Developing Hybrid cell-edge and cell-node Dissipative Compact Scheme for Complex Geometry Flows

Developing high resolution finite difference scheme and enabling the use of this scheme on complex geometry are the aims of this study.High resolution has been achieved by Dissipative Compact Schemes(DCS),however,according to the recent research,applications of DCS on complex geometry may have serious problem for that the Geometric Conservation Law(GCL)is not satisfied,and this may cause numerical instability.To cope with this problem,a new scheme named Hybrid cell-edge and cell-node Dissipative Compact Scheme(HDCS)has been formulated.The formulation of the HDCS contains two steps.First,a new central compact scheme is formulated for the purpose of conveniently fulfilling the GCL,and then dissipation is added on the central scheme by high-order dissipative interpolation of cell-edge variables.The solutions of Euler and Navier-Stokes equations show that the HDCS can be applied successfully on complex geometry,while the DCS may suffer numerical instabilities.Moreover,high resolution of the HDCS may be observed in the test of scattering of acoustic waves by multiple cylinders.

Multiderivative Combined Dissipative Compact Scheme Satisfying Geometric Conservation Law III: Characteristic-Wise Hybrid Method

Based on newly developed weight-based smoothness detectors and non-linear interpolations designed to capture discontinuities for the multiderivative com-bined dissipative compact scheme(MDCS),hybrid linear and nonlinear interpolations are proposed to form hybrid MDCS.These detectors are derived from the weights used for the nonlinear interpolations and can provide suitable switches between the linear and the nonlinear schemes to realize the characteristics for the hybrid MDCS of capturing discontinuities and maintaining high resolution in the region without large discontinuities.To save computational cost,the nonlinear scheme with characteris-tic decomposition is only applied in the detected discontinuities region by specially designed hybrid strategy.Typical tests show that the hybrid MDCS is capable of cap-turing discontinuities and maintaining high resolution power for the smooth region at the same time.With the satisfaction of the geometric conservative law(GCL),the MDCS is further applied on curvilinear mesh to present its promising capability of handling pragmatic simulations.