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

摘要

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 fifth-order 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 Padé scheme. 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.