(untitled) (Advances in Applied Mathematics and Mechanics, 2022)
Based on newly developed weight-based smoothness detectors and nonlinear interpolations designed to capture discontinuities for the multiderivative combined 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 characteristic decomposition is only applied in the detected discontinuities region by specially designed hybrid strategy. Typical tests show that the hybrid MDCS is capable of capturing 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.