Application of the method of manufactured solutions to the verification of a pressure-based finite-volume numerical scheme

The present study reports a numerical procedure based on a series of tests that make use of the method of manufactured solutions (MMS) and allow to evaluate the effective numerical performance with respect to the theoretical order of accuracy. The method is applied to a pressure-based finite volume numerical scheme suited to variable density flows representative of those encountered in combustion applications. The algorithm is based on a predictor-corrector time integration scheme that employs a projection method for the momentum equations. A physically consistent constraint is retained to ensure that the velocity field is solved correctly. The MMS application shows that the combination of this velocity constraint and the variable-coefficient Poisson solver is of fundamental importance to ensure both the numerical stability and the expected order of accuracy. Especially, the resort to an inner iteration procedure gives rise to undeniable improvements in terms of both the order of accuracy and error magnitude. The MMS applications confirm the interest of the method to conduct a preliminary check of the performance of any numerical algorithm applied to both fully incompressible and variable density flows. Finally, the analysis is ended by the application of the retained pressure-based finite-volume scheme to the numerical simulation of mixing layers featuring increasing values of the density contrast. The corresponding results shed some light onto the stability and robustness of the numerical scheme, important issues that are not addressed through MMS analyses. (C) 2011 Elsevier Ltd. All rights reserved.