A second order upwind method for linear hyperbolic systems
Commun. Korean Math. Soc. 2002 Vol. 17, No. 1, 103-120 Printed March 1, 2002
Sung-Ik Sohn and Jun Yong Shin Tongmyong University of Information Technology, Pukyung National University
Abstract : A second order upwind method for linear hyperbolic systems is studied in this paper. The method approximates solutions as piecewise linear functions, and state variables and slopes of the linear functions for next time step are computed separately. We present a new method for the computation of slopes, derived from an upwinding difference for a derivative. For nonoscillatory solutions, a monotonicity algorithm is also proposed by modifying an existing algorithm. To validate our second order upwind method, numerical results for linear advection equations and linear systems for elastic and acoustic waves are given.
Keywords : upwind method, linear hyperbolic systems, slope limiter