Volume 10, Issue 3
A New High-Order Conservative Patched Grid Strategy Based on Collapsed Edge

Yidao Dong, Xiaogang Deng, Yaming Chen, Dan Xu & Guangxue Wang

Adv. Appl. Math. Mech., 10 (2018), pp. 611-633.

Published online: 2018-10

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  • Abstract

A new high-order conservative patched grid strategy is developed with the concept of collapsed edge. Different from the traditional patched grid algorithm, where the patched interface is a line in two-dimensional space, the new strategy employs a transition region, where a collapsed edge is located within to form four point matched blocks. The introduction of the collapsed edge ensures that the grid generation of neighbouring blocks connected by the transition region is independent. The biggest advantage of this new strategy is that conservation is satisfied automatically since the numerical flux at the collapsed edge is zero. Furthermore, when applied in the framework of high-order finite difference methods based on the coordinate transformation, no essential modifications are needed. Some typical numerical examples are simulated with the new patched grid strategy combined with the fifth-order Weighted Compact Nonlinear Schemes (WCNS) to verify the capability of this new method.

  • Keywords

Patched grid, high-order, conservative, collapsed-edge, WCNS.

  • AMS Subject Headings

65N06, 65N22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-611, author = {}, title = {A New High-Order Conservative Patched Grid Strategy Based on Collapsed Edge}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {3}, pages = {611--633}, abstract = {A new high-order conservative patched grid strategy is developed with the concept of collapsed edge. Different from the traditional patched grid algorithm, where the patched interface is a line in two-dimensional space, the new strategy employs a transition region, where a collapsed edge is located within to form four point matched blocks. The introduction of the collapsed edge ensures that the grid generation of neighbouring blocks connected by the transition region is independent. The biggest advantage of this new strategy is that conservation is satisfied automatically since the numerical flux at the collapsed edge is zero. Furthermore, when applied in the framework of high-order finite difference methods based on the coordinate transformation, no essential modifications are needed. Some typical numerical examples are simulated with the new patched grid strategy combined with the fifth-order Weighted Compact Nonlinear Schemes (WCNS) to verify the capability of this new method.}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2017-0163}, url = {http://global-sci.org/intro/article_detail/aamm/12227.html} }
TY - JOUR T1 - A New High-Order Conservative Patched Grid Strategy Based on Collapsed Edge JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 611 EP - 633 PY - 2018 DA - 2018/10 SN - 10 DO - http://dor.org/10.4208/aamm.OA-2017-0163 UR - https://global-sci.org/intro/aamm/12227.html KW - Patched grid, high-order, conservative, collapsed-edge, WCNS. AB - A new high-order conservative patched grid strategy is developed with the concept of collapsed edge. Different from the traditional patched grid algorithm, where the patched interface is a line in two-dimensional space, the new strategy employs a transition region, where a collapsed edge is located within to form four point matched blocks. The introduction of the collapsed edge ensures that the grid generation of neighbouring blocks connected by the transition region is independent. The biggest advantage of this new strategy is that conservation is satisfied automatically since the numerical flux at the collapsed edge is zero. Furthermore, when applied in the framework of high-order finite difference methods based on the coordinate transformation, no essential modifications are needed. Some typical numerical examples are simulated with the new patched grid strategy combined with the fifth-order Weighted Compact Nonlinear Schemes (WCNS) to verify the capability of this new method.
Yidao Dong, Xiaogang Deng, Yaming Chen, Dan Xu & Guangxue Wang. (2020). A New High-Order Conservative Patched Grid Strategy Based on Collapsed Edge. Advances in Applied Mathematics and Mechanics. 10 (3). 611-633. doi:10.4208/aamm.OA-2017-0163
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