A fifth-order finite volume weighted compact scheme for solving one-dimensional Burgers' equation

In the present paper, a high-order finite volume compact scheme is proposed to solve one dimensional Burgers' equation. The nonlinear advective terms are computed by the fifthorder finite volume weighted upwind compact scheme, in which the nonlinear weighted essentially non-oscillatory weights are coupled with lower order compact stencils. The diffusive terms are discretized by using the finite volume six-order Padscheme. The strong stability preserving third-order Runge-Kutta time discretizations is used in this work. Numerical results are compared with the exact and some existing numerical solutions to demonstrate the essentially non-oscillatory and high resolution of the proposed method. The numerical results are shown to be more accurate than some numerical results given in the literature. (C) 2016 Elsevier Inc. All rights reserved.