Local subcell monolithic DG/FV convex property preserving scheme on unstructured grids and entropy consideration

DOI10.1016/j.jcp.2024.113535MaRDI QIDQ6670712

François Vilar

Publication date: 24 January 2025

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

zbMATH Keywords

hyperbolic conservation lawsentropy stabilitypositivity-preserving schemestructure-preserving schemearbitrary high-orderDG subcell FV formulationsubcell monolithic scheme

Mathematics Subject Classification ID

Fluid mechanics (76-XX) Numerical analysis (65-XX)

Cites Work

• High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains
• A discontinuous Galerkin discretization for solving the two-dimensional gas dynamics equations written under total Lagrangian formulation on general unstructured grids
• A parameter-free smoothness indicator for high-resolution finite element schemes
• Cell-centered discontinuous Galerkin discretizations for two-dimensional scalar conservation laws on unstructured grids and for one-dimensional Lagrangian hydrodynamics
• A high-order finite volume method for systems of conservation laws-multi-dimensional optimal order detection (MOOD)
• On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes
• A simple robust and accurate \textit{a posteriori} sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes
• Fully multidimensional flux-corrected transport algorithms for fluids
• Subcell flux limiting for high-order Bernstein finite element discretizations of scalar hyperbolic conservation laws
• A vertex-based hierarchical slope limiter for \(p\)-adaptive discontinuous Galerkin methods
• On maximum-principle-satisfying high order schemes for scalar conservation laws
• The numerical simulation of two-dimensional fluid flow with strong shocks
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Parallel, adaptive finite element methods for conservation laws
• On discretely entropy conservative and entropy stable discontinuous Galerkin methods
• A new vertex-based limiting approach for nodal discontinuous Galerkin methods on arbitrary unstructured meshes
• Artificial viscosity in Godunov-type schemes to cure the carbuncle phenomenon
• Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws
• Flux-corrected transport algorithms for continuous Galerkin methods based on high order Bernstein finite elements
• On positivity-preserving high order discontinuous Galerkin schemes for compressible Navier-Stokes equations
• Efficient implementation of weighted ENO schemes
• Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems
• Algebraic entropy fixes and convex limiting for continuous finite element discretizations of scalar hyperbolic conservation laws
• Subcell limiting strategies for discontinuous Galerkin spectral element methods
• Bound-preserving flux limiting for high-order explicit Runge-Kutta time discretizations of hyperbolic conservation laws
• A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations
• Entropy stable, robust and high-order DGSEM for the compressible multicomponent Euler equations
• \textit{A posteriori} finite-volume local subcell correction of high-order discontinuous Galerkin schemes for the nonlinear shallow-water equations
• \textit{A posteriori} correction of high-order discontinuous Galerkin scheme through subcell finite volume formulation and flux reconstruction
• Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting
• Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations
• Limiters for high-order discontinuous Galerkin methods
• An evaluation of several differencing methods for inviscid fluid flow problems
• Solutions of multi-dimensional hyperbolic systems of conservation laws by square entropy condition satisfying discontinuous Galerkin method
• Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids
• Monolithic convex limiting in discontinuous Galerkin discretizations of hyperbolic conservation laws
• 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
• Shock Capturing for Discontinuous Galerkin Methods using Finite Volume Subcells
• Invariant Domains and First-Order Continuous Finite Element Approximation for Hyperbolic Systems
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• Adaptive Semidiscrete Central-Upwind Schemes for Nonconvex Hyperbolic Conservation Laws
• Numerical Viscosity and the Entropy Condition for Conservative Difference Schemes
• Riemann Solvers, the Entropy Condition, and Difference
• The Numerical Viscosity of Entropy Stable Schemes for Systems of Conservation Laws. I
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• On a Cell Entropy Inequality for Discontinuous Galerkin Methods
• On the Choice of Wavespeeds for the HLLC Riemann Solver
• Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems
• Second-Order Invariant Domain Preserving Approximation of the Euler Equations Using Convex Limiting
• High-Resolution Conservative Algorithms for Advection in Incompressible Flow
• A simple shock‐capturing technique for high‐order discontinuous Galerkin methods
• Multidimensional Summation-by-Parts Operators: General Theory and Application to Simplex Elements
• Flux-corrected transport. I: SHASTA, a fluid transport algorithm that works
• A problem-independent limiter for high-order Runge-Kutta discontinuous Galerkin methods
• Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes
• Invariant Domain Preserving High-Order Spectral Discontinuous Approximations of Hyperbolic Systems
• A Posteriori Local Subcell Correction of High-Order Discontinuous Galerkin Scheme for Conservation Laws on Two-Dimensional Unstructured Grids
• Free-boundary problems for wave-structure interactions in shallow-water: DG-ALE description and local subcell correction
• High order entropy stable discontinuous Galerkin spectral element methods through subcell limiting
• Monolithic convex limiting for Legendre-Gauss-Lobatto discontinuous Galerkin spectral-element methods
• Unnamed Item

This page was built for publication: Local subcell monolithic DG/FV convex property preserving scheme on unstructured grids and entropy consideration