A 2D well-balanced shallow flow model for unstructured grids with novel slope source term treatment |
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| Institution: | 1. Chair of Water Resources Management and Modeling of Hydrosystems, Department of Civil Engineering, Technische Universität Berlin, TIB 1-B14, Gustav-Meyer-Allee 25, 13355 Berlin, Germany;2. School of Civil Engineering & Geosciences, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK;1. DICATeA, University of Parma, v.le Parco Area delle Scienze 181/A, 43124 Parma, Italy;2. Department of Mathematics and Computer Science, University of Parma, v.le Parco Area delle Scienze 53/A, 43124 Parma, Italy;1. Department of Civil and Environmental Engineering and Architecture, University of Parma, Parco Area delle Scienze 181/A, 43124, Parma, Italy;2. Department of Mathematics and Computer Science, University of Parma, Parco Area delle Scienze 53/A, 43124, Parma, Italy;1. Dpto. Matemáticas, Edificio Einstein - Universidad de Córdoba, Campus de Rabanales, 14014 Córdoba, Spain;2. Université Paris-Est, Laboratoire d''Analyse et de Mathématiques Appliquées (UMR 8050), CNRS, UPEM, UPEC, F-77454, Marne-la-Vallée, France;3. Dpto. Matemática Aplicada I, ETS Arquitectura - Universidad de Sevilla, Avda. Reina Mercedes S/N, 41012 Sevilla, Spain;4. Institut de Physique du Globe de Paris, Seismology team, University Paris-Diderot, Sorbonne Paris Cité, 75238, Paris, France;5. ANGE team, CEREMA, INRIA, Lab. J. Louis Lions, 75252, Paris, France;1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China;2. Hydrology Bureau, Yangtze River Water Resource Commission, Wuhan 430010, China;3. Yangtze River Scientific Research Institute, Wuhan 430015, China;1. Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, Université de Nantes, 2 rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France;2. Centre of Mathematics, Minho University, Campus de Gualtar - 4710-057 Braga, Portugal;3. École Centrale de Nantes, 1 rue de La Noë, BP 92101 44321 Nantes Cedex 3, France |
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| Abstract: | Within the framework of the Godunov-type cell-centered finite volume (CCFV) scheme, this paper proposes a 2D well-balanced shallow water model for unstructured grids. In this model, the face-based van Albada limiting scheme is employed in conjunction with a directional correction to reconstruct second order spatial values at the midpoint of the considered face. The Harten, Lax and van Leer approximate Riemann solver with the Contact wave restored (HLLC) is applied to compute the fluxes of mass and momentum, while the splitting implicit method is utilized to solve the friction source terms. The novel aspects of the model include the new limited directional correction with which the new local extrema caused by the unlimited correction are prevented efficiently, the simplified non-negative water depth reconstruction used to get rid of numerical instabilities and in turn to preserve mass conservation at wet–dry interfaces and the novel slope source term treatment which suits complex unstructured grids well by transforming the slope source of a cell into fluxes at its faces. This model is able to preserve the C-property and mass conservation, to achieve good convergence to steady state, to capture discontinuous flows and to handle complex flows involving wetting and drying over uneven beds on unstructured grids with poor connectivity in an accurate, efficient and robust way. These capabilities are verified against analytical solutions, numerical results of alternative models and experimental and field data. |
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