An arbitrary high order well-balanced ADER-DG numerical scheme for the multilayer shallow-water model with variable density
From MaRDI portal
Publication:2063176
DOI10.1007/s10915-021-01734-2OpenAlexW4200237312MaRDI QIDQ2063176
T. Morales de Luna, Michael Dumbser, E. Guerrero Fernández, Manuel Jesús Castro-Díaz
Publication date: 10 January 2022
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-021-01734-2
well-balancedvariable pressuredensity-stratified fluida posteriori subcell finite volume limiterADER discontinous Galerkin methodsmultilayer shallow-water model
Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Hyperbolic equations and hyperbolic systems (35Lxx)
Related Items
SUPG formulation augmented with YZβ shock‐capturing for computing shallow‐water equations, Free-boundary problems for wave-structure interactions in shallow-water: DG-ALE description and local subcell correction, An entropy stable discontinuous Galerkin method for the two-layer shallow water equations on curvilinear meshes
Uses Software
Cites Work
- Unnamed Item
- \textit{A posteriori} subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws
- A high order semi-implicit discontinuous Galerkin method for the two dimensional shallow water equations on staggered unstructured meshes
- A multilayer method for the hydrostatic Navier-Stokes equations: a particular weak solution
- Approximation of the hydrostatic Navier-Stokes system for density stratified flows by a multilayer model: kinetic interpretation and numerical solution
- A high-order finite volume method for systems of conservation laws-multi-dimensional optimal order detection (MOOD)
- Explicit one-step time discretizations for discontinuous Galerkin and finite volume schemes based on local predictors
- ADER schemes for nonlinear systems of stiff advection-diffusion-reaction equations
- On the quadrature and weak form choices in collocation type discontinuous Galerkin spectral element methods
- FORCE schemes on unstructured meshes. II: Non-conservative hyperbolic systems
- A space-time discontinuous Galerkin method for Boussinesq-type equations
- A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes
- A robust well-balanced scheme for multi-layer shallow water equations
- ADER schemes on unstructured meshes for nonconservative hyperbolic systems: applications to geophysical flows
- TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
- The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
- Upwind methods for hyperbolic conservation laws with source terms
- ADER: Arbitrary high-order Godunov approach
- A hierarchy of dispersive layer-averaged approximations of Euler equations for free surface flows
- High order well-balanced discontinuous Galerkin methods based on hydrostatic reconstruction for shallow water equations
- Multilayer shallow water models with locally variable number of layers and semi-implicit time discretization
- Design and analysis of ADER-type schemes for model advection-diffusion-reaction equations
- On the eigenvalues of the ADER-WENO Galerkin predictor
- ADER schemes for three-dimensional non-linear hyperbolic systems
- A well-balanced positivity preserving ``second-order scheme for shallow water flows on unstructured meshes
- Semi-implicit finite difference methods for the two-dimensional shallow water equations
- Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. II: Efficient flux quadrature.
- Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. I: General formulation.
- An entropy stable discontinuous Galerkin method for the shallow water equations on curvilinear meshes with wet/dry fronts accelerated by GPUs
- On high order ADER discontinuous Galerkin schemes for first order hyperbolic reformulations of nonlinear dispersive systems
- An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemes
- Discontinuous Galerkin methods for multi-layer ocean modeling: viscosity and thin layers
- 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
- Flexible and efficient discretizations of multilayer models with variable density
- A semi-implicit, semi-Lagrangian, \(p\)-adaptive discontinuous Galerkin method for the shallow water equations
- An energy-consistent depth-averaged Euler system: derivation
- Efficient high order accurate staggered semi-implicit discontinuous Galerkin methods for natural convection problems
- Well-balanced high-order finite volume methods for systems of balance laws
- Non-hydrostatic pressure shallow flows: GPU implementation using finite volume and finite difference scheme
- Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomials
- Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws
- A staggered semi-implicit spectral discontinuous Galerkin scheme for the shallow water equations
- Reliability of first order numerical schemes for solving shallow water system over abrupt topography
- Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations
- Space-time discontinuous Galerkin method for the compressible Navier--Stokes equations
- Extension of the spectral volume method to high-order boundary representation
- Derivative Riemann solvers for systems of conservation laws and ader methods
- A well-balanced ADER discontinuous Galerkin method based on differential transformation procedure for shallow water equations
- A hyperbolic reformulation of the Serre-Green-Naghdi model for general bottom topographies
- AQ-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system
- A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation
- A Class of Computationally Fast First Order Finite Volume Solvers: PVM Methods
- The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
- The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
- WELL-BALANCED NUMERICAL SCHEMES BASED ON A GENERALIZED HYDROSTATIC RECONSTRUCTION TECHNIQUE
- Finite-Volume Solvers for a Multilayer Saint-Venant System
- A high-resolution wetting and drying algorithm for free-surface hydrodynamics
- TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
- Derivation of Efficient, Continuous, Explicit Runge–Kutta Methods
- Semi‐implicit finite difference methods for three‐dimensional shallow water flow
- A semi-implicit finite difference method for non-hydrostatic, free-surface flows
- Solution of the generalized Riemann problem for advection–reaction equations
- A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
- A WELL-BALANCED SCHEME USING NON-CONSERVATIVE PRODUCTS DESIGNED FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS WITH SOURCE TERMS
- Gravity current flow over obstacles
- A semi‐implicit numerical method for the free‐surface Navier–Stokes equations
- A rapid numerical method for solving Serre–Green–Naghdi equations describing long free surface gravity waves
- Derivation of a Multilayer Approach to Model Suspended Sediment Transport: Application to Hyperpycnal and Hypopycnal Plumes
- A High Order Central DG method of the Two-Layer Shallow Water Equations
- A dynamic multilayer shallow water model for polydisperse sedimentation
- High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems
- Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
