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Volume 12, Issue 4
A Finite Volume Upwind-Biased Centred Scheme for Hyperbolic Systems of Conservation Laws: Application to Shallow Water Equations

Guglielmo Stecca, Annunziato Siviglia & Eleuterio F. Toro

DOI: 10.4208/cicp.180511.071211a

Commun. Comput. Phys., 12 (2012), pp. 1183-1214.

Published online: 2012-12

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  • Abstract

We construct a new first-order central-upwind numerical method for solving systems of hyperbolic equations in conservative form. It applies in multidimensional structured and unstructured meshes. The proposed method is an extension of the UFORCE method developed by Stecca, Siviglia and Toro [25], in which the upwind bias for the modification of the staggered mesh is evaluated taking into account the smallest and largest wave of the entire Riemann fan. The proposed first-order method is shown to be identical to the Godunov upwind method in applications to a 2×2 linear hyperbolic system. The method is then extended to non-linear systems and its performance is assessed by solving the two-dimensional inviscid shallow water equations. Extension to second-order accuracy is carried out using an ADER-WENO approach in the finite volume framework on unstructured meshes. Finally, numerical comparison with current competing numerical methods enables us to identify the salient features of the proposed method.

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@Article{CiCP-12-1183, author = {Guglielmo Stecca, Annunziato Siviglia and Eleuterio F. Toro}, title = {A Finite Volume Upwind-Biased Centred Scheme for Hyperbolic Systems of Conservation Laws: Application to Shallow Water Equations}, journal = {Communications in Computational Physics}, year = {2012}, volume = {12}, number = {4}, pages = {1183--1214}, abstract = {

We construct a new first-order central-upwind numerical method for solving systems of hyperbolic equations in conservative form. It applies in multidimensional structured and unstructured meshes. The proposed method is an extension of the UFORCE method developed by Stecca, Siviglia and Toro [25], in which the upwind bias for the modification of the staggered mesh is evaluated taking into account the smallest and largest wave of the entire Riemann fan. The proposed first-order method is shown to be identical to the Godunov upwind method in applications to a 2×2 linear hyperbolic system. The method is then extended to non-linear systems and its performance is assessed by solving the two-dimensional inviscid shallow water equations. Extension to second-order accuracy is carried out using an ADER-WENO approach in the finite volume framework on unstructured meshes. Finally, numerical comparison with current competing numerical methods enables us to identify the salient features of the proposed method.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.180511.071211a}, url = {http://global-sci.org/intro/article_detail/cicp/7331.html} }
TY - JOUR T1 - A Finite Volume Upwind-Biased Centred Scheme for Hyperbolic Systems of Conservation Laws: Application to Shallow Water Equations AU - Guglielmo Stecca, Annunziato Siviglia & Eleuterio F. Toro JO - Communications in Computational Physics VL - 4 SP - 1183 EP - 1214 PY - 2012 DA - 2012/12 SN - 12 DO - http://doi.org/10.4208/cicp.180511.071211a UR - https://global-sci.org/intro/article_detail/cicp/7331.html KW - AB -

We construct a new first-order central-upwind numerical method for solving systems of hyperbolic equations in conservative form. It applies in multidimensional structured and unstructured meshes. The proposed method is an extension of the UFORCE method developed by Stecca, Siviglia and Toro [25], in which the upwind bias for the modification of the staggered mesh is evaluated taking into account the smallest and largest wave of the entire Riemann fan. The proposed first-order method is shown to be identical to the Godunov upwind method in applications to a 2×2 linear hyperbolic system. The method is then extended to non-linear systems and its performance is assessed by solving the two-dimensional inviscid shallow water equations. Extension to second-order accuracy is carried out using an ADER-WENO approach in the finite volume framework on unstructured meshes. Finally, numerical comparison with current competing numerical methods enables us to identify the salient features of the proposed method.

Guglielmo Stecca, Annunziato Siviglia and Eleuterio F. Toro. (2012). A Finite Volume Upwind-Biased Centred Scheme for Hyperbolic Systems of Conservation Laws: Application to Shallow Water Equations. Communications in Computational Physics. 12 (4). 1183-1214. doi:10.4208/cicp.180511.071211a
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