TVD algorithms for the solution of the compressible Euler equations on unstructured meshes

Abstract

Abstract The Galerkin finite element method is used as the basis for the construction of schemes for the solution of the two‐dimensional compressible Euler equations on unstructured triangular grids. The use of a side‐based data structure readily allows for the construction of a local (structured) stencil and the incorporation of a high‐resolution shock‐capturing method formulated within the TVD concept. The essential features of the finite element side‐based scheme and the ID TVD approach are described and their numerical implementation is discussed. The choice of limiters and the support for their computation are analysed and the solutions of some inviscid flows, obtained by advancing explicitly in time, are presented.