A local space-time conservation scheme and its application in shock wave propagation

In this paper, a local space–time conservation scheme based on non-staggered grids is introduced which is a variation of Space–Time Conservation Element and Solution Element (CE/SE) scheme. It inherits most features and advantages of CE/SE method, including unified treatment of space and time, and high-accuracy resolution of hyperbolic conservation equations. Moreover, Riemann solvers are not needed to capture shocks, and dimensional splitting methods are not needed in the multi-dimensional schemes. The stability of the present scheme is verified through von Neumann analysis. Moreover, several shock wave problems including one-, two-, and three-dimensional cases are simulated by the present scheme. By carefully comparing the present scheme’s numerical results with exact solutions, experimental results, original CE/SE scheme’s numerical results and third-order ENO scheme’s numerical results, it can be conclude that, the present scheme is efficient and accurate. 2012 Elsevier Inc. All rights reserved.