Semi-Discrete Central Scheme for Hyperbolic Conservation Laws
Chen Jianzhong(1),Feng Jianhu(2),Shi Zhongke(1),Hu Yanmei(2)
(1 Northwestern Polytechnical University, Xi'an 710072) (2 College of Scien ce, Chang'an University, Xi'an 710064)

Abstract: A third-order semi-discrete central scheme for approximate solution of the hyperbolic conservation laws was presented based on a new reconstruction, where local wave propagation velocity was taken into account. The cell ave rages over the nonuniform, staggered grid were computed, which then were projec ted back onto the original grid of the uniform, non-staggered cells to obtain the fully discrete third-order central scheme with a semi-discrete formulation. This scheme retains the main advantage of the central scheme-simplicity, hence Riemann solvers were unnecessary for characteristic decompositions. The numerical results confirm the desired accuracy and high resolution of the scheme with a conservative form and a consistent numerical flux.
Keywords: hyperbolic conservation laws, central difference schemes, semi-discre te, reconstruction.