Well-balanced fifth-order finite difference Hermite WENO scheme for the shallow water equations

DOI10.1016/j.jcp.2022.111860OpenAlexW4313549249MaRDI QIDQ2683082

Min Zhang, Zhuang Zhao

Publication date: 3 February 2023

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

Full work available at URL: https://arxiv.org/abs/2208.01260

zbMATH Keywords

shallow water equationscompactnessfinite differencewell-balancedHermite WENO scheme

Mathematics Subject Classification ID

Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Incompressible inviscid fluids (76Bxx)

Related Items

High-order accurate well-balanced energy stable adaptive moving mesh finite difference schemes for the shallow water equations with non-flat bottom topography

Cites Work

• Unnamed Item
• Positivity-preserving well-balanced discontinuous Galerkin methods for the shallow water equations on unstructured triangular meshes
• Hybrid well-balanced WENO schemes with different indicators for shallow water equations
• Simulations of shallow water equations with finite difference Lax-Wendroff weighted essentially non-oscillatory schemes
• ENO and WENO schemes with the exact conservation property for one-dimensional shallow water equations
• A gas-kinetic scheme for shallow-water equations with source terms
• High-order central Hermite WENO schemes: dimension-by-dimension moment-based reconstructions
• Fifth-order Hermite targeted essentially non-oscillatory schemes for hyperbolic conservation laws
• Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method. II: Two dimensional case
• 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
• Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: One-dimensional case.
• High order well-balanced discontinuous Galerkin methods based on hydrostatic reconstruction for shallow water equations
• Seventh order Hermite WENO scheme for hyperbolic conservation laws
• HWENO schemes based on compact difference for hyperbolic conservation laws
• Efficient implementation of weighted ENO schemes
• A high-order well-balanced positivity-preserving moving mesh DG method for the shallow water equations with non-flat bottom topography
• Positivity-preserving well-balanced arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for the shallow water equations
• A fifth-order finite difference HWENO scheme combined with limiter for hyperbolic conservation laws
• Multi-resolution HWENO schemes for hyperbolic conservation laws
• High order well-balanced finite difference WENO interpolation-based schemes for shallow water equations
• A new fifth-order finite difference well-balanced multi-resolution WENO scheme for solving shallow water equations
• A modified fifth order finite difference Hermite WENO scheme for hyperbolic conservation laws
• Finite difference Hermite WENO schemes for hyperbolic conservation laws
• A new well-balanced non-oscillatory central scheme for the shallow water equations on rectangular meshes
• High-order well-balanced finite volume WENO schemes for shallow water equation with moving water
• A Hermite upwind WENO scheme for solving hyperbolic conservation laws
• High order finite difference WENO schemes with the exact conservation property for the shallow water equations
• High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms
• A well-balanced weighted compact nonlinear scheme for shallow water equations on curvilinear grids
• High order well-balanced asymptotic preserving finite difference WENO schemes for the shallow water equations in all Froude numbers
• A new well-balanced Hermite weighted essentially non-oscillatory scheme for shallow water equations
• Solution of the shallow‐water equations using an adaptive moving mesh method
• A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
• A Well-Balanced Positivity-Preserving Quasi-Lagrange Moving Mesh DG Method for the Shallow Water Equations
• A Well-Balanced Runge-Kutta Discontinuous Galerkin Method for Multilayer Shallow Water Equations with Non-Flat Bottom Topography
• High Order Well-Balanced Weighted Compact Nonlinear Schemes for Shallow Water Equations
• A Well-Balanced Gas Kinetic Scheme for Navier-Stokes Equations with Gravitational Potential
• High Order Discretely Well-Balanced Methods for Arbitrary Hydrostatic Atmospheres
• The surface gradient method for the treatment of source terms in the shallow-water equations