Improved Riemann solvers for complex transport in two-dimensional unsteady shallow flow

DOI10.1016/j.jcp.2011.05.022zbMath1408.76083OpenAlexW1969703907MaRDI QIDQ655041

J. Murillo, P. García-Navarro

Publication date: 28 December 2011

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2011.05.022

zbMATH Keywords

weak solutionsRoe solverwell-balanced approachdiffusion correctionmulti-component transportHLLC solversolute fixupwind reactive terms

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Finite volume methods applied to problems in fluid mechanics (76M12) Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs (65M25) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items (6)

A Roe type energy balanced solver for 1D arterial blood flow and transport ⋮ Design and analysis of ADER-type schemes for model advection-diffusion-reaction equations ⋮ A Riemann solver for unsteady computation of 2D shallow flows with variable density ⋮ A robust well-balanced model on unstructured grids for shallow water flows with wetting and drying over complex topography ⋮ A stable 2D unstructured shallow flow model for simulations of wetting and drying over rough terrains ⋮ Pollutant transport by shallow water equations on unstructured meshes: hyperbolization of the model and numerical solution via a novel flux splitting scheme

Uses Software

• HLLE

Cites Work

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• Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography
• An Exner-based coupled model for two-dimensional transient flow over erodible bed
• Conservative numerical simulation of multi-component transport in two-dimensional unsteady shallow water flow
• Weak solutions for partial differential equations with source terms: application to the shallow water equations
• FORCE schemes on unstructured meshes. I: Conservative hyperbolic systems
• Self-adjusting grid methods for one-dimensional hyperbolic conservation laws
• Approximate Riemann solvers, parameter vectors, and difference schemes
• Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry
• Restoration of the contact surface in the HLL-Riemann solver
• A new theoretically motivated higher order upwind scheme on unstructured grids of simplices
• Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
• Generalized Roe schemes for 1D two-phase, free-surface flows over a mobile bed
• Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation
• Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry
• The influence of source terms on stability, accuracy and conservation in two-dimensional shallow flow simulation using triangular finite volumes
• 1-D numerical modelling of shallow flows with variable horizontal density
• On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
• On the Accuracy of Stable Schemes for 2D Scalar Conservation Laws
• Some exact solutions to the nonlinear shallow-water wave equations
• Numerical solutions of the shallow water equations with discontinuous bed topography
• Finite Volume Methods for Hyperbolic Problems
• A Well-balanced and Non-negative Numerical Scheme for Solving the Integrated Shallow Water and Solute Transport Equations
• Analysis of a second‐order upwind method for the simulation of solute transport in 2D shallow water flow
• Preserving bounded and conservative solutions of transport in one‐dimensional shallow‐water flow with upwind numerical schemes: Application to fertigation and solute transport in rivers
• Coupling between shallow water and solute flow equations: analysis and management of source terms in 2D
• Flux difference splitting and the balancing of source terms and flux gradients
• The surface gradient method for the treatment of source terms in the shallow-water equations

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