A Fourth-Order Central Runge-Kutta Scheme for Hyperbolic Conservation Laws

作者：Dehghan Mehdi^*; Jazlanian Rooholah

来源：Numerical Methods for Partial Differential Equations, 2010, 26(6): 1675-1692.

DOI：10.1002/num.20530

• central Runge-Kutta(CRK) scheme
• central scheme
• hyperbolic conservation laws
• nonlinear limiters
• nonoscillatory scheme
• weighted essentially nonoscillatory (WENO) technique

In this work, a new formulation for a central scheme recently introduced by A. A. I. Peer et al. is performed. It is based on the staggered grids. For this work, first a time discritization is carried out, followed by the space discritization. Spatial accuracy is obtained using a piecewise cubic polynomial and fourth-order numerical derivatives. Time accuracy is obtained applying a Runge-Kutta(RK) scheme. The scheme proposed in this work has a simpler structure than the central scheme developed in (Peer et al., Appl Numer Math 58 (2008), 674-688). Several standard one-dimensional test cases are used to verify high-order accuracy, nonoscillatory behavior, and good resolution properties for smooth and discontinuous solutions.

• 出版日期2010-11