Efficient Code Verification Using the Residual Formulation of the Method of Manufactured Solutions
Clarence O. E. Burg, Vasanth Siruvallur Murali · 34th AIAA Fluid Dynamics Conference and Exhibit · 2004
The Method of Manufactured Solutions is a code verification m ethod that modifies the governing equations solved within a code by adding a source term to drive the solution towards a predetermined analytic function. By solving the modified equations on a sequence of grids and co mparing the differences between the converged solution and manufactured solution, the order of accuracy of the implementation can be determined. The method of manufactured solutions combines the benefits of co mparing with an exact solution without the need to derive an exact solution to the governing equations. However, in its current form, highly converged solutions on a sequence of grids are required which can be quite costly and difficult to obtain. In this paper, the method of manufactured solutions is used in a different fashion that removes the need for converged solutions by considering only the residual of the discretized governing equations rather than the solution, thus avoiding the computational cost and difficulties inherent in obtaini ng highly converged solutions. Furthermore, this new approach is quite similar to the method for analyzing a discretization method to determine the order of accuracy of that method via Taylor’s series expansions. T his new approach is demonstrated to yield the same order of accuracy as the original method of manufactured solutions using three different cases - onedimensional porous media equation, one-dimensional St. Venant equations and two-dimensional unstructured Euler simulations.