Abstract We derive in this paper a time stable seventh-order dissipative compact finite difference scheme with simultaneous approximation terms (SATs) for solving two-dimensional Euler equations. To stabilize the scheme, the choice of penalty coefficients for SATs is studied in detail. It is demonstrated that the derived scheme is quite suitable for multi-block problems with different spacial steps. The implementation of the scheme for the case with curvilinear grids is also discussed. Numerical experiments show that the proposed scheme is stable and achieves the design seventh-order convergence rate.
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11601517) and the Basic Research Foundation of National University of Defense Technology (Grant No. ZDYYJ-CYJ20140101).
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