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# Numerical schemes for compressible fluid solver

D 5 May 2009

All parameters for the numerical scheme applied to convective and diffusive fluxes are defined in BLOCK:SPAT section.

### Numerical Flux

The numerical flux applied to the hyperbolic part is defined with SCHEME=<key> where key could be

• RUSANOV for Rusanov upwind scheme
• HLL or HLLE for HLLE upwind scheme
• HLLC for HLLC upwind scheme (cf Toro, Batten)
• AUSMM for AUSM-M upwind scheme
• EFM or KFVS for EFM/KFVS upwind scheme (cf Pullin, 1981 or Deshpande, 1986). A total enthalpy preserving variant is available with EFMH key.
• VLEERH or VLH for van Leer/Hänel FVS scheme (total enthalpy preserving) [1]

### High-Order

Default computation is a a first order scheme. One can use a high-order extension with HIGHRES=<key> parameter such as:

• for MUSCL second order extension
• HIGHRES = MUSCL
• HIGHRES = MUSCL-UNS
• HIGHRES = MUSCL-FAST for high quality grids)
with TVD limiters: Minmod, van Albada (default), van Leer, Superbee, Kim (3rd order)
LIMITER = NONE / MINMOD / ALBADA / VAN_ALBADA / VAN_LEER / VANLEER / SUPERBEE / KIM3 / LIM03
• Spectral Volume Method for high order extrapolation (currently only on 2D tri grids) (HIGHRES=SVM)
• 2nd order : SVM = 2 or 2QUAD
• 3rd order : SVM = 3, 3WANG, 3KRIS or 3KRIS2
• 4th order : SVM = 4, 4WANG, 4KRIS or 4KRIS2

Whatever the high-order extrapolation method is, a post-limitation process is possible through POST-LIMITER=<key> option. The limiting process compares face-extrapolated states and cell states and corrects them if necessary. Current limiters are:

• NONE (default) does not limit states
• MONOTONIC0 only ensures face states are in the range of cell states
• MONOTONIC1 ensures monotonicity variation of the four values
• MONOTONIC2 limits cell to face difference to be half the variation between both cells
• BARTH is similar to Minmod or Monotonic2 but adds a limitation to all faces of a cell
• SUPERBARTH is similar to Superbee or Monotonic0 but adds a limitation to all faces of a cell [2]

### Time integration

• Explicit multi-level Runge-Kutta time integration (2nd and 3rd order)
• Implicit backward Euler
• Linear Implicit resolution (BiCG-Stab, GMRes)
• Approximate upwind fluxes jacobian
• Viscous fluxes jacobian

[1available in r698

[2available in r662

# Also in this section

Time integration Time integration methods are implemented for all solvers. It can be defined in BLOCK:TIME_PARAM set of options. (...)

Tuesday 9 June 2009