Volume 28, Issue 4
A High-Order Cell-Centered Discontinuous Galerkin Multi-Material Arbitrary Lagrangian-Eulerian Method

Fang Qing, Xijun Yu, Zupeng Jia, Meilan QiuXiaolong Zhao

Commun. Comput. Phys., 28 (2020), pp. 1464-1501.

Published online: 2020-08

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  • Abstract

In this paper, a high-order cell-centered discontinuous Galerkin (DG) multi-material arbitrary Lagrangian-Eulerian (MMALE) method is developed for compressible fluid dynamics. The MMALE method utilizes moment-of-fluid (MOF) interface reconstruction technology to simulate multi-materials of immiscible fluids. It is an explicit time-marching Lagrangian plus remap type. In the Lagrangian phase, an updated high-order discontinuous Galerkin Lagrangian method is applied for the discretization of hydrodynamic equations, and Tipton's pressure relaxation closure model is used in the mixed cells. A robust moment-of-fluid interface reconstruction algorithm is used to provide the information of the material interfaces for remapping. In the rezoning phase, Knupp's algorithm is used for mesh smoothing. For the remapping phase, a high-order accurate remapping method of the cell-intersection-based type is proposed. It can be divided into four stages: polynomial reconstruction, polygon intersection, integration, and detection of problematic cells and limiting. Polygon intersection is based on the "clipping and projecting" algorithm, and detection of problematic cells depends on a troubled cell marker, and a posteriori multi-dimensional optimal order detection (MOOD) limiting strategy is used for limiting. Numerical tests are given to demonstrate the robustness and accuracy of our method.

  • Keywords

Multi-material ALE, discontinuous Galerkin, moment-of-fluid, Tipton's pressure relaxation closure model, a posteriori MOOD limiting strategy.

  • AMS Subject Headings

65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-28-1464, author = {Qing , Fang and Yu , Xijun and Jia , Zupeng and Qiu , Meilan and Zhao , Xiaolong}, title = {A High-Order Cell-Centered Discontinuous Galerkin Multi-Material Arbitrary Lagrangian-Eulerian Method}, journal = {Communications in Computational Physics}, year = {2020}, volume = {28}, number = {4}, pages = {1464--1501}, abstract = {

In this paper, a high-order cell-centered discontinuous Galerkin (DG) multi-material arbitrary Lagrangian-Eulerian (MMALE) method is developed for compressible fluid dynamics. The MMALE method utilizes moment-of-fluid (MOF) interface reconstruction technology to simulate multi-materials of immiscible fluids. It is an explicit time-marching Lagrangian plus remap type. In the Lagrangian phase, an updated high-order discontinuous Galerkin Lagrangian method is applied for the discretization of hydrodynamic equations, and Tipton's pressure relaxation closure model is used in the mixed cells. A robust moment-of-fluid interface reconstruction algorithm is used to provide the information of the material interfaces for remapping. In the rezoning phase, Knupp's algorithm is used for mesh smoothing. For the remapping phase, a high-order accurate remapping method of the cell-intersection-based type is proposed. It can be divided into four stages: polynomial reconstruction, polygon intersection, integration, and detection of problematic cells and limiting. Polygon intersection is based on the "clipping and projecting" algorithm, and detection of problematic cells depends on a troubled cell marker, and a posteriori multi-dimensional optimal order detection (MOOD) limiting strategy is used for limiting. Numerical tests are given to demonstrate the robustness and accuracy of our method.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0207}, url = {http://global-sci.org/intro/article_detail/cicp/18108.html} }
TY - JOUR T1 - A High-Order Cell-Centered Discontinuous Galerkin Multi-Material Arbitrary Lagrangian-Eulerian Method AU - Qing , Fang AU - Yu , Xijun AU - Jia , Zupeng AU - Qiu , Meilan AU - Zhao , Xiaolong JO - Communications in Computational Physics VL - 4 SP - 1464 EP - 1501 PY - 2020 DA - 2020/08 SN - 28 DO - http://doi.org/10.4208/cicp.OA-2019-0207 UR - https://global-sci.org/intro/article_detail/cicp/18108.html KW - Multi-material ALE, discontinuous Galerkin, moment-of-fluid, Tipton's pressure relaxation closure model, a posteriori MOOD limiting strategy. AB -

In this paper, a high-order cell-centered discontinuous Galerkin (DG) multi-material arbitrary Lagrangian-Eulerian (MMALE) method is developed for compressible fluid dynamics. The MMALE method utilizes moment-of-fluid (MOF) interface reconstruction technology to simulate multi-materials of immiscible fluids. It is an explicit time-marching Lagrangian plus remap type. In the Lagrangian phase, an updated high-order discontinuous Galerkin Lagrangian method is applied for the discretization of hydrodynamic equations, and Tipton's pressure relaxation closure model is used in the mixed cells. A robust moment-of-fluid interface reconstruction algorithm is used to provide the information of the material interfaces for remapping. In the rezoning phase, Knupp's algorithm is used for mesh smoothing. For the remapping phase, a high-order accurate remapping method of the cell-intersection-based type is proposed. It can be divided into four stages: polynomial reconstruction, polygon intersection, integration, and detection of problematic cells and limiting. Polygon intersection is based on the "clipping and projecting" algorithm, and detection of problematic cells depends on a troubled cell marker, and a posteriori multi-dimensional optimal order detection (MOOD) limiting strategy is used for limiting. Numerical tests are given to demonstrate the robustness and accuracy of our method.

Fang Qing, Xijun Yu, Zupeng Jia, Meilan Qiu & Xiaolong Zhao. (2020). A High-Order Cell-Centered Discontinuous Galerkin Multi-Material Arbitrary Lagrangian-Eulerian Method. Communications in Computational Physics. 28 (4). 1464-1501. doi:10.4208/cicp.OA-2019-0207
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