Volume 9, Issue 3
On the Order of Accuracy and Numerical Performance of Two Classes of Finite Volume WENO Schemes

Rui Zhang, Mengping Zhang & Chi-Wang Shu

Commun. Comput. Phys., 9 (2011), pp. 807-827.

Published online: 2011-03

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  • Abstract

In this paper we consider two commonly used classes of finite volume weighted essentially non-oscillatory (WENO) schemes in two dimensional Cartesian meshes. We compare them in terms of accuracy, performance for smooth and shocked solutions, and efficiency in CPU timing. For linear systems both schemes are high order accurate, however for nonlinear systems, analysis and numerical simulation results verify that one of them (Class A) is only second order accurate, while the other (Class B) is high order accurate. The WENO scheme in Class A is easier to implement and costs less than that in Class B. Numerical experiments indicate that the resolution for shocked problems is often comparable for schemes in both classes for the same building blocks and meshes, despite of the difference in their formal order of accuracy. The results in this paper may give some guidance in the application of high order finite volume schemes for simulating shocked flows.

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@Article{CiCP-9-807, author = {}, title = {On the Order of Accuracy and Numerical Performance of Two Classes of Finite Volume WENO Schemes}, journal = {Communications in Computational Physics}, year = {2011}, volume = {9}, number = {3}, pages = {807--827}, abstract = {

In this paper we consider two commonly used classes of finite volume weighted essentially non-oscillatory (WENO) schemes in two dimensional Cartesian meshes. We compare them in terms of accuracy, performance for smooth and shocked solutions, and efficiency in CPU timing. For linear systems both schemes are high order accurate, however for nonlinear systems, analysis and numerical simulation results verify that one of them (Class A) is only second order accurate, while the other (Class B) is high order accurate. The WENO scheme in Class A is easier to implement and costs less than that in Class B. Numerical experiments indicate that the resolution for shocked problems is often comparable for schemes in both classes for the same building blocks and meshes, despite of the difference in their formal order of accuracy. The results in this paper may give some guidance in the application of high order finite volume schemes for simulating shocked flows.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.291109.080410s}, url = {http://global-sci.org/intro/article_detail/cicp/7522.html} }
TY - JOUR T1 - On the Order of Accuracy and Numerical Performance of Two Classes of Finite Volume WENO Schemes JO - Communications in Computational Physics VL - 3 SP - 807 EP - 827 PY - 2011 DA - 2011/03 SN - 9 DO - http://doi.org/10.4208/cicp.291109.080410s UR - https://global-sci.org/intro/article_detail/cicp/7522.html KW - AB -

In this paper we consider two commonly used classes of finite volume weighted essentially non-oscillatory (WENO) schemes in two dimensional Cartesian meshes. We compare them in terms of accuracy, performance for smooth and shocked solutions, and efficiency in CPU timing. For linear systems both schemes are high order accurate, however for nonlinear systems, analysis and numerical simulation results verify that one of them (Class A) is only second order accurate, while the other (Class B) is high order accurate. The WENO scheme in Class A is easier to implement and costs less than that in Class B. Numerical experiments indicate that the resolution for shocked problems is often comparable for schemes in both classes for the same building blocks and meshes, despite of the difference in their formal order of accuracy. The results in this paper may give some guidance in the application of high order finite volume schemes for simulating shocked flows.

Rui Zhang, Mengping Zhang & Chi-Wang Shu. (2020). On the Order of Accuracy and Numerical Performance of Two Classes of Finite Volume WENO Schemes. Communications in Computational Physics. 9 (3). 807-827. doi:10.4208/cicp.291109.080410s
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