Numerical Accuracy in CFD

Numerical Accuracy in CFD

Numerical accuracy is of prime importance when one is playing with numbers especially in CFD. In CFD the naive understanding of numerical accuracy has to be shed off. It pertains to the scheme, grid, the problem involved, and many other factors. However, I will try to portray some of the predominant  ones. The sources of numerical accuracy are;

1. Numerical scheme

• Discretisation - order of accuracy of the convective terms, minimal amount of artificial viscosity
• Tunable parameters - like co-effcients in JST scheme and in turbulence models
• Boundary conditions - especially pressure based
• Temporal accuracy

2. Grid - Mesh dependency

3. Convergence

• Linear Solvers used - for implicit or multi-grid or multi-stepping schemes
• Stopping criterion for iterative solvers - tolerance, pre-conditioning, etc

4. Validation / Verification - proper choice of analytical, benchmark & experimental test cases with the above requirements for specific class of problems that you are dealing with

CFD developers and application engineers likewise should be able to demonstrate the above before going ahead with simulating the class of problems. When using an industrial CFD solver ( which in most cases guarantees the above criteria), it is good practice to understand or play around to get the above criterion. 

Useful documents on this.
1. PPT on Numerical accuracy - Good one
2. Journal of Fluids Engineering - Numerical Accuracy