Well-Balanced and Positivity-Preserving Surface Reconstruction Schemes Solving Ripa Systems With Nonflat Bottom Topography

Finite difference methods applied to problems in fluid mechanics (76M20) Finite volume methods applied to problems in fluid mechanics (76M12) Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing (76B10) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Cites Work

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A well-balanced reconstruction of wet/dry fronts for the shallow water equations
Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients
Well-balanced central finite volume methods for the Ripa system
A new finite volume method for flux-gradient and source-term balancing in shallow water equations
Efficient implementation of essentially nonoscillatory shock-capturing schemes
Upwind methods for hyperbolic conservation laws with source terms
Well-balanced finite difference WENO schemes for the ripa model
The space-time CESE scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients
A robust second-order surface reconstruction for shallow water flows with a discontinuous topography and a Manning friction
The Riemann problem for the shallow water equations with horizontal temperature gradients
High order still-water and moving-water equilibria preserving discontinuous Galerkin methods for the Ripa model
Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
Reliability of first order numerical schemes for solving shallow water system over abrupt topography
A second-order well-balanced positivity preserving central-upwind scheme for the Saint-Venant system
High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms
Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
Well-balanced schemes to capture non-explicit steady states: Ripa model
Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
Common Hamiltonian structure of the shallow water equations with horizontal temperature gradients and magnetic fields
High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
On the Artificial Compression Method for Second-Order Nonoscillatory Central Difference Schemes for Systems of Conservation Laws
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
On improving a one-layer ocean model with thermodynamics
Finite Volume Evolution Galerkin Methods for the Shallow Water Equations with Dry Beds
A New Hydrostatic Reconstruction Scheme Based on Subcell Reconstructions
Two Interface-Type Numerical Methods for Computing Hyperbolic Systems with Geometrical Source Terms Having Concentrations

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