Code verification for governing equations with arbitrary functions using adjusted method of manufactured solutions

A new, adjusted approach to code verification using the method of manufactured solutions is presented. It is applicable for the physical problems, represented by mathematical models that include partial differential governing equations, which contain one or more functions that can vary from case to case. For the verification of such codes it has to be presumed that the varying functions are arbitrary and that is why this adjusted method is called the MMS-A. The aim of the new approach is further simplification of the existing methods that can become complex, time consuming and less convenient in general, when used for problems with arbitrary functions. With some additional programming the MMS-A can also be used for verifying codes, in which it is difficult to access the right-hand side of the governing equations (black box codes). In the present article the new method is described in detail and it is compared to the original method of manufactured solutions. It is demonstrated that using the MMS-A, the additional source term can be omitted. The use of the MMS-A is shown through examples that display the effectiveness of the new method.