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Time integration

Tuesday 4 June 2013, by J. Gressier

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

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