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ARS Home » Southeast Area » Oxford, Mississippi » National Sedimentation Laboratory » Watershed Physical Processes Research » Research » Publications at this Location » Publication #319925

Title: Edge gradients evaluation for 2D hybrid finite volume method model

item ZHANG, YAOXIN - University Of Mississippi
item JIA, YAFEI - University Of Mississippi
item ZHU, TINGTING - University Of Mississippi

Submitted to: Journal of Hydraulic Research IAHR
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 3/9/2015
Publication Date: 4/20/2015
Citation: Zhang, Y., Jia, Y., Zhu, T. 2015. Edge gradients evaluation for 2D hybrid finite volume method model. Journal of Hydraulic Research IAHR. pp 1-17. DOI:10.1080/00221686.2015.1029017.

Interpretive Summary: This paper presents a two-dimensional depth-integrated hydrodynamic flow model using the Finite Volume Method (FVM) on a hybrid unstructured mesh system with a collocated variable arrangement. A new evaluation method for computing the gradients at the cell edges, derived based on the second-order Taylor series expansion, is proposed to improve the solution due to mesh irregularity and non-uniformity. In this method, no interpolation for variables at cell vertices is necessary. The cross-edge flux is evaluated by using the momentum interpolation. The convergence, robustness and accuracy of this model based on the new evaluation method of edge gradients have been demonstrated by several numerical convergence tests and applications to natural rivers with complex geometries and instream structures.

Technical Abstract: In this study, a two-dimensional depth-integrated hydrodynamic model was developed using FVM on a hybrid unstructured collocated mesh system. To alleviate the negative effects of mesh irregularity and non-uniformity, a conservative evaluation method for edge gradients based on the second-order Taylor’s series expansion was proposed, which can effectively reduce non-physical oscillation due to the non-monotonic, inaccurate, or non-conservative interpolations for the cell vertices. This method also considers additional corrections due to the effect of mesh irregularity that the location of an edge centre and the intercept point of centroid connection line differ.