A semi-automatic approach based on the method of manufactured solutions to assess the convergence order in OpenFOAM

Abstract

Code verification is an intricate but crucial part of numerical code development. Due to the complexity of the partial differential equations, an analytical solution might not exist. In those situations and aiming at proving that the code is solving appropriately the governing equations, the method of manufactured solutions (MMS) is a powerful tool. In this method, a source term is derived to enforce the solution to a predetermined function. By performing a mesh refinement study, one can verify if the code is correctly solving the desired equations. In this work, a methodology that allows the automation of the MMS within the OpenFOAM© framework is proposed. The developed computational framework comprises a set of tools prepared, in an open-source environment, for the symbolic computation of the associated source term, and to generate the code required for its implementation as well as appropriate boundary conditions and functions to calculate the error norms.