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Volume 31, Issue 2
Mesh Adaptation for Curing the Pathological Behaviors of an Upwind Scheme

Yifan Xia, Jianjing Zheng, Jianfeng Zou, Jifa Zhang, Gaofeng Wang & Yao Zheng

DOI: 10.4208/cicp.OA-2021-0131

Commun. Comput. Phys., 31 (2022), pp. 626-644.

Published online: 2022-01

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  • Abstract

In present paper, mesh adaptation is applied for curing the pathological behaviors of the enhanced time-accurate upwind scheme (Loh & Jorgenson, AIAAJ 2016). In the original ETAU (enhanced time-accurate upwind) scheme, a multi-dimensional dissipation model is required to cure the pathological behaviors. The multi-dimensional dissipation model will increase the global dissipation level reducing numerical resolution. In present work, the metric-based mesh adaptation strategy provides an alternative way to cure the pathological behaviors of the shock capturing. The Hessian matrix of flow variables is applied to construct the metric, which represents the curvature of the physical solution. The adapting operation can well refine the anisotropic meshes at the location with large gradients. The numerical results show that the adaptation of mesh provides a possible way to cure the pathological behaviors of upwind schemes.

  • Keywords

Metric tensor, mesh adaptation, finite volume scheme, unstructured grid.

  • AMS Subject Headings

65M08, 65M12, 65M55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-31-626, author = {Xia , YifanZheng , JianjingZou , JianfengZhang , JifaWang , Gaofeng and Zheng , Yao}, title = {Mesh Adaptation for Curing the Pathological Behaviors of an Upwind Scheme}, journal = {Communications in Computational Physics}, year = {2022}, volume = {31}, number = {2}, pages = {626--644}, abstract = {

In present paper, mesh adaptation is applied for curing the pathological behaviors of the enhanced time-accurate upwind scheme (Loh & Jorgenson, AIAAJ 2016). In the original ETAU (enhanced time-accurate upwind) scheme, a multi-dimensional dissipation model is required to cure the pathological behaviors. The multi-dimensional dissipation model will increase the global dissipation level reducing numerical resolution. In present work, the metric-based mesh adaptation strategy provides an alternative way to cure the pathological behaviors of the shock capturing. The Hessian matrix of flow variables is applied to construct the metric, which represents the curvature of the physical solution. The adapting operation can well refine the anisotropic meshes at the location with large gradients. The numerical results show that the adaptation of mesh provides a possible way to cure the pathological behaviors of upwind schemes.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0131}, url = {http://global-sci.org/intro/article_detail/cicp/20217.html} }
TY - JOUR T1 - Mesh Adaptation for Curing the Pathological Behaviors of an Upwind Scheme AU - Xia , Yifan AU - Zheng , Jianjing AU - Zou , Jianfeng AU - Zhang , Jifa AU - Wang , Gaofeng AU - Zheng , Yao JO - Communications in Computational Physics VL - 2 SP - 626 EP - 644 PY - 2022 DA - 2022/01 SN - 31 DO - http://doi.org/10.4208/cicp.OA-2021-0131 UR - https://global-sci.org/intro/article_detail/cicp/20217.html KW - Metric tensor, mesh adaptation, finite volume scheme, unstructured grid. AB -

In present paper, mesh adaptation is applied for curing the pathological behaviors of the enhanced time-accurate upwind scheme (Loh & Jorgenson, AIAAJ 2016). In the original ETAU (enhanced time-accurate upwind) scheme, a multi-dimensional dissipation model is required to cure the pathological behaviors. The multi-dimensional dissipation model will increase the global dissipation level reducing numerical resolution. In present work, the metric-based mesh adaptation strategy provides an alternative way to cure the pathological behaviors of the shock capturing. The Hessian matrix of flow variables is applied to construct the metric, which represents the curvature of the physical solution. The adapting operation can well refine the anisotropic meshes at the location with large gradients. The numerical results show that the adaptation of mesh provides a possible way to cure the pathological behaviors of upwind schemes.

Xia , YifanZheng , JianjingZou , JianfengZhang , JifaWang , Gaofeng and Zheng , Yao. (2022). Mesh Adaptation for Curing the Pathological Behaviors of an Upwind Scheme. Communications in Computational Physics. 31 (2). 626-644. doi:10.4208/cicp.OA-2021-0131
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