This formulation provides C-grid like pressure-flux staggering on an
unstructured mesh which is hugely beneficial for Euler-Euler multiphase
equations as it allows for all forces to be treated in a consistent
manner on the cell-faces which provides better balance, stability and
accuracy. However, to achieve face-force consistency the momentum
transport terms must be interpolated to the faces reducing accuracy of
this part of the system but this is offset by the increase in accuracy
of the force-balance.
Currently it is not clear if this face-based momentum equation
formulation is preferable for all Euler-Euler simulations so I have
included it on a switch to allow evaluation and comparison with the
previous cell-based formulation. To try the new algorithm simply switch
it on, e.g.:
PIMPLE
{
nOuterCorrectors 3;
nCorrectors 1;
nNonOrthogonalCorrectors 0;
faceMomentum yes;
}
It is proving particularly good for bubbly flows, eliminating the
staggering patterns often seen in the air velocity field with the
previous algorithm, removing other spurious numerical artifacts in the
velocity fields and improving stability and allowing larger time-steps
For particle-gas flows the advantage is noticeable but not nearly as
pronounced as in the bubbly flow cases.
Please test the new algorithm on your cases and provide feedback.
Henry G. Weller
CFD Direct
Improves stability and convergence of systems in which drag dominates
e.g. small particles in high-speed gas flow.
Additionally a new ddtPhiCorr strategy is included in which correction
is applied only where the phases are nearly pure. This reduces
staggering patters near the free-surface of bubble-column simulations.
Allows the specification of a reference height, for example the height
of the free-surface in a VoF simulation, which reduces the range of p_rgh.
hRef is a uniformDimensionedScalarField specified via the constant/hRef
file, equivalent to the way in which g is specified, so that it can be
looked-up from the database. For example see the constant/hRef file in
the DTCHull LTSInterFoam and interDyMFoam cases.
Disadvantage is that the BC values have to be specified in terms of hU
rather than U. The alternative would be to add complex code to map h
and U BCs into the equivalent for hU.
Resolves bug-report http://www.openfoam.org/mantisbt/view.php?id=1566
This is an experimental feature demonstrating the potential of MULES to
create bounded solution which are 2nd-order in time AND space.
Crank-Nicolson may be selected on U and/or alpha but will only be fully
2nd-order if used on both within the PIMPLE-loop to converge the
interaction between the flux and phase-fraction. Note also that
Crank-Nicolson may not be used with sub-cycling but all the features of
semi-implicit MULES are available in particular MULESCorr and
alphaApplyPrevCorr.
Examples of ddt specification:
ddtSchemes
{
default Euler;
}
ddtSchemes
{
default CrankNicolson 0.9;
}
ddtSchemes
{
default none;
ddt(alpha) CrankNicolson 0.9;
ddt(rho,U) CrankNicolson 0.9;
}
ddtSchemes
{
default none;
ddt(alpha) Euler;
ddt(rho,U) CrankNicolson 0.9;
}
ddtSchemes
{
default none;
ddt(alpha) CrankNicolson 0.9;
ddt(rho,U) Euler;
}
In these examples a small amount of off-centering in used to stabilize
the Crank-Nicolson scheme. Also the specification for alpha1 is via the
generic phase-fraction name to ensure in multiphase solvers (when
Crank-Nicolson support is added) the scheme is identical for all phase
fractions.
