A Fifth-Order Low-Dissipative Conservative Upwind Compact Scheme Using Centered Stencil

Abstract

In this paper, a conservative fifth-order upwind compact scheme using centered stencil is introduced. This scheme uses asymmetric coefficients to achieve the upwind property since the stencil is symmetric. Theoretical analysis shows that the proposed scheme is low-dissipative and has a relatively large stability range. To maintain the convergence rate of the whole spatial discretization, a proper non-periodic boundary scheme is also proposed. A detailed analysis shows that the spatial discretization implemented with the boundary scheme proposed by Pirozzoli [J. Comput. Phys., 178 (2001),  pp. 81-117] is approximately fourth-order. Furthermore, a hybrid methodology, coupling the compact scheme with WENO scheme, is adopted for problems with discontinuities. Numerical results demonstrate the effectiveness of the proposed scheme.