A compact high-order unstructured grids method for the solution of Euler equations

Two compact higher‐order methods are presented for solving the Euler equations in two dimensions. The flow domain is discretized by triangles. The methods use a characteristic‐based approach with a cell‐centered finite volume method. Polynomials of order 0 through 3 are used in each cell to represent the conservation flow variables. Solutions are demonstrated to achieve up to fourth‐order accuracy. Computations are presented for a variety of fluid flow applications. Numerical results demonstrate a substantial gain in efficiency using compact higher‐order elements over the lower‐order elements. Copyright © 1999 John Wiley & Sons, Ltd.