High-end Semi-discrete Central Upwind Method Research And Application

In this paper, a new fourth-order semi-discrete central-upwind scheme for hyperbolic system of conservation laws, convection-diffusion equations and shallow water equations was presented. The integration over the Riemann fans by more accurate information about one-sided local speed of wave propagation was augmented. By using the fourth-order CWENO reconstruction, the new scheme has properties of higher order accuracy and higher resolution for discontinuities. In the meantime our new scheme enjoys the main advantage of the central schemes over the upwind ones: first, no Riemann solvers are required, and second, its generalization and realization for complicated multidimensional system are considerably simpler than in the upwind case. Because the new scheme has less dissipation, which is independent of time-steps, than the staggered central scheme, it can be efficiently used with time-steps as small as the requirement of the numerical stability. A number of numerical experiments for one and two-dimensional equations were presented to illustrate the accuracy and high-resolution properties of the new central scheme. Satisfactory results were obtained.