A Fifth-Order Low-Dissipative Conservative Upwind Compact Scheme Using Centered Stencil (Advances in Applied Mathematics and Mechanics, 2021)
In this paper, a conservative fifth-order upwind compact scheme using centered stencilis introduced. This scheme uses asymmetric coefficients to achieve the upwind propertysince the stencil is symmetric. Theoretical analysis shows that the proposed scheme islow-dissipative and has a relatively large stability range. To maintain the convergencerate of the whole spatial discretization, a proper non-periodic boundary scheme is alsoproposed. A detailed analysis shows that the spatial discretization implemented with theboundary scheme proposed by Pirozzoli [J. Comput. Phys., 178 (2001),  pp. 81-117] isapproximately fourth-order. Furthermore, a hybrid methodology, coupling the compactscheme with WENO scheme, is adopted for problems with discontinuities. Numerical resultsdemonstrate the effectiveness of the proposed scheme.