Analysis of a new Kolgan-type scheme motivated by the shallow water equations

DOI10.1016/j.apnum.2011.06.002zbMath1237.76092OpenAlexW2068527949MaRDI QIDQ412321

Luis Cea, María Elena Vázquez-Cendón

Publication date: 4 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2011.06.002

zbMATH Keywords

finite volume methodshallow water equationshigh-order schemesKolgan scheme\(C\)-propertyupwind sources

Mathematics Subject Classification ID

Finite volume methods applied to problems in fluid mechanics (76M12) Hyperbolic conservation laws (35L65)

Related Items (7)

A staggered semi-implicit hybrid FV/FE projection method for weakly compressible flows ⋮ Operator-Splitting on Hyperbolic Balance Laws ⋮ Design and analysis of ADER-type schemes for model advection-diffusion-reaction equations ⋮ Unstructured finite volume discretisation of bed friction and convective flux in solute transport models linked to the shallow water equations ⋮ A projection hybrid high order finite volume/finite element method for incompressible turbulent flows ⋮ A bounded linear integrator for some diffusive nonlinear time-dependent partial differential equations ⋮ POD-Galerkin reduced order methods for combined Navier-Stokes transport equations based on a hybrid FV-FE solver

Cites Work

• A historical oversight: Vladimir P. Kolgan and his high-resolution scheme
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• A hybrid second order scheme for shallow water flows
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• Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm
• Upwind methods for hyperbolic conservation laws with source terms
• A study of numerical methods for hyperbolic conservation laws with stiff source terms
• High-order well-balanced finite volume WENO schemes for shallow water equation with moving water
• Depth-averaged modelling of turbulent shallow water flow with wet-dry fronts
• Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
• High-order well-balanced finite difference WENO schemes for a class of hyperbolic systems with source terms
• Unstructured finite volume discretization of two-dimensional depth-averaged shallow water equations with porosity
• Riemann Solvers and Numerical Methods for Fluid Dynamics
• Multiple Steady States for 1-D Transonic Flow
• A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
• High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems
• Flux difference splitting and the balancing of source terms and flux gradients

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