Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients

DOI10.1007/s00211-013-0597-6zbMath1342.76081OpenAlexW2121878816MaRDI QIDQ398753

Alexander Kurganov, Yu Liu, Alina E. Chertock

Publication date: 15 August 2014

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-013-0597-6

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Hydrology, hydrography, oceanography (86A05) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Finite volume methods applied to problems in fluid mechanics (76M12) Hyperbolic conservation laws (35L65) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items

Well-balanced high-order finite difference methods for systems of balance laws ⋮ Axisymmetric solutions of the shallow water equations with bottom topography ⋮ Well-Balanced and Positivity-Preserving Surface Reconstruction Schemes Solving Ripa Systems With Nonflat Bottom Topography ⋮ Well-balanced finite difference WENO schemes for the ripa model ⋮ Well-balanced positivity preserving cell-vertex central-upwind scheme for shallow water flows ⋮ Thermal versus isothermal rotating shallow water equations: comparison of dynamical processes by simulations with a novel well-balanced central-upwind scheme ⋮ Extension of a well-balanced central upwind scheme for variable density shallow water flow equations on triangular grids ⋮ Propagation of diffusing pollutant by kinetic flux-vector splitting method ⋮ Flux globalization based well-balanced path-conservative central-upwind schemes for shallow water models ⋮ A multi well-balanced scheme for the shallow water MHD system with topography ⋮ A modified high-resolution non-staggered central scheme with adjustable numerical dissipation ⋮ Kinetic flux vector splitting method for numerical study of two-dimensional Ripa model ⋮ A hybrid method to solve shallow water flows with horizontal density gradients ⋮ Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Scheme for the Thermal Rotating Shallow Water Equations ⋮ A well-balanced moving mesh discontinuous Galerkin method for the Ripa model on triangular meshes ⋮ Adaptive Central-Upwind Scheme on Triangular Grids for the Shallow Water Model with Variable Density ⋮ Simulating the dusty gas flow model via NHRS scheme ⋮ Transport of pollutant in shallow flows: a space-time CE/SE scheme ⋮ High order well-balanced discontinuous Galerkin methods for shallow water flow under temperature fields ⋮ The space-time CESE scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients ⋮ A HLLC scheme for Ripa model ⋮ Central-upwind scheme for 2D turbulent shallow flows using high-resolution meshes with scalable wall functions ⋮ A High-Order Well-Balanced Discontinuous Galerkin Method Based on the Hydrostatic Reconstruction for the Ripa Model ⋮ A well-balanced high-order scheme on van Leer-type for the shallow water equations with temperature gradient and variable bottom topography ⋮ The Riemann problem for the shallow water equations with horizontal temperature gradients ⋮ Well-balanced schemes to capture non-explicit steady states: Ripa model ⋮ High order still-water and moving-water equilibria preserving discontinuous Galerkin methods for the Ripa model ⋮ Godunov-type numerical scheme for the shallow water equations with horizontal temperature gradient ⋮ Well-balanced numerical schemes for shallow water equations with horizontal temperature gradient ⋮ Well-balancing via flux globalization: applications to shallow water equations with wet/dry fronts ⋮ A well-balanced central-upwind scheme for the thermal rotating shallow water equations ⋮ Dimensional splitting well-balanced schemes on Cartesian mesh for 2D shallow water equations with variable topography ⋮ Well-balanced path-conservative central-upwind schemes based on flux globalization ⋮ Flux globalization based well-balanced path-conservative central-upwind scheme for two-layer thermal rotating shallow water equations

Uses Software

• HE-E1GODF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Well-balanced finite volume evolution Galerkin methods for the shallow water equations
• Non-oscillatory central differencing for hyperbolic conservation laws
• Computing interface motion in compressible gas dynamics
• An interface tracking method for hyperbolic systems of conservation laws
• A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
• A kinetic scheme for the Saint-Venant system with a source term
• Some approximate Godunov schemes to compute shallow-water equations with topography.
• New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
• Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
• High-order well-balanced finite volume WENO schemes for shallow water equation with moving water
• A second-order well-balanced positivity preserving central-upwind scheme for the Saint-Venant system
• 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
• Strong Stability-Preserving High-Order Time Discretization Methods
• Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton--Jacobi Equations
• A steady-state capturing method for hyperbolic systems with geometrical source terms
• Interface tracking method for compressible multifluids
• Common Hamiltonian structure of the shallow water equations with horizontal temperature gradients and magnetic fields
• Riemann Solvers and Numerical Methods for Fluid Dynamics
• Central-Upwind Schemes for the Saint-Venant System
• Finite Volume Methods for Hyperbolic Problems
• Conservative front tracking and level set algorithms
• A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
• Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers
• On improving a one-layer ocean model with thermodynamics
• Two Interface-Type Numerical Methods for Computing Hyperbolic Systems with Geometrical Source Terms Having Concentrations
• Computations of compressible multifluids.