Source Term Discretization Effects on the Steady-State Accuracy of Finite Volume Schemes

Source terms often arise in Computational Fluid Dynamics to describe a variety of physical phenomena, including turbulence, chemical reactions, and certain methods used for code verification, such as the method of manufactured solutions. While much has already been published on the treatment of source terms, here we follow an uncommon approach, designing compatible source term discretizations in terms of spatial truncation error for finite volume schemes in multiple dimensions. In this work we examine the effect of source term discretization on three finite volume flux schemes applied to steady flows: constant reconstruction, linear reconstruction, and a recently published third-order flux correction method. Three source term discretization schemes are considered, referred to as point, Galerkin, and corrected. The corrected source discretization is a new method that extends our previous work on flux correction to equations with source terms. In all cases, computational grid refinement studies confirm the compatibility (or lack thereof) of various flux-source combinations predicted through detailed truncation error analysis.