An entropy stable discontinuous Galerkin method for the two-layer shallow water equations on curvilinear meshes
DOI10.1007/s10915-024-02451-2arXiv2306.12699OpenAlexW4391717727MaRDI QIDQ6202019
Patrick Ersing, Andrew R. Winters
Publication date: 21 February 2024
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2306.12699
entropy stabilitywell-balanced methoddiscontinuous Galerkin spectral element methodtwo-layer shallow water system
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Hydrology, hydrography, oceanography (86A05) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Spectral methods applied to problems in fluid mechanics (76M22) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Navier-Stokes equations (35Q30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Initial-boundary value problems for first-order hyperbolic systems (35L50) Numerical quadrature and cubature formulas (65D32) Liquid-liquid two component flows (76T06)
Cites Work
- Unnamed Item
- Unnamed Item
- Runge-Kutta discontinuous Galerkin method for the approximation of Baer and Nunziato type multiphase models
- Local absorbent boundary condition for nonlinear hyperbolic problems with unknown Riemann invariants
- A fast adaptive quadtree scheme for a two-layer shallow water model
- A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations
- A robust well-balanced scheme for multi-layer shallow water equations
- Ideal GLM-MHD: about the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations
- An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry
- A polynomial spectral calculus for analysis of DG spectral element methods
- Shallow water equations: split-form, entropy stable, well-balanced, and positivity preserving numerical methods
- Well-balanced schemes for the shallow water equations with Coriolis forces
- Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
- Definition and weak stability of nonconservative products
- Mimetic properties of difference operators: product and chain rules as for functions of bounded variation and entropy stability of second derivatives
- An arbitrary high order well-balanced ADER-DG numerical scheme for the multilayer shallow-water model with variable density
- An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. I: Theory and numerical verification
- A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations
- An entropy stable high-order discontinuous Galerkin spectral element method for the Baer-Nunziato two-phase flow model
- A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics
- An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. II: Subcell finite volume shock capturing
- Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations
- A high-order velocity-based discontinuous Galerkin scheme for the shallow water equations: local conservation, entropy stability, well-balanced property, and positivity preservation
- Entropy stable discontinuous Galerkin methods for balance laws in non-conservative form: applications to the Euler equations with gravity
- Entropy stable DGSEM for nonlinear hyperbolic systems in nonconservative form with application to two-phase flows
- High-order entropy stable discontinuous Galerkin methods for the shallow water equations: curved triangular meshes and GPU acceleration
- A discontinuous Galerkin method for two-layer shallow water equations
- Construction of modern robust nodal discontinuous Galerkin spectral element methods for the compressible Navier-Stokes equations
- A comparison of two entropy stable discontinuous Galerkin spectral element approximations for the shallow water equations with non-constant topography
- Affordable, entropy conserving and entropy stable flux functions for the ideal MHD equations
- Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations
- Models and methods for two-layer shallow water flows
- Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: theory and boundary conditions
- Metric identities and the discontinuous spectral element method on curvilinear meshes
- On the efficient implementation of PVM methods and simple Riemann solvers. Application to the Roe method for large hyperbolic systems
- Entropy-stable Gauss collocation methods for ideal magneto-hydrodynamics
- A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods
- Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces
- Two-Layer Shallow Water System: A Relaxation Approach
- Central-Upwind Schemes for Two-Layer Shallow Water Equations
- Implementing Spectral Methods for Partial Differential Equations
- The Numerical Viscosity of Entropy Stable Schemes for Systems of Conservation Laws. I
- The motion of a finite mass of granular material down a rough incline
- Theoretical and Practical Aspects of Some Initial Boundary Value Problems in Fluid Dynamics
- Energy Conservative and Stable Schemes for the Two-layer Shallow Water Equations
- Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
- On the Partial Difference Equations of Mathematical Physics
- Initial boundary value problems for hyperbolic systems
- A flux-differencing formula for split-form summation by parts discretizations of non-conservative systems. Applications to subcell limiting for magneto-hydrodynamics
