Numerical scheme for solving a porous Saint-Venant type model for water flow on vegetated hillslopes

DOI10.1016/j.apnum.2021.09.019zbMath1484.76048OpenAlexW3203382819MaRDI QIDQ2057277

Dorin Marinescu, Stelian Ion, Stefan Gicu Cruceanu

Publication date: 9 December 2021

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2021.09.019

zbMATH Keywords

finite volume methodporosityshallow-water equationsnon-homogeneous hyperbolic systemhydrological processwell-balance property

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Finite volume methods applied to problems in fluid mechanics (76M12)

Related Items

Path-conservative positivity-preserving well-balanced finite volume WENO method for porous shallow water equations

Uses Software

• Triangle

Cites Work

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• A well-balanced scheme for the shallow-water equations with topography
• Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography
• A Godunov-type method for the shallow water equations with discontinuous topography in the resonant regime
• A simple finite volume method for the shallow water equations
• Dam break flow computation based on an efficient flux vector splitting
• Discontinuous differential equations. I
• Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm
• Delaunay refinement algorithms for triangular mesh generation
• Numerical modelling of free-surface shallow flows over irregular topography with complex geometry
• Definition and weak stability of nonconservative products
• A second-order well-balanced positivity preserving central-upwind scheme for the Saint-Venant system
• The Riemann problem for the shallow water equations with discontinuous topography
• Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry
• High order finite difference WENO schemes with the exact conservation property for the shallow water equations
• Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
• Moving boundary shallow water flow in a region with quadratic bathymetry
• Exact Riemann solutions to shallow water equations
• Hyperbolic systems of conservation laws II
• Evaluation of well-balanced bore-capturing schemes for 2D wetting and drying processes
• Some exact solutions to the nonlinear shallow-water wave equations
• Finite Volume Methods for Hyperbolic Problems
• Performance of numerical methods on the non‐unique solution to the Riemann problem for the shallow water equations
• SWASHES: a compilation of shallow water analytic solutions for hydraulic and environmental studies
• Constructive Approach of the Solution of Riemann Problem for Shallow Water Equations with Topography and Vegetation
• Riemann Problem for Shallow Water Equation with Vegetation
• On the well-balance property of Roe's method for nonconservative hyperbolic systems. applications to shallow-water systems
• On the Construction and Comparison of Difference Schemes
• The surface gradient method for the treatment of source terms in the shallow-water equations
• Exact solutions to the Riemann problem of the shallow water equations with a bottom step