Conservative multidimensional upwinding for the steady two-dimensional shallow water equations

DOI10.1006/jcph.1997.5823zbMath0902.76065OpenAlexW2024356719MaRDI QIDQ1383022

D. Massart

Publication date: 10 December 1998

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

Full work available at URL: https://doi.org/10.1006/jcph.1997.5823

zbMATH Keywords

frictionsource termsEuler equationssystem decompositionchannel flowsunstructured triangular gridsfluctuation distributionbed slopeflux balance distribution methods

Mathematics Subject Classification ID

Hydrology, hydrography, oceanography (86A05) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Finite difference methods applied to problems in fluid mechanics (76M20)

Related Items (16)

Unsteady free surface flow simulation over complex topography with a multidimensional upwind technique. ⋮ Streamline upwind Petrov-Galerkin methods for the steady-state Boltzmann transport equation ⋮ Unconditionally stable space-time discontinuous residual distribution for shallow-water flows ⋮ Application of conservative residual distribution schemes to the solution of the shallow water equations on unstructured meshes ⋮ On the accuracy of one-dimensional models of steady converging/diverging open channel flows ⋮ Unstructured finite volume discretisation of bed friction and convective flux in solute transport models linked to the shallow water equations ⋮ Higher order cell-based multidimensional upwind schemes for flow in porous media on unstructured grids ⋮ Multidimensional upwind schemes and higher resolution methods for three-component two-phase systems including gravity driven flow in porous media on unstructured grids ⋮ Continuous elliptic and multi-dimensional hyperbolic Darcy-flux finite-volume methods ⋮ Residual distribution for general time-dependent conservation laws ⋮ Stabilized residual distribution for shallow water simulations ⋮ Multi-dimensional wave-oriented upwind schemes with reduced cross-wind diffusion for flow in porous media ⋮ Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids ⋮ An entropy-stable residual distribution scheme for the system of two-dimensional inviscid shallow water equations ⋮ Conservative upwind difference schemes for the shallow water equations ⋮ Conservative upwind difference schemes for the Euler equations

Cites Work

• A multidimensional generalization of Roe's flux difference splitter for the Euler equations
• Approximate Riemann solvers, parameter vectors, and difference schemes
• The importance of eigenvectors for local preconditioners of the Euler equations
• Genuinely multidimensional upwinding for the 2D shallow water equations
• A high-resolution Godunov-type scheme in finite volumes for the 2D shallow-water equations
• Flux difference splitting for open‐channel flows
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