Verification and accuracy comparison of commercial CFD codes using hydrodynamic instability

Abstract

Code verification is mainly concerned with programming errors. Once a code is free of such errors, the verification of results can characterize the code accuracy, in particular the truncation error is of interest. Accuracy is an important feature of any code and the verification results provide some measure that can be used to compare code performance. Code verification requires an exact solution to which the numerical solution can be compared and the error precisely quantified. In the computational fluid dynamics community the method of manufactured solutions (MMS) is recommended as it can produce an exact solution sufficiently complex to test all code routines. However, it requires the addition of source terms in the equations of motion, a possibility that is almost never available in commercial codes. Exact solutions are also employed, but they represent very simplified flows that cannot test all code routines. Other verification tests exist, but they are also limited in comparison with MMS. Yet, even some of these limited tests are impossible to perform in many commercial codes. This paper presents a test based on linear stability theory. It is shown that the test is very demanding. It is also shown that the test could be performed even on codes that are very restrictive on what a user is allowed to do. It is not as complete as the MMS, but it is substantially more general than simple exact solutions of the Navier–Stokes equations. For instance it can account for three-dimensionality and compressibility effects, among other generalizations. The results enable a comparison of several codes in terms of refinement necessary for a grid-independent solution and the accuracy of the converged solution.