An entropy-residual shock detector for solving conservation laws using high-order discontinuous Galerkin methods

DOI10.1016/j.jcp.2016.06.052zbMath1351.76068OpenAlexW2461650694MaRDI QIDQ729603

Yee Chee See, Matthias Ihme, Yu Lv

Publication date: 20 December 2016

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2016.06.052

zbMATH Keywords

discontinuous Galerkin methodshock-capturinghigh-order methodentropy residual

Mathematics Subject Classification ID

Shock waves and blast waves in fluid mechanics (76L05) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (14)

A \(p\)-weighted limiter for the discontinuous Galerkin method on one-dimensional and two-dimensional triangular grids ⋮ A neural network based shock detection and localization approach for discontinuous Galerkin methods ⋮ A coupled discontinuous Galerkin-finite volume framework for solving gas dynamics over embedded geometries ⋮ On underresolved simulations of compressible turbulence using an entropy-bounded DG method: solution stabilization, scheme optimization, and benchmark against a finite-volume solver ⋮ Positivity-preserving entropy stable schemes for the 1-D compressible Navier-Stokes equations: high-order flux limiting ⋮ High-order discontinuous Galerkin method for applications to multicomponent and chemically reacting flows ⋮ An adaptive viscosity regularization approach for the numerical solution of conservation laws: application to finite element methods ⋮ An oscillation-free bound-preserving discontinuous Galerkin method for multi-component chemically reacting flows ⋮ Discontinuous Galerkin spectral element method for shock capturing with summation by parts properties ⋮ Bounded and compact weighted essentially nonoscillatory limiters for discontinuous Galerkin schemes: triangular elements ⋮ A Multi-Dimensional Shock-Capturing Limiter for High-Order Least Square-Based Finite Difference-Finite Volume Method on Unstructured Grids ⋮ A hybrid kinetic WGVC-WENO scheme for compressible flows ⋮ Entropy and adjoint methods ⋮ Shock capturing for discontinuous Galerkin methods with application to predicting heat transfer in hypersonic flows

Cites Work

• Unnamed Item
• Unnamed Item
• Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes
• Multiwavelet troubled-cell indicator for discontinuity detection of discontinuous Galerkin schemes
• \textit{A posteriori} subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws
• Entropy-bounded discontinuous Galerkin scheme for Euler equations
• Implementation of the entropy viscosity method with the discontinuous Galerkin method
• Entropy viscosity method for nonlinear conservation laws
• A minimum entropy principle in the gas dynamics equations
• An adaptive high-order hybrid scheme for compressive, viscous flows with detailed chemistry
• A modified artificial viscosity approach for compressible turbulence simulations
• Shock capturing with PDE-based artificial viscosity for DGFEM. I: Formulation
• Entropy-based nonlinear viscosity for Fourier approximations of conservation laws
• The numerical simulation of two-dimensional fluid flow with strong shocks
• Efficient implementation of essentially nonoscillatory shock-capturing schemes. II
• 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
• Large-eddy simulation of the shock/turbulence interaction
• An analysis of the discontinuous Galerkin method for wave propagation problems
• Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws.
• Multiresolution wavelet-based adaptive numerical dissipation control for high-order methods
• Spectral (finite) volume method for conservation laws on unstructured grids. Basic formulation
• Computation of flows with shocks using the spectral difference method with artificial viscosity. I: Basic formulation and application
• Efficient implementation of weighted ENO schemes
• A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids
• Limiters for high-order discontinuous Galerkin methods
• The Optimal Convergence Rate of the p-Version of the Finite Element Method
• Solution of Two-Dimensional Riemann Problems of Gas Dynamics by Positive Schemes
• A Comparison of Troubled-Cell Indicators for Runge--Kutta Discontinuous Galerkin Methods Using Weighted Essentially Nonoscillatory Limiters
• Adaptive discontinuous Galerkin methods with shock‐capturing for the compressible Navier–Stokes equations

This page was built for publication: An entropy-residual shock detector for solving conservation laws using high-order discontinuous Galerkin methods