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.