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Discretisation and Solution Method

1.      Choose appropriate spatial & temporal discretisation schemes.

  • If using a finite element method, ensure that the type of element used is chosen on a sound basis.
  • Wherever possible, use higher-order accurate discretisation schemes to minimise numerical diffusion errors.

2.      If the problem is time-dependent, ensure that; the initial condition is appropriate; time-step allows resolution of key phenomena & respects any Courant No. limits.

3.      Ensure that the numerical treatment of boundary conditions is appropriate.

  • Particularly for high speed flow.
  • Discretisation scheme accuracy may degrade.

4.      A solution strategy may have to be developed.

  • Optimising under-relaxation factors, plus real or false time­stepping to a steady solution, may be beneficial.
  • Start simple & include complex physics step-by-step.

5.      Establish appropriate solution convergence criteria:  Use of a mass residual criteria or change in solution value at a single monitoring node as sole methods for judging convergence may be very misleading.- Consider monitoring: a range of residuals; global balances of mass, momentum and energy; as well as solution values.