A Generic 4th Order 2D Unstructured Euler Solver for the CESE Method

Abstract : Previously, Chang reported a new class of high-order Conservation Element Solution Element, CESE, methods for solving nonlinear hyperbolic partial differential equations. The scheme was then extended by Bilyeu, et al. to solve a 1D vector equation with an arbitrary order of convergence. This new high-order CESE method shares many favorable attributes of the original second-order CESE method, including: (i) compact mesh stencil involving only the immediate mesh nodes surrounding the node where the solution is sought, (ii) the CFL stability constraint remains the same, i.e., < or = 1, as, and (iii) superb shock capturing capability without using an approximate Riemann solver. In the present extended abstract, we extend the 1D formulation to 2D. A general formulation is presented for solving the coupled equations with 4thorder accuracy. To demonstrate the formulation, two linear cases are reported. The linear test cases shown are the convection equation and the linear acoustic equation. In the final paper we plan to present non-linear test cases and solve the equations on a quad mesh.