A 3D Unstructured Mesh Euler Solver Based on the Fourth-Order CESE Method

In this paper, the CESE method is extended and employed to construct a fourth-order, three-dimensional, unstructured-mesh solver for hyperbolic Partial Differential Equations (PDEs). This new CESE method retains all favorable attributes of the original second-order CESE method, including: (i) flux conservation in space and time without using a one-dimensional Riemann solver, (ii) genuinely multi-dimensional treatment without dimensional splitting (iii) the CFL constraint remains to be less than or equal to 1, and (iv) the use of a compact mesh stencil involving only the immediate neighboring nodes surrounding the node where the solution is sought. Two validation cases are presented. First higher order convergence is demonstrated by the linear advection equation. Second supersonic flow over a spherical body is simulated to demonstrates the schemes ability to accurately resolve discontinuities. The original document contains color images. Conference paper for the AIAA CFD conference, San Diego, CA, June 2013.