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System of Linear Equations

Finite Volume Method converts the system of differential equations to the system of linear equations:

img194 1

Such a linear algebra problem can be solved with following methods implemented in OpenFOAM:

Linear system solver method:

  • GAMG (Geometric-Algebraic Multi-Grid) for both symmetric and asymmetric matrices
  • PBiCG (Preconditioned Biconjugate Gradient ) for asymmetric matrices
  • PCG (Preconditioned Conjugate Gradient) for symmetric matrices
  • smoothSolver (solver using a smoother for both symmetric and asymmetric matrices )
  • ICCG (Incomplete Cholesky preconditioned PCG solver, i.e. PBiCG with DIC )8.2
  • BICCG (Diagonal Incomplete LU preconditioned PBiCG solver, i.e. PCG with DILU)8.3

Method preconditioner:

  • DILU (Diagonal Incomplete LU decomposition)
  • DIC (Diagonal incomplete-Cholesky) for symmetric matrices
  • FDIC (Faster diagonal incomplete-Cholesky) for symmetric matrices
  • diagonal (Diagonal)
  • GAMG (Geometric-Algebraic Multi-Grid)
  • none (No preconditioning)
  • DICGaussSeidel, GaussSeidel, nonBlockingGaussSeidel, symGaussSeidel (for symmetric matrices)

For more details see e.g. [9].