12.0
|
|
/(12288.0*pow(s,13)*(6.0*pow(c,2)-1.0))*sk
|
|
-(88128.0*pow(c,14)-208224.0*pow(c,12)+70848.0*pow(c,10)+54000.0*pow(c,8)
|
|
-21816.0*pow(c,6)+6264.0*pow(c,4)-54.0*pow(c,2)-81.0)*12.0*c*ck
|
|
/(12288.0*pow(s,12)*pow((6.0*pow(c,2)-1.0),2));
|
|
|
|
return B;
|
|
}
|
|
|
|
double B44 (double h, double k)
|
|
{
|
|
double s = sinh(k*h);
|
|
double c = cosh(k*h);
|
|
|
|
double B =
|
|
(768.0*pow(c,10)-448.0*pow(c,8)-48.0*pow(c,6)+48.0*pow(c,4)+106.0*pow(c,2)-21.0)*c
|
|
/
|
|
(384.0*pow(s,9)*(6.0*pow(c,2)-1.0));
|
|
|
|
return B;
|
|
}
|
|
|
|
double B55 (double h, double k)
|
|
{
|
|
double s = sinh(k*h);
|
|
double c = cosh(k*h);
|
|
|
|
double B =
|
|
(192000.0*pow(c,16)-262720.0*pow(c,14)+83680.0*pow(c,12)+20160.0*pow(c,10)-7280.0*pow(c,8)+7160.0*pow(c,6)-1800.0*pow(c,4)-1050.0*pow(c,2)+225.0)
|
|
/
|
|
(12288.0*pow(s,10)*(6.0*pow(c,2)-1.0)*(8.0*pow(c,4)-11.0*pow(c,2)+3.0));
|
|
|
|
return B;
|
|
}
|
|
|
|
double B55k (double h, double k) // d B55 / d k
|
|
{
|
|
double s = sinh(k*h);
|
|
double c = cosh(k*h);
|
|
|
|
double sk = h*s;
|
|
double ck = h*c;
|
|
|
|
double B =
|
|
(16.0*192000.0*pow(c,15)*ck-14.0*262720.0*pow(c,13)*ck
|
|
+12.0*83680.0*pow(c,11)*ck+10.0*20160.0*pow(c,9)*ck
|
|
-8.0*7280.0*pow(c,7)*ck+6.0*7160.0*pow(c,5)*ck
|
|
-4.0*1800.0*pow(c,3)*ck-2.0*1050.0*pow(c,1)*ck)
|
|
/(12288.0*pow(s,10)*(6.0*pow(c,2)-1.0)*(8.0*pow(c,4)-11.0*pow(c,2)+3.0))
|
|
-(192000.0*pow(c,16)-262720.0*pow(c,14)+83680.0*pow(c,12)+20160.0*pow(c,10)
|
|
-7280.0*pow(c,8)+7160.0*pow(c,6)-1800.0*pow(c,4)-1050.0*pow(c,2)+225.0)*10.0
|
|
/(12288.0*pow(s,11)*(6.0*pow(c,2)-1.0)*(8.0*pow(c,4)-11.0*pow(c,2)+3.0))*sk
|
|
-(192000.0*pow(c,16)-262720.0*pow(c,14)+83680.0*pow(c,12)+20160.0*pow(c,10)
|
|
-7280.0*pow(c,8)+7160.0*pow(c,6)-1800.0*pow(c,4)-1050.0*pow(c,2)+225.0)
|
|
*12.0*c*ck
|
|
/(12288.0*pow(s,10)*pow((6.0*pow(c,2)-1.0),2)*(8.0*pow(c,4)-11.0*pow(c,2)+3.0))
|
|
-(192000.0*pow(c,16)-262720.0*pow(c,14)+83680.0*pow(c,12)+20160.0*pow(c,10)
|
|
-7280.0*pow(c,8)+7160.0*pow(c,6)-1800.0*pow(c,4)-1050.0*pow(c,2)+225.0)
|
|
*(32.0*pow(c,3)-22.0*c)*ck
|
|
/(12288.0*pow(s,10)*(6.0*pow(c,2)-1.0)*pow((8.0*pow(c,4)-11.0*pow(c,2)+3.0),2));
|
|
|
|
return B;
|
|
}
|
|
|
|
double C1 (double h, double k)
|
|
{
|
|
double s = sinh(k*h);
|
|
double c = cosh(k*h);
|
|
|
|
double C =
|
|
(8.0*pow(c,4)-8.0*pow(c,2)+9.0)
|
|
/
|
|
(8.0*pow(s,4));
|
|
|
|
return C;
|
|
}
|
|
|
|
double C1k (double h, double k)
|
|
{
|
|
double s = sinh(k*h);
|
|
double c = cosh(k*h);
|
|
|
|
double sk = h*s;
|
|
double ck = h*c;
|
|
|
|
double C =
|
|
(4.0*8.0*pow(c,3)*ck-2.0*8.0*c*ck)/(8.0*pow(s,4))
|
|
-(8.0*pow(c,4)-8.0*pow(c,2)+9.0)*4.0*sk/(8.0*pow(s,5));
|
|
|
|
return C;
|
|
}
|
|
|
|
double C2 (double h, double k)
|
|
{
|
|
double s = sinh(k*h);
|
|
double c = cosh(k*h);
|
|
|
|
double C =
|
|
(3840.0*pow(c,12)-4096.0*pow(c,10) + 2592.0*pow(c,8)-1008.0*pow(c,6)+5944.0*pow(c,4)-1830.0*pow(c,2)+147.0) // - 2592
|
|
/
|
|
(512.0*pow(s,10)*(6.0*pow(c,2)-1.0));
|
|
|
|
return C;
|
|
}
|
|
|
|
double C2k (double h, double k)
|
|
{
|
|
double s = sinh(k*h);
|
|
double c = cosh(k*h);
|
|
|
|
double sk = h*s;
|
|
double ck = h*c;
|
|
|
|
double C =
|
|
(12.0*3840.0*pow(c,11)*ck-10.0*4096.0*pow(c,9)*ck
|
|
+8.0*2592.0*pow(c,7)*ck-6.0*1008.0*pow(c,5)*ck+
|
|
4.0*5944.0*pow(c,3)*ck-2.0*1830.0*c*ck)
|
|
/(512.0*pow(s,10)*(6.0*pow(c,2)-1.0))
|
|
-(3840.0*pow(c,12)-4096.0*pow(c,10)+2592.0*pow(c,8)-1008.0*pow(c,6)+
|
|
5944.0*pow(c,4)-1830.0*pow(c,2)+147.0)*10.0*sk/
|
|
(512.0*pow(s,11)*(6.0*pow(c,2)-1.0))
|
|
-(3840.0*pow(c,12)-4096.0*pow(c,10)+2592.0*pow(c,8)-1008.0*pow(c,6)+
|
|
5944.0*pow(c,4)-1830.0*pow(c,2)+147.0)*12.0*c*ck
|
|
/(512.0*pow(s,10)*pow((6.0*pow(c,2)-1.0),2));
|
|
|
|
return C;
|
|
}
|
|
|
|
double C3 (double h, double k)
|
|
{
|
|
double s = sinh(k*h);
|
|
double c = cosh(k*h);
|
|
|
|
double C =
|
|
(-1.0)
|
|
/
|
|
(4.0*s*c);
|
|
|
|
return C;
|
|
}
|
|
|
|
double C4 (double h, double k)
|
|
{
|
|
double s = sinh(k*h);
|
|
double c = cosh(k*h);
|
|
|
|
double C =
|
|
(12.0*pow(c,8)+36.0*pow(c,6)-162.0*pow(c,4)+141.0*pow(c,2)-27.0)
|
|
/
|
|
(192.0*c*pow(s,9));
|
|
|
|
return C;
|
|
}
|
|
|
|
int StokesVNR (double H, double d, double T, double* kOut, double* LambdaOut, double* f1Out, double* f2Out )
|
|
{
|
|
double f1 = 1;
|
|
double f2 = 1;
|
|
|
|
double k = 2.0*PII/(sqrt(G*d)*T);
|
|
double Lambda = H/2.0*k;
|
|
|
|
double Bmat11, Bmat12, Bmat21, Bmat22;
|
|
double b33, b35, b55, b33k, b35k, b55k;
|
|
double c1, c2, c1k, c2k;
|
|
double kPr, LambdaPr;
|
|
|
|
int n = 0;
|
|
|
|
while ( (fabs(f1)>1.0e-12 || fabs(f2)>1.0e-12) && n<10000 )
|
|
{
|
|
b33 = B33(d, k);
|
|
b35 = B35(d, k);
|
|
b55 = B55(d, k);
|
|
c1 = C1(d, k);
|
|
c2 = C2(d, k);
|
|
|
|
b33k = B33k(d, k);
|
|
b35k = B35k(d, k);
|
|
b55k = B55k(d, k);
|
|
c1k = C1k(d, k);
|
|
c2k = C2k(d, k);
|
|
|
|
Bmat11 = 2.0*PII/(pow(k,2)*d)*(Lambda+pow(Lambda,3)*b33+pow(Lambda,5)*(b35+b55))
|
|
-2.0*PII/(k*d)*(pow(Lambda,3)*b33k+pow(Lambda,5)*(b35k+b55k));
|
|
|
|
Bmat12 = -2.0*PII/(k*d)*
|
|
(1.0+3.0*pow(Lambda,2)*b33+5.0*pow(Lambda,4)*(b35+b55));
|
|
|
|
Bmat21 = -d/(2.0*PII)*tanh(k*d)*(1.0+pow(Lambda,2)*c1+pow(Lambda,4)*c2)
|
|
-k*d/(2.0*PII)*(1.0-pow((tanh(k*d)),2))*d*
|
|
(1.0+pow(Lambda,2)*c1+pow(Lambda,4)*c2)
|
|
-k*d/(2.0*PII)*tanh(k*d)
|
|
*(pow(Lambda,2)*c1k+pow(Lambda,4)*c2k);
|
|
|
|
Bmat22 = -k*d/(2.0*PII)*tanh(k*d)
|
|
*(2.0*Lambda*c1+4.0*pow(Lambda,3)*c2);
|
|
|
|
f1 = PII*H/d-2.0*PII/(k*d)*(Lambda+pow(Lambda,3)*b33+pow(Lambda,5)*(b35+b55));
|
|
|
|
f2 = (2.0*PII*d)/(G*pow(T,2))-k*d/(2.0*PII)*tanh(k*d)
|
|
*(1.0+pow(Lambda,2)*c1+pow(Lambda,4)*c2);
|
|
|
|
LambdaPr = (f1*Bmat21-f2*Bmat11)/(Bmat11*Bmat22-Bmat12*Bmat21);
|
|
kPr = (f2*Bmat12-f1*Bmat22)/(Bmat11*Bmat22-Bmat12*Bmat21);
|
|
|
|
Lambda += LambdaPr;
|
|
k += kPr;
|
|
|
|
n++;
|
|
}
|
|
|
|
*kOut = k;
|
|
*LambdaOut = Lambda;
|
|
|
|
*f1Out = fabs(f1);
|
|
*f2Out = fabs(f2);
|
|
|
|
return 1;
|
|
}
|
|
|
|
double eta (double h, double kx, double ky, double lambda, double T, double x, double y, double t, double phase)
|
|
{
|
|
double k = sqrt(kx*kx + ky*ky);
|
|
|
|
double b22 = B22(h, k);
|
|
double b24 = B24(h, k);
|
|
double b33 = B33(h, k);
|
|
double b35 = B35(h, k);
|
|
double b44 = B44(h, k);
|
|
double b55 = B55(h, k);
|
|
|
|
double amp1 = lambda/k;
|
|
double amp2 = (b22*pow(lambda,2)+b24*pow(lambda,4))/k;
|
|
double amp3 = (b33*pow(lambda,3)+b35*pow(lambda,5))/k;
|
|
double amp4 = b44*pow(lambda,4)/k;
|
|
double amp5 = b55*pow(lambda,5)/k;
|
|
|
|
double theta = kx*x + ky*y - 2.0*PII/T*t + phase;
|
|
|
|
double C = amp1*cos(theta)
|
|
+ amp2*cos(2*theta)
|
|
+ amp3*cos(3*theta)
|
|
+ amp4*cos(4*theta)
|
|
+ amp5*cos(5*theta);
|
|
|
|
return C;
|
|
}
|
|
|
|
double U (double d, double kx, double ky, double lambda, double T, double x, double y, double t, double phase, double z)
|
|
{
|
|
double k = sqrt(kx*kx + ky*ky);
|
|
|
|
double a11 = A11(d, k);
|
|
double a13 = A13(d, k);
|
|
double a15 = A15(d, k);
|
|
double a22 = A22(d, k);
|
|
double a24 = A24(d, k);
|
|
double a33 = A33(d, k);
|
|
double a35 = A35(d, k);
|
|
double a44 = A44(d, k);
|
|
double a55 = A55(d, k);
|
|
|
|
double a1u=2.0*PII/T/k*(lambda*a11+pow(lambda,3)*a13+pow(lambda,5)*a15);
|
|
double a2u=2.0*2.0*PII/T/k*(pow(lambda,2)*a22+pow(lambda,4)*a24);
|
|
double a3u=3.0*2.0*PII/T/k*(pow(lambda,3)*a33+pow(lambda,5)*a35);
|
|
double a4u=4.0*2.0*PII/T/k*(pow(lambda,4)*a44);
|
|
double a5u=5.0*2.0*PII/T/k*(pow(lambda,5)*a55);
|
|
|
|
double velU = 0;
|
|
|
|
double theta = kx*x + ky*y - 2.0*PII/T*t + phase;
|
|
|
|
velU = a1u*cosh(k*z)*cos(theta)
|
|
+ a2u*cosh(2.0*k*z)*cos(2.0*(theta))
|
|
+ a3u*cosh(3.0*k*z)*cos(3.0*(theta))
|
|
+ a4u*cosh(4.0*k*z)*cos(4.0*(theta))
|
|
+ a5u*cosh(5.0*k*z)*cos(5.0*(theta));
|
|
|
|
return velU;
|
|
}
|
|
|
|
double W (double d, double kx, double ky, double lambda, double T, double x, double y, double t, double phase, double z)
|
|
{
|
|
double k = sqrt(kx*kx + ky*ky);
|
|
|
|
double a11 = A11(d, k);
|
|
double a13 = A13(d, k);
|
|
double a15 = A15(d, k);
|
|
double a22 = A22(d, k);
|
|
double a24 = A24(d, k);
|
|
double a33 = A33(d, k);
|
|
double a35 = A35(d, k);
|
|
double a44 = A44(d, k);
|
|
double a55 = A55(d, k);
|
|
|
|
double a1u=2.0*PII/T/k*(lambda*a11+pow(lambda,3)*a13+pow(lambda,5)*a15);
|
|
double a2u=2.0*2.0*PII/T/k*(pow(lambda,2)*a22+pow(lambda,4)*a24);
|
|
double a3u=3.0*2.0*PII/T/k*(pow(lambda,3)*a33+pow(lambda,5)*a35);
|
|
double a4u=4.0*2.0*PII/T/k*(pow(lambda,4)*a44);
|
|
double a5u=5.0*2.0*PII/T/k*(pow(lambda,5)*a55);
|
|
|
|
double velV = 0;
|
|
|
|
double theta = kx*x+ky*y-2.0*PII/T*t+phase;
|
|
|
|
velV = a1u*sinh(k*z)*sin(theta)
|
|
+ a2u*sinh(2.0*k*z)*sin(2.0*(theta))
|
|
+ a3u*sinh(3.0*k*z)*sin(3.0*(theta))
|
|
+ a4u*sinh(4.0*k*z)*sin(4.0*(theta))
|
|
+ a5u*sinh(5.0*k*z)*sin(5.0*(theta));
|
|
|
|
return velV;
|
|
}
|
|
}
|
|
|
|
namespace BoussinesqFun
|
|
{
|
|
#define PII 3.1415926535897932384626433832795028
|
|
#define G 9.81
|
|
|
|
double eta (double H, double h, double x, double y, double theta, double t, double X0)
|
|
{
|
|
double C = sqrt(G*(H+h));
|
|
double ts = 3.5*h/sqrt(H/h);
|
|
double aux = sqrt(3.0*H/(4.0*h))/h;
|
|
double Xa = -C * t + ts - X0 + x * cos(theta) + y * sin(theta);
|
|
|
|
double sup = H * 1.0/pow(cosh( aux * Xa ),2);
|
|
|
|
return sup;
|
|
}
|
|
|
|
double Deta1 (double H, double h, double x, double y, double theta, double t, double X0)
|
|
{
|
|
double C = sqrt(G*(H+h));
|
|
double ts = 3.5*h/sqrt(H/h);
|
|
double aux = sqrt(3.0*H/(4.0*h))/h;
|
|
double Xa = -C * t + ts - X0 + x * cos(theta) + y * sin(theta);
|
|
|
|
double deta = 8.0*aux*h * exp(2.0*aux*Xa) * (1.0-exp(2.0*aux*Xa))
|
|
/ pow(1.0+exp(2.0*aux*Xa),3);
|
|
|
|
return deta;
|
|
}
|
|
|
|
double Deta2 (double H, double h, double x, double y, double theta, double t, double X0)
|
|
{
|
|
double C = sqrt(G*(H+h));
|
|
double ts = 3.5*h/sqrt(H/h);
|
|
double aux = sqrt(3.0*H/(4.0*h))/h;
|
|
double Xa = -C * t + ts - X0 + x * cos(theta) + y * sin(theta);
|
|
|
|
double deta = 16.0*pow(aux,2)*h * exp(2.0*aux*Xa) * (exp(4.0*aux*Xa)
|
|
- 4.0*exp(2.0*aux*Xa)+1.0) / pow(1.0+exp(2.0*aux*Xa),4);
|
|
|
|
return deta;
|
|
}
|
|
|
|
double Deta3 (double H, double h, double x, double y, double theta, double t, double X0)
|
|
{
|
|
double C = sqrt(G*(H+h));
|
|
double ts = 3.5*h/sqrt(H/h);
|
|
double aux = sqrt(3.0*H/(4.0*h))/h;
|
|
double Xa = -C * t + ts - X0 + x * cos(theta) + y * sin(theta);
|
|
|
|
double deta = -32.0*pow(aux,3)*h * exp(2.0*aux*Xa) * (exp(6.0*aux*Xa)
|
|
- 11.0*exp(4.0*aux*Xa) + 11.0*exp(2.0*aux*Xa)-1.0) / pow(1.0+exp(2.0*aux*Xa),5);
|
|
|
|
return deta;
|
|
}
|
|
|
|
double U (double H, double h, double x, double y, double theta, double t, double X0, double z)
|
|
{
|
|
double C = sqrt(G*(H+h));
|
|
double etaSolit = eta( H, h, x, y, theta, t, X0);
|
|
double Detas2 = Deta2( H, h, x, y, theta, t, X0);
|
|
|
|
double vel = C*etaSolit/h
|
|
*(1.0 - etaSolit/(4.0*h) +
|
|
pow(h,2)/(3.0*etaSolit)
|
|
*(1.0 - 3.0/2.0*pow(z/h,2))
|
|
*Detas2);
|
|
|
|
return vel;
|
|
}
|
|
|
|
double W (double H, double h, double x, double y, double theta, double t, double X0, double z)
|
|
{
|
|
double C = sqrt(G*(H+h));
|
|
double etaSolit = eta( H, h, x, y, theta, t, X0);
|
|
double Detas1 = Deta1( H, h, x, y, theta, t, X0);
|
|
double Detas3 = Deta3( H, h, x, y, theta, t, X0);
|
|
|
|
double vel = -C*z/h
|
|
*((1.0 - etaSolit/(2.0*h))*Detas1 +
|
|
pow(h,2)/3.0
|
|
*(1.0 - 1.0/2.0*pow(z/h,2))
|
|
*Detas3);
|
|
|
|
return vel;
|
|
}
|
|
}
|
|
|