Volume 9, Issue 1
An $h$-Adaptive RKDG Method for Two-Dimensional Detonation Wave Simulations

Hongqiang Zhu & Zhen Gao

East Asian J. Appl. Math., 9 (2019), pp. 165-184.

Published online: 2019-01

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  • Abstract

An $h$-adaptive Runge-Kutta discontinuous Galerkin (RKDG) method with a positivity-preserving technique to simulate classical two-dimensional detonation waves is developed. The KXRCF troubled-cell indicator is used to detect the troubled cells with possible discontinuities or high gradients. At each time-level, an adaptive mesh is generated by refining troubled cells and coarsening others. In order to avoid the situations where detonation front moves too fast and there are not enough cells to describe detonation front before it leaves, a recursive multi-level mesh refinement technique is designed. The numerical results show that for smooth solutions, this $h$-adaptive method does not degrade the optimal convergence order of the nonadaptive method and outperforms it in terms of computational storage for shocked flows.

  • Keywords

Runge-Kutta discontinuous Galerkin method troubled-cell indicator h-adaptive method detonation wave.

  • AMS Subject Headings

65M60 65M99 35L65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-9-165, author = {}, title = {An $h$-Adaptive RKDG Method for Two-Dimensional Detonation Wave Simulations}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {1}, pages = {165--184}, abstract = {

An $h$-adaptive Runge-Kutta discontinuous Galerkin (RKDG) method with a positivity-preserving technique to simulate classical two-dimensional detonation waves is developed. The KXRCF troubled-cell indicator is used to detect the troubled cells with possible discontinuities or high gradients. At each time-level, an adaptive mesh is generated by refining troubled cells and coarsening others. In order to avoid the situations where detonation front moves too fast and there are not enough cells to describe detonation front before it leaves, a recursive multi-level mesh refinement technique is designed. The numerical results show that for smooth solutions, this $h$-adaptive method does not degrade the optimal convergence order of the nonadaptive method and outperforms it in terms of computational storage for shocked flows.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.100318.010718}, url = {http://global-sci.org/intro/article_detail/eajam/12940.html} }
TY - JOUR T1 - An $h$-Adaptive RKDG Method for Two-Dimensional Detonation Wave Simulations JO - East Asian Journal on Applied Mathematics VL - 1 SP - 165 EP - 184 PY - 2019 DA - 2019/01 SN - 9 DO - http://dor.org/10.4208/eajam.100318.010718 UR - https://global-sci.org/intro/article_detail/eajam/12940.html KW - Runge-Kutta discontinuous Galerkin method KW - troubled-cell indicator KW - h-adaptive method KW - detonation wave. AB -

An $h$-adaptive Runge-Kutta discontinuous Galerkin (RKDG) method with a positivity-preserving technique to simulate classical two-dimensional detonation waves is developed. The KXRCF troubled-cell indicator is used to detect the troubled cells with possible discontinuities or high gradients. At each time-level, an adaptive mesh is generated by refining troubled cells and coarsening others. In order to avoid the situations where detonation front moves too fast and there are not enough cells to describe detonation front before it leaves, a recursive multi-level mesh refinement technique is designed. The numerical results show that for smooth solutions, this $h$-adaptive method does not degrade the optimal convergence order of the nonadaptive method and outperforms it in terms of computational storage for shocked flows.

Hongqiang Zhu & Zhen Gao. (2020). An $h$-Adaptive RKDG Method for Two-Dimensional Detonation Wave Simulations. East Asian Journal on Applied Mathematics. 9 (1). 165-184. doi:10.4208/eajam.100318.010718
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