A Novel Boundary Treatment Method for Global Seventh-Order Dissipative Compact Finite-Difference Scheme

摘要

Using a global conservative boundary treatment method, we construct in this paper a global seventh-order dissipative compact finite-difference scheme for conservation laws. While uniform solution points are used in the computational space for traditional algorithms, the solution points near boundaries are not uniformly distributed here any more. Instead, they are determined by both the global conservation property of the scheme and the required order of accuracy of boundary closures. From the comparison of the eigenvalue distributions of the coefficient matrices of the new algorithm with the traditional one, we see that the new boundary treatment method greatly improves the asymptotic stability of the algorithm. Linear advection equations in one and two dimensions and also an isentropy compressible flow through a channel with a smooth bump are used to show the designed order of accuracy of the scheme.