Parallel adaptive mesh refinement method based on WENO finite difference scheme for the simulation of multi-dimensional detonation

Cheng Wang Beijing Institute of Technology XinZhuang Dong Beijing Institute of Technology Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1610.25025

Journal of Computational Physics, 298, 161-175, 2015
For numerical simulation of detonation, computational cost using uniform meshes is large due to the vast separation in both time and space scales. Adaptive mesh refinement (AMR) is advantageous for problems with vastly different scales. This paper aims to propose an AMR method with high order accuracy for numerical investigation of multi-dimensional detonation. A well-designed AMR method based on finite difference weighted essentially non-oscillatory (WENO) scheme, named as AMR\&WENO is proposed. A new cell-based data structure is used to organize the adaptive meshes. The new data structure makes it possible for cells to communicate with each other quickly and easily. In order to develop an AMR method with high order accuracy, high order prolongations in both space and time are utilized in the data prolongation procedure. Based on the message passing interface (MPI) platform, we have developed a workload balancing parallel AMR\&WENO code using the Hilbert space-filling curve algorithm. Our numerical experiments with detonation simulations indicate that the AMR\&WENO is accurate and have a high resolution. Moreover, we evaluate and compare the performance between the uniform mesh WENO scheme and the parallel AMR\&WENO method. The comparison results provide us further insight into the high performance of the parallel AMR\&WENO method.
AMR, WENO, high order accuracy, unstable detonations, detonation structure
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@inproceedings{cheng2015parallel,
  title={Parallel adaptive mesh refinement method based on WENO finite difference scheme for the simulation of multi-dimensional detonation},
  author={Cheng Wang, XinZhuang Dong, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161011120302587487139},
  booktitle={Journal of Computational Physics},
  volume={298},
  pages={161-175},
  year={2015},
}
Cheng Wang, XinZhuang Dong, and Chi-Wang Shu. Parallel adaptive mesh refinement method based on WENO finite difference scheme for the simulation of multi-dimensional detonation. 2015. Vol. 298. In Journal of Computational Physics. pp.161-175. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161011120302587487139.
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