The Stability of the Central Scheme for Hyperbolic Conservation Laws


Guoxian Chen


In this talk we discuss the stability of the central scheme in two dimensions. We introduce a one-parameter convex decomposition of interpolated solutions in projection steps, then give a unified stability analysis is given for any conservation laws. The parameter is determined by the initial data reconstruction. The dimension-splitting limiting process (DS reconstruction) leads to a small parameter and then to a small CFL number, which even becomes zero for some successful limiters. Such small CFL number problem is a common problem in the existing literature regarding the stability condition of the central scheme. The stability condition is relaxed by applying the multi-dimensional limiting process (MD reconstruction), which is consistent with the updating process of the scheme. The smallest CFL number due to the MD reconstruction is equal to the largest CFL number due to the DS reconstruction. Thus a practical central scheme in 2D is obtained. Some numerical examples verify these assertions and the robustness of the enhanced central scheme.