A HIGH-RESOLUTION SPACE-TIME CONSERVATIVE METHOD FOR NON-LINEAR HYPERBOLIC CONSERVATION LAWS

We present a second-order scheme for the numerical solution of hyperbolic systems which treats space and time in a unified manner. The flow variables and their slopes are the basic unknowns in the scheme. The scheme utilizes the advantages of the space-time conservation element and solution element (CE/SE) method of Chang [1995] as well as central schemes of Nessyahu and Tadmor [1990]. However, unlike the CE/SE method the present scheme is Jacobian-free and hence like the central schemes can also be applied to any hyperbolic system. In Chang's method, a finite difference approach is being used for the slope calculation in case of non-linear hyperbolic equations. We propose to propagate the slopes by a scheme even in the case of non-linear systems. By introducing a suitable limiter for the slopes of flow variables, we can apply the same scheme to linear and non-linear problems with discontinuities. The scheme is simple, efficient and has a good resolution especially at contact discontinuities. We derive the scheme for one-and two-space dimensions. In two-space dimensions we use structured triangular meshes. The second-order accuracy of the scheme has been verified by numerical experiments. Several numerical tests presented in this article validate the accuracy and robustness of the present scheme.