A modified space-time Conservation Element and Solution Element Method for Euler and Navier-Stokes equations

Abstract

In this paper, we report a variation of Chang’s SpaceTime Conservation Element and Solution Element CE/SE Method for structured mesh. The algorithm of the present modified CE/SE method is even simpler than the original CE/SE method. Nevertheless, all advantageous features of the original CE/SE method have been retained, including a unified treatment of space and time, accurate calculation of the space-time flux, high-fidelity resolution of unsteady flow motions, and full compliance with the physics of initial valued problems. The present modified method is also extended to solve Navier Stokes equations. To calculate the viscous flux terms, a ‘midpoint rule’ is used. In the setting of space-time flux conservation, two boundary-condition treatments for solid wall are introduced. Numerical results show that the present Navier Stokes solver can be used for high-speed flows as well as low-Mach-number flows without preconditioning. Results of several standard flow problems show that the present method is efficient and accurate.