\textit{A posteriori} correction of high-order discontinuous Galerkin scheme through subcell finite volume formulation and flux reconstruction
From MaRDI portal
Publication:2220568
DOI10.1016/j.jcp.2018.10.050zbMath1452.65251OpenAlexW2900397291MaRDI QIDQ2220568
Publication date: 25 January 2021
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2018.10.050
hyperbolic conservation lawdiscontinuous Galerkin schemearbitrary high-order\textit{a posteriori} subcell limitationdiscontinuous Galerkin subcell finite volume formulationflux reconstruction (CPR)
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) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)
Related Items (35)
Flux reconstruction using Jacobi correction functions in discontinuous spectral element method ⋮ Limiting and divergence cleaning for continuous finite element discretizations of the MHD equations ⋮ An arbitrary high-order spectral difference method for the induction equation ⋮ A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations ⋮ An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. II: Subcell finite volume shock capturing ⋮ \textit{A posteriori} finite-volume local subcell correction of high-order discontinuous Galerkin schemes for the nonlinear shallow-water equations ⋮ Oscillation-free nodal discontinuous spectral element method for the simulation of compressible multicomponent flows ⋮ A discontinuous Galerkin method for shock capturing using a mixed high-order and sub-grid low-order approximation space ⋮ A priori subcell limiting based on compact nonuniform nonlinear weighted schemes of high-order CPR method for hyperbolic conservation laws ⋮ Monolithic convex limiting in discontinuous Galerkin discretizations of hyperbolic conservation laws ⋮ Matrix-free subcell residual distribution for Bernstein finite element discretizations of linear advection equations ⋮ Bound-preserving flux limiting schemes for DG discretizations of conservation laws with applications to the Cahn-Hilliard equation ⋮ Matrix-free subcell residual distribution for Bernstein finite elements: monolithic limiting ⋮ A modified a posteriori subcell limiter for high order flux reconstruction scheme for one-dimensional detonation simulation ⋮ ``\textit{A posteriori} limited high order and robust schemes for transient simulations of fluid flows in gas dynamics ⋮ Neural network-based limiter with transfer learning ⋮ A sub-element adaptive shock capturing approach for discontinuous Galerkin methods ⋮ On the convergence of residual distribution schemes for the compressible Euler equations via dissipative weak solutions ⋮ A flux-differencing formula for split-form summation by parts discretizations of non-conservative systems. Applications to subcell limiting for magneto-hydrodynamics ⋮ A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations ⋮ Admissibility preserving subcell limiter for Lax-Wendroff flux reconstruction ⋮ A Posteriori Local Subcell Correction of High-Order Discontinuous Galerkin Scheme for Conservation Laws on Two-Dimensional Unstructured Grids ⋮ Space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell WENO finite-volume limiting for simulation of non-stationary compressible multicomponent reactive flows ⋮ Free-boundary problems for wave-structure interactions in shallow-water: DG-ALE description and local subcell correction ⋮ A combination of residual distribution and the active flux formulations or a new class of schemes that can combine several writings of the same hyperbolic problem: application to the 1D Euler equations ⋮ Positivity preserving and entropy consistent approximate Riemann solvers dedicated to the high-order MOOD-based finite volume discretization of Lagrangian and Eulerian gas dynamics ⋮ A Study of Several Artificial Viscosity Models within the Discontinuous Galerkin Framework ⋮ A priori neural networks versus a posteriori MOOD loop: a high accurate 1D FV scheme testing bed ⋮ Algebraic entropy fixes and convex limiting for continuous finite element discretizations of scalar hyperbolic conservation laws ⋮ A MOOD-MUSCL hybrid formulation for the non-conservative shallow-water system ⋮ Assessment of a non-conservative four-equation multiphase system with phase transition ⋮ Subcell limiting strategies for discontinuous Galerkin spectral element methods ⋮ Hybrid discontinuous Galerkin-finite volume techniques for compressible flows on unstructured meshes ⋮ Conservative and Accurate Solution Transfer Between High-Order and Low-Order Refined Finite Element Spaces ⋮ A p-adaptive discontinuous Galerkin method with hp-shock capturing
Uses Software
Cites Work
- Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes
- 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
- \textit{A posteriori} subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws
- On the non-linear stability of flux reconstruction schemes
- Connections between the filtered discontinuous Galerkin method and the flux reconstruction approach to high order discretizations
- 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)
- A new class of high-order energy stable flux reconstruction schemes
- A simple robust and accurate \textit{a posteriori} sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes
- Hierarchical multi-dimensional limiting strategy for correction procedure via reconstruction
- A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids
- A vertex-based hierarchical slope limiter for \(p\)-adaptive discontinuous Galerkin methods
- Efficient implementation of essentially nonoscillatory shock-capturing schemes
- TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
- 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
- High-order methods for computational fluid dynamics: a brief review of compact differential formulations on unstructured grids
- A new vertex-based limiting approach for nodal discontinuous Galerkin methods on arbitrary unstructured meshes
- Extended skew-symmetric form for summation-by-parts operators and varying Jacobians
- Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws
- Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. II: Efficient flux quadrature.
- Efficient implementation of weighted ENO schemes
- Some remarks about conservation for residual distribution schemes
- A simple weighted essentially non-oscillatory limiter for the correction procedure via reconstruction (CPR) framework
- Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
- Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomials
- Summation-by-parts operators for correction procedure via reconstruction
- Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations
- A sub-cell based indicator for troubled zones in RKDG schemes and a novel class of hybrid RKDG+HWENO schemes
- Limiters for high-order discontinuous Galerkin methods
- Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids
- 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
- Edge Functions for Spectral Element Methods
- 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
- 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
- A Review of Residual Distribution Schemes for Hyperbolic and Parabolic Problems: The July 2010 State of the Art
- Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
- High-Resolution Conservative Algorithms for Advection in Incompressible Flow
- A simple shock‐capturing technique for high‐order discontinuous Galerkin methods
- Superconvergence of Discontinuous Galerkin Methods for Scalar Nonlinear Conservation Laws in One Space Dimension
- Analysis of Optimal Superconvergence of Discontinuous Galerkin Method for Linear Hyperbolic Equations
- The Multidimensional Optimal Order Detection method in the three‐dimensional case: very high‐order finite volume method for hyperbolic systems
- Connections between the discontinuous Galerkin method and high‐order flux reconstruction schemes
- One‐dimensional shock‐capturing for high‐order discontinuous Galerkin methods
- Slope limiting for discontinuous Galerkin approximations with a possibly non‐orthogonal Taylor basis
- A problem-independent limiter for high-order Runge-Kutta discontinuous Galerkin methods
- Hybrid DG/FV schemes for magnetohydrodynamics and relativistic hydrodynamics
This page was built for publication: \textit{A posteriori} correction of high-order discontinuous Galerkin scheme through subcell finite volume formulation and flux reconstruction
