Multiderivative Combined Dissipative Compact Scheme Satisfying Geometric Conservation Law III: Characteristic-Wise Hybrid Method (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 interpolationsare proposed to form hybrid MDCS. These detectors are derived from the weightsused for the nonlinear interpolations and can provide suitable switches between thelinear and the nonlinear schemes to realize the characteristics for the hybrid MDCS ofcapturing discontinuities and maintaining high resolution in the region without largediscontinuities. To save computational cost, the nonlinear scheme with characteristic decomposition is only applied in the detected discontinuities region by speciallydesigned hybrid strategy. Typical tests show that the hybrid MDCS is capable of capturing discontinuities and maintaining high resolution power for the smooth regionat the same time. With the satisfaction of the geometric conservative law (GCL), theMDCS is further applied on curvilinear mesh to present its promising capability ofhandling pragmatic simulations.