Solution of the steady Euler equations using Fluctuation Splitting schemes on quadrilateral elements

Abstract

Fluctuation Splitting (FS) schemes, also known as Residual Distribution schemes, are a well-established technique for solving hyperbolic problems on triangular meshes, see [1] and the references therein. As such, they are not adequate for solving high Reynolds number viscous flows, where an accurate resolution of the boundary layer requires high aspect ratio quadrilateral cells. Therefore, there has been a renewed interest in the application of this methodology on quadrilateral meshes. In [2] the authors presented a thorough analysis of the properties of FS schemes when applied to quadrilateral elements, with reference to the solution of the linear advection and advection-diffusion equations.