Discretizations

code_saturne is based on a co-located Finite Volume approach that handles unstructured meshes with any type of cell (tetrahedral, hexahedral, prismatic, pyramidal, polyhedral…)

It can solve flows in pseudo-steady or unsteady mode. It uses a theta scheme for the time discretization.

Velocity-pressure coupling

code_saturne uses a fractional step method, similar to SIMPLEC.

  1. Velocity prediction: Solve the momentum equation with an explicit pressure gradient and obtain a predicted velocity
  2. Pressure correction: Use the continuity equation to enforce mass conservation
  3. Update velocity fi eld using ∇ P

After the velocity has been updated, the resolution of turbulent variables and scalars is done according to their time scheme.
Rhie & Chow interpolation is used when solving the pressure to avoid oscillations (or checkerboarding).

Linear system resolution

Several linear system solvers are available:

  • Gauss-Seidel (default for velocity, temperature, turbulent variables, passive scalars)
  • Jacobi
  • Conjugate gradient (default for pressure)
    • With algebraic multigrid, jacobi, or polynomial preconditioning
  • Algebraic multigrid
  • Stabilized bi-conjugate gradient (BI-CGSTAB or Bi-CGSTAB2)
  • GMRES, GCR
  • solvers provided by external libaries
    • PETSc
    • AmgX

Convective scheme

Different schemes for convective terms are available:

  • First order Upwind Scheme
  • Centered scheme
  • Second Order Linear Upwind (SOLU) Scheme
  • Blended scheme between upwind and second order scheme

A slope test is activated by default for second order schemes to switch from second order to upwind in case of overshoots

Gradient calculation

Several options are available:

  • Green-Gauss method with iterative reconstruction of the non-orthogonalities (initialization by zero or based on the least-square method)
  • Least squares method (with a standard, extended or partial extended neighborhood)
  • Green-Gauss method with least-squares based estimation of face values