Numerics in OpenFoam - PBiCG vs. PCG
So the numerical scheme (fvScheme) will affect the property of the matrix to invert and we should choose properly the solver/solving algorithm (fvSolution) in order to solve it properly. Depending on the form of matrix depended on structured or unstructured mesh something like that.
Quote:
Originally Posted by thg
Hi Frog,
Meindert already mentioned, the difference between a PCG or a PBiCG,...
you can find in any textbook about linear iterative solvers like
Wessling, Saad, Trefethen, Stran,.... I think the book from Saad you find free on the www.
But I think your problems are a bit different.
Sine OF is a segregated solver, for every field (variable) there has to be solved a
linear system (i.e. for U, p,...) you have AU=b, Bp=c, A;B matrices.
Your choice of the numerical schemes
(entries for the operator discretization in fvSchemes, i.e.
(linear, upwind, limitedLinear,...)
for the operators is respobsible of the coefficients of this matrices.
So the choice of operators regarding f.i. U are responsible for the
properties/coefficients of the matrix A
The choice of your solution/solving algorithm (i.e. entries in fvSolution)
is responsible which iterative solver is used to solve your linear system.
So choosing f.i. PCG for U and PBiCG for p,
AU=b is solved iteratively bc PCG, Bp=c with PBiCG
and so forth.
Being also a mathematician, as a book enlighting CFD and numerics, I would also recommend Ferziger/Peric: Computational methods for fluid dynamics
Th.
Meindert already mentioned, the difference between a PCG or a PBiCG,...
you can find in any textbook about linear iterative solvers like
Wessling, Saad, Trefethen, Stran,.... I think the book from Saad you find free on the www.
But I think your problems are a bit different.
Sine OF is a segregated solver, for every field (variable) there has to be solved a
linear system (i.e. for U, p,...) you have AU=b, Bp=c, A;B matrices.
Your choice of the numerical schemes
(entries for the operator discretization in fvSchemes, i.e.
(linear, upwind, limitedLinear,...)
for the operators is respobsible of the coefficients of this matrices.
So the choice of operators regarding f.i. U are responsible for the
properties/coefficients of the matrix A
The choice of your solution/solving algorithm (i.e. entries in fvSolution)
is responsible which iterative solver is used to solve your linear system.
So choosing f.i. PCG for U and PBiCG for p,
AU=b is solved iteratively bc PCG, Bp=c with PBiCG
and so forth.
Being also a mathematician, as a book enlighting CFD and numerics, I would also recommend Ferziger/Peric: Computational methods for fluid dynamics
Th.
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