Volume 22, Issue 5
A Novel Multi-Dimensional Limiter for High-Order Finite Volume Methods on Unstructured Grids

Yilang Liu, Weiwei Zhang & Chunna Li

Commun. Comput. Phys., 22 (2017), pp. 1385-1412.

Published online: 2017-11

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  • Abstract

This paper proposes a novel distance derivative weighted ENO (DDWENO) limiter based on fixed reconstruction stencil and applies it to the second- and high-order finite volume method on unstructured grids. We choose the standard deviation coefficients of the flow variables as the smooth indicators by using the k-exact reconstruction method, and obtain the limited derivatives of the flow variables by weighting all derivatives of each cell according to smoothness. Furthermore, an additional weighting coefficient related to distance is introduced to emphasize the contribution of the central cell in smooth regions. The developed limiter, combining the advantages of the slope limiters and WENO-type limiters, can achieve the similar effect of WENO schemes in the fixed stencil with high computational efficiency. The numerical cases demonstrate that the DDWENO limiter can preserve the numerical accuracy in smooth regions, and capture the shock waves clearly and steeply as well.

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@Article{CiCP-22-1385, author = {}, title = {A Novel Multi-Dimensional Limiter for High-Order Finite Volume Methods on Unstructured Grids}, journal = {Communications in Computational Physics}, year = {2017}, volume = {22}, number = {5}, pages = {1385--1412}, abstract = {

This paper proposes a novel distance derivative weighted ENO (DDWENO) limiter based on fixed reconstruction stencil and applies it to the second- and high-order finite volume method on unstructured grids. We choose the standard deviation coefficients of the flow variables as the smooth indicators by using the k-exact reconstruction method, and obtain the limited derivatives of the flow variables by weighting all derivatives of each cell according to smoothness. Furthermore, an additional weighting coefficient related to distance is introduced to emphasize the contribution of the central cell in smooth regions. The developed limiter, combining the advantages of the slope limiters and WENO-type limiters, can achieve the similar effect of WENO schemes in the fixed stencil with high computational efficiency. The numerical cases demonstrate that the DDWENO limiter can preserve the numerical accuracy in smooth regions, and capture the shock waves clearly and steeply as well.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0039}, url = {http://global-sci.org/intro/article_detail/cicp/10447.html} }
TY - JOUR T1 - A Novel Multi-Dimensional Limiter for High-Order Finite Volume Methods on Unstructured Grids JO - Communications in Computational Physics VL - 5 SP - 1385 EP - 1412 PY - 2017 DA - 2017/11 SN - 22 DO - http://doi.org/10.4208/cicp.OA-2017-0039 UR - https://global-sci.org/intro/article_detail/cicp/10447.html KW - AB -

This paper proposes a novel distance derivative weighted ENO (DDWENO) limiter based on fixed reconstruction stencil and applies it to the second- and high-order finite volume method on unstructured grids. We choose the standard deviation coefficients of the flow variables as the smooth indicators by using the k-exact reconstruction method, and obtain the limited derivatives of the flow variables by weighting all derivatives of each cell according to smoothness. Furthermore, an additional weighting coefficient related to distance is introduced to emphasize the contribution of the central cell in smooth regions. The developed limiter, combining the advantages of the slope limiters and WENO-type limiters, can achieve the similar effect of WENO schemes in the fixed stencil with high computational efficiency. The numerical cases demonstrate that the DDWENO limiter can preserve the numerical accuracy in smooth regions, and capture the shock waves clearly and steeply as well.

Yilang Liu, Weiwei Zhang & Chunna Li. (2020). A Novel Multi-Dimensional Limiter for High-Order Finite Volume Methods on Unstructured Grids. Communications in Computational Physics. 22 (5). 1385-1412. doi:10.4208/cicp.OA-2017-0039
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