Central Difference Scheme For Solving Hyperbolic Conservation Laws Method

This paper deals with initial problems of one-dimensional hyperbolic systems of conservation laws. Based on studying second order and third order central schemes, a new modified third-order central scheme is presented, especially a new reconstruction is proposed. A semi-discrete form of our scheme is also presented. This new reconstruction is a third order accuracy in smooth regions and non-oscillations at cell interfaces. Our scheme enjoys the main advantage of the central schemes -simplicity, namely it does not employ Riemann solvers and hence the intricate and time-consuming characteristic decomposition are avoided. Numerical experiments with our scheme and other central schemes for the initial value problems of convective equation, Burgers equation and Euler equations have been implemented. These results demonstrate the desired accuracy and high resolution of our scheme. Also our scheme can be easily applied and implemented to a wide variety of problems. It may serve as effective finite-difference methods for hyperbolic conservation laws.