TY - JOUR
T1 - Multiderivative Combined Dissipative Compact Scheme Satisfying Geometric Conservation Law III: Characteristic-Wise Hybrid Method
AU - Jiang , Yi
AU - Mao , Meiliang
AU - Deng , Xiaogang
AU - Liu , Huayong
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 415
EP - 441
PY - 2022
DA - 2022/01
SN - 14
DO - http://doi.org/10.4208/aamm.OA-2020-0257
UR - https://global-sci.org/intro/article_detail/aamm/20204.html
KW - Hybrid multiderivative combined dissipative compact scheme, high resolution power, discontinuities capturing, geometric conservation law, curvilinear mesh complex geometry.
AB - <p style="text-align: justify;">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.</p>