IMPLEMENTATION OF ENO AND WENO SCHEMES FOR FINITE VOLUME UNSTRUCTURED GRID SOLUTIONS OF COMPRESSIBLE AERODYNAMIC FLOWS

Abstract

In this work the essentially non-oscillatory schemes (ENO) and the weighted essentially non-oscillatory schemes (WENO) are implemented in a cell centered finite volume context on unstructured meshes. The 2-D Euler equations will be considered to represent the flows of interest. The ENO and WENO schemes have been developed with the purpose of accurately capturing discontinuities appearing in problems governed by hyperbolic conservation laws. In the high Mach number aerodynamic studies of interest in the present paper, these discontinuities are mainly represented by shock waves and contact discontinuities. The entire reconstruction process of ENO and WENO schemes is described in detail for linear polynomials and, therefore, second-order of accuracy. An extension to higher orders of accuracy is presented in the paper in a straightforward manner and applications for compressible flows are shown. These applications compare the accuracy of the schemes with some related data that appear in the references cited in this paper or that come from analytical solutions.