A two-dimensional fourth-order unstructured-meshed Euler solver based on the CESE method

In this paper, Changʼs one-dimensional high-order CESE method [1] is extended to a two-dimensional, unstructured-triangular-meshed Euler solver. This fourth-order CESE method retains all favorable attributes of the original second-order CESE method, including: (i) flux conservation in space and time without using an approximated Riemann solver, (ii) genuine multi-dimensional algorithm without dimensional splitting, (iii) the CFL constraint for stable calculation remains to be ⩽1, (iv) the use of the most compact mesh stencil, involving only the immediate neighboring cells surrounding the cell where the solution at a new time step is sought, and (v) an explicit, unified space-time integration procedure without using a quadrature integration procedure. To demonstrate the new algorithm, three numerical examples are presented: (i) a moving vortex, (ii) acoustic wave interaction, and (iii) supersonic flow over a blunt body. Case 1 shows fourth-order convergence through mesh refinement. In Case 2, the nonlinear Euler solver is applied to simulate linear waves. In Case 3, superb shock capturing capabilities of the new fourth-order method without the carbuncle effect is demonstrated.