Unstructured Grid Finite-Volume Algorithm for Shallow-Water Flow and Scalar Transport with Wetting and Drying
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- 1 April 2006
- journal article
- Published by American Society of Civil Engineers (ASCE) in Journal of Hydraulic Engineering
- Vol. 132 (4), 371-384
- https://doi.org/10.1061/(asce)0733-9429(2006)132:4(371)
Abstract
A high-resolution, unstructured grid, finite-volume algorithm is developed for unsteady, two-dimensional, shallow-water flow and scalar transport over arbitrary topography with wetting and drying. The algorithm uses a grid of triangular cells to facilitate grid generation and localized refinement when modeling natural waterways. The algorithm uses Roe’s approximate Riemann solver to compute fluxes, a multidimensional limiter for second-order spatial accuracy, and predictor–corrector time stepping for second-order temporal accuracy. The novel aspect of the algorithm is a robust and efficient procedure to consistently track fluid volume and the free surface elevation in partially submerged cells. This leads to perfect conservation of both fluid and dissolved mass, preservation of stationarity, and near elimination of artificial concentration and dilution of scalars at stationary or moving wet/dry interfaces. Multi-dimensional slope limiters, variable reconstruction, and flux evaluation schemes are optimized in the algorithm on the basis of accuracy per computational effort.Keywords
This publication has 18 references indexed in Scilit:
- Zero mass error using unsteady wetting–drying conditions in shallow flows over dry irregular topographyInternational Journal for Numerical Methods in Fluids, 2004
- Unsteady free surface flow simulation over complex topography with a multidimensional upwind techniqueJournal of Computational Physics, 2003
- A numerical model for the flooding and drying of irregular domainsInternational Journal for Numerical Methods in Fluids, 2002
- Multidimensional Slope Limiters for MUSCL-Type Finite Volume Schemes on Unstructured GridsJournal of Computational Physics, 1999
- Solution of the 2D shallow water equations using the finite volume method on unstructured triangular meshesInternational Journal for Numerical Methods in Fluids, 1997
- Triangle: Engineering a 2D quality mesh generator and Delaunay triangulatorLecture Notes in Computer Science, 1996
- Upwind finite-volume Navier-Stokes computations on unstructured triangular meshesAIAA Journal, 1993
- Finite element method for moving boundary problems in river flowInternational Journal for Numerical Methods in Fluids, 1986
- Approximate Riemann solvers, parameter vectors, and difference schemesJournal of Computational Physics, 1981
- Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's methodJournal of Computational Physics, 1979