The Method of Manufactured Solutions for Code Verification

Abstract

Verification of codes that numerically approximate solutions of partial differential equations consists in demonstrating that the code is free of coding errors and is capable, given sufficient discretization, of approaching exact mathematical solutions. This requires the evaluation of discretization errors using known benchmark solutions. The best benchmarks are exact analytical solutions with a sufficiently complex solution structure; they need not be physically realistic since verification is a purely mathematical exercise. The Method of Manufactured Solutions (MMS) provides a straightforward and general procedure for generating such solutions. For complex codes, the method utilizes symbolic manipulation, but here it is illustrated with simple examples. When used with systematic grid refinement studies, which are remarkably sensitive, MMS can produce robust code verifications with a strong completion point.