A stable dissipative compact finite difference scheme with global accuracy of ninth order

Abstract We consider in this paper a ninth-order dissipative compact finite difference scheme. To stabilize the scheme for initial boundary value problems, we introduce the so-called conservative solution points (Deng and Chen, 2018) [9] near the boundaries of computational domain, such that the scheme is stable with global accuracy of ninth order. Various aspects of the scheme are discussed, including the resolution property with respect to the free dissipative parameter appearing in the scheme, the strict stability property for one-dimensional scalar linear advection equations and the issue at the stage of grid generation. Some two-dimensional problems on curvilinear grids are computed to show validity of the scheme.