Method of Manufactured Solutions. The Method of Manufactured Solutions is a general and very powerful method for verification. However, immediately it must be acknowledged that implementing MMS requires access to source code, and is time intensive, and so is unlikely to be used by practitioners, the key audience for this document. So its description here is relatively high level, and those wishing to pursue this technique may follow the many references available. MMS is a response to the challenge of finding an exact solution to the complete partial differential equations in many fields of simulation, particularly fluid dynamics. As will be shown below, only the simplest equations and geometrical domains permit e.g. analytical (exact) solutions against which the outputs of the numerical scheme can be compared. MMS works the problem the other way around. The method proposes a form of a solution (which might be given by analytical sine/cosine/exponential terms) and then works out how to modify the equations to produce that solution. The modification is done by adding source terms to the governing equations; these can be thought of as “pushing” the solution towards the desired form. The benefits of MMS is that it can provide solutions to governing equations of high complexity, allowing all terms to be fully exercised (tested for correct implementation). However this does come at a cost. The approach of working the “reverse problem” is non-intuitive, and some may object to the lack of any clear physical analogue in the results (even though there is no requirement for any verification solution to be related to a physically realistic problem10). Perhaps the greatest barrier is the implementation of the source terms, which not only requires access to source code, but great care must be taken when implementing the many terms in the resulting (modified) equations. An extensive discussion on the use of MMS for code verification is presented by Xxxxx and Xxxxxx (2003).
