Abstract
In this paper, we present new results concerning the construction of upwind residual distribution schemes on unstructured meshes. These schemes are tailored to the steady state numerical solution of systems of first order conservation laws in more than one space dimension. The schemes under consideration have been previously introduced by P.L. Roe, H. Decon-inck and their coworkers (Roe, 87; Roe, 90; Struijs, Deconinck and Roe, 91; Roe and Sidilkover, 92; Deconinck,Roe and Struijs, 93; Deconinck, Struijs, Bourgeois and Roe, 93) and developed specifically for use on simplicial (triangulated) meshes. In the present work, two separate but related topics are addressed: (1) how to construct mathematically well-founded variants of these schemes that are second order accurate at steady state, and (2) how to generalise these new schemes to more general systems of conservation laws and/or general (non-simplicial) element meshes. Numerical examples of transonic Euler flow are provided to verify the analysis and validate the solution quality improvements obtained with the new schemes.
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