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# Time integration

D 9 June 2009

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=<value> (if not, project criterion is used).
• a maximum number of iterations through CYCLE_MAX_IT=<value> 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=<value> parameter

### Timestep

Three methods are implemented

• the time step is specified DTCALC=GIVEN and given with DT=<value>
• 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=<value>
• compressible fluid: CFL=<value>. The optional parameter CFLMAX=<value> 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=<int> for the maximum number of inversion iteration
• INV_RES=<value> for the convergence of the iterative algebraic system

# Also in this section

Numerical schemes for compressible fluid solver All parameters for the numerical scheme applied to convective and diffusive fluxes are defined in BLOCK:SPAT (...)

Tuesday 5 May 2009