A family of hybrid cell-edge and cell-node dissipative compact schemes satisfying geometric conservation law

Growing evidences show that the Symmetrical Conservative Metric Method (SCMM) is essential in preserving freestream conservation and orders of accuracy for high-order finite difference schemes to simulate flows with complex geometries. In this paper, a new family of Hybrid cell-edge and cell-node Dissipative Compact Schemes (HDCSs) has been developed for geometry-complex flows by fulfilling the SCMM as well as by introducing dissipation according to the concept adopted in the construction of the high-order Dissipative Compact Schemes (DCSs). The resolution and dissipation properties of HDCSs are investigated by the Fourier analysis, and the stability property of HDCSs is also investigated by asymptotic stability analysis and amplification factor analysis. HDCSs are validated by computing several benchmark test cases. The vortex convection test case demonstrates that the orders of accuracy of the HDCSs are preserved unless the GCL is satisfied. Although high resolution of HDCSs is observed in the test of acoustic wave scattering of multiple cylinders, the solutions can be contaminated if the GCL is not satisfied. Moreover, the numerical solutions of flow past a high lift trapezoidal wing demonstrate the promising ability of the newly developed HDCSs in solving complex flow problems.