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Volume 14, Issue 2
Multiderivative Combined Dissipative Compact Scheme Satisfying Geometric Conservation Law III: Characteristic-Wise Hybrid Method

Yi Jiang, Meiliang Mao, Xiaogang Deng & Huayong Liu

Adv. Appl. Math. Mech., 14 (2022), pp. 415-441.

Published online: 2022-01

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  • Abstract

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.

  • Keywords

Hybrid multiderivative combined dissipative compact scheme, high resolution power, discontinuities capturing, geometric conservation law, curvilinear mesh complex geometry.

  • AMS Subject Headings

76Fxx, 76Gxx

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-14-415, author = {Yi and Jiang and and 22058 and and Yi Jiang and Meiliang and Mao and and 22059 and and Meiliang Mao and Xiaogang and Deng and and 22060 and and Xiaogang Deng and Huayong and Liu and and 22061 and and Huayong Liu}, title = {Multiderivative Combined Dissipative Compact Scheme Satisfying Geometric Conservation Law III: Characteristic-Wise Hybrid Method}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {2}, pages = {415--441}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0257}, url = {http://global-sci.org/intro/article_detail/aamm/20204.html} }
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 -

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.

Yi Jiang, Meiliang Mao, Xiaogang Deng & Huayong Liu. (2022). Multiderivative Combined Dissipative Compact Scheme Satisfying Geometric Conservation Law III: Characteristic-Wise Hybrid Method. Advances in Applied Mathematics and Mechanics. 14 (2). 415-441. doi:10.4208/aamm.OA-2020-0257
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