Elimination of Spurious Loss in Euler Equation Computations

The accuracy of a standard implicit conservative Euler equation solver is greatly improved by incorporation of an entropy-conservation equation, used in lieu of the streamwise momentum equation in all regions of the flow except at shock waves. A slight modification is also required at stagnation points to maintain wellposedness. The overall method completely eliminates spurious entropy errors, and thus reduces the grid density required to achieve any particular level of accuracy. Results are presented for subsonic and transonic airfoil flows. Although the derivation and results are for 2-D Euler equations, the approach has no inherent limitations which preclude extension to 3-D or viscous flows. A brief discussion of these extensions is presented. 1 Introduction Most current Euler equation solution methods solve the mass, momentum, and energy equations discretized in strongly-conservative form. @ae @t + r \Delta (ae~q) = 0 (1) @(aeu) @t + r \Delta (ae~qu + p--) = 0 (2) @(aev) @t ..