Aspects of the Flux Correction Method for Solving the Navier-Stokes Equations on Unstructured Meshes

Abstract

This work examines the feasibility of a novel high-order numerical method, termed Flux Correction. Flux Correction “corrects” the flux terms of a traditional finite volume scheme, canceling truncation terms and promoting the method to a higher order. To accomplish this, higher-order gradients of solution variables, as well as gradients of the fluxes are introduced in the method. Gradients are computed using Lagrange interpolations in a fashion reminiscent of Finite Element techniques. For the Euler equations, Flux Correction is compared with Flux Reconstruction, a recently introduced class of schemes of which Discontinuous Galerkin and Spectral Difference methods are subsets. Flux Correction is found to compare favorably in terms of accuracy, and exceeds expectations for convergence rates. For the full Navier-Stokes equations, the effect of curved elements on Flux Correction is examined.