Methods

Time integration

GRESSIER Jérémie — 2009-06-09T22:00:00Z

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

One can specify

method to compute time step by iteration in the cycle
time integration method

End of cycle

For unsteady computations, the end of cycle is triggered when time integration reaches cycle duration.

For steady computations, the end of cycle is triggered by

a residual criterion which can be optionally specified with RESIDUALS= (if not, project criterion is used).
a maximum number of iterations through CYCLE_MAX_IT= parameter

Note that an existing typhon_stop file triggers end of cycle and end of computation. A maximum total number of iterations can be specified through MAX_IT= parameter

Timestep

Three methods are implemented

the time step is specified DTCALC=GIVEN and given with
DT=
A global time step (default) can be computed according to a stability condition: DTCALC=STABILITY_CONDITION. The stabilty condition is given according to the solver
- heat transfer: FOURIER=
- compressible fluid: CFL=. The optional parameter CFLMAX= can be specified in order to automatically increase the CFL number with convergence up to CFLMAX.
A local time step can be computed according the a stability condition as in previous point with DTCALC=LOCAL_STABILITY_CONDITION. Note that this method is not consistent for unsteady problems.

Time integration method

The time integration method can be specified with METHOD parameter.

METHOD=EXPLICIT (default)
METHOD=RK2
METHOD=RK2-TVD or RK2-SSP
METHOD=RK3-SSP
METHOD=RK4
METHOD=RK25BB for 5 steps Bogey and Bailly optimized RK
METHOD=RK26BB for 6 steps Bogey and Bailly optimized RK
METHOD=IMPLICIT

For `IMPLICIT` methods, one must specify the inversion method:

INVERSION=JACOBI
INVERSION=CGS
INVERSION=BICG
INVERSION=BICG-JACOBI
INVERSION=BICGSTAB
INVERSION=GMRES
INVERSION=GMRESFREE (under development)

Optional parameters are (default values depends on the inversion method)

MAX_IT= for the maximum number of inversion iteration
INV_RES= for the convergence of the iterative algebraic system

Numerical schemes for compressible fluid solver

GRESSIER Jérémie — 2009-05-05T07:30:00Z

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= 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= 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= 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

These parameters are decribed in this article

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

[1] available in r698

[2] available in r662

Methods

Time integration

End of cycle

Timestep

Time integration method

For IMPLICIT methods, one must specify the inversion method:

Numerical schemes for compressible fluid solver

Numerical Flux

High-Order

Time integration

For `IMPLICIT` methods, one must specify the inversion method: