Solution of the Euler equations on unstructured grids for two-dimensional compressible flow

Abstract

AbstractA method for the numerical solution of the two-dimensional Euler equations on unstructured grids has been developed. The cell-centred symmetric finite-volume spatial discretisation is applied in a general formulation that allows the use of arbitrary polygonal computational cells. The integration in time, to a steady-state solution, is performed using an explicit, multi-stage procedure, with standard convergence acceleration techniques such as local time stepping, enthalpy damping and implicit residual smoothing. Accuracy of solution, in terms of minimising spurious entropy production, is achieved through careful treatment of the artificial dissipative terms near boundaries. Standard test cases for both subcritical and supercritical flows, including single- and multi-element aerofoils have been used to validate the method.