Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter on Unstructured Meshes

DOI10.4208/cicp.221015.160816azbMath1488.65493OpenAlexW2586937927MaRDI QIDQ5158713

Chi-Wang Shu, Jianxian Qiu, Xinghui Zhong, Jun Zhu

Publication date: 26 October 2021

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

Full work available at URL: https://doi.org/10.4208/cicp.221015.160816a

zbMATH Keywords

unstructured meshRunge-Kutta discontinuous Galerkin methodHWENO limiter

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) 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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Compressible fluids and gas dynamics (76N99) Euler equations (35Q31)

Related Items (28)

Essentially non-oscillatory and weighted essentially non-oscillatory schemes ⋮ A Well-Balanced Positivity-Preserving Quasi-Lagrange Moving Mesh DG Method for the Shallow Water Equations ⋮ An improved simple WENO limiter for discontinuous Galerkin methods solving hyperbolic systems on unstructured meshes ⋮ A DDG Method with a Residual-Based Artificial Viscosity for the Transonic/Supersonic Compressible Flow ⋮ A Priori Subcell Limiting Approach for the FR/CPR Method on Unstructured Meshes ⋮ The compact and accuracy preserving limiter for high-order finite volume schemes solving compressible flows ⋮ Stencil selection algorithms for WENO schemes on unstructured meshes ⋮ Dissipation-based WENO stabilization of high-order finite element methods for scalar conservation laws ⋮ An indicator-based hybrid limiter in discontinuous Galerkin methods for hyperbolic conservation laws ⋮ A new troubled cell indicator and a new limiter based on TENO schemes for RKDG methods ⋮ Element centered smooth artificial viscosity in discontinuous Galerkin method for propagation of acoustic shock waves on unstructured meshes ⋮ Bounded and compact weighted essentially nonoscillatory limiters for discontinuous Galerkin schemes: triangular elements ⋮ A quasi-Lagrangian moving mesh discontinuous Galerkin method for hyperbolic conservation laws ⋮ A new WENO based Chebyshev spectral volume method for solving one- and two-dimensional conservation laws ⋮ An efficient class of WENO schemes with adaptive order for unstructured meshes ⋮ A hybrid Hermite WENO scheme for hyperbolic conservation laws ⋮ A new WENO weak Galerkin finite element method for time dependent hyperbolic equations ⋮ High-order IMEX-WENO finite volume approximation for nonlinear age-structured population model ⋮ High-order Runge-Kutta discontinuous Galerkin methods with a new type of multi-resolution WENO limiters on triangular meshes ⋮ A Generalization of a Troubled-Cell Indicator to $h$-Adaptive Meshes for Discontinuous Galerkin Methods ⋮ Arbitrary high order central non-oscillatory schemes on mixed-element unstructured meshes ⋮ A new troubled-cell indicator for discontinuous Galerkin methods for hyperbolic conservation laws ⋮ A New Type of High-Order WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes ⋮ A simple, high-order and compact WENO limiter for RKDG method ⋮ Stencil selection algorithms for WENO schemes on unstructured meshes ⋮ A New Troubled-Cell Indicator for Discontinuous Galerkin Methods Using K-Means Clustering ⋮ Well-balanced discontinuous Galerkin method for shallow water equations with constant subtraction techniques on unstructured meshes ⋮ A compact subcell WENO limiting strategy using immediate neighbors for Runge-Kutta discontinuous Galerkin methods for unstructured meshes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes
• \textit{A posteriori} subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws
• Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method. II: Two dimensional case
• Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems
• Runge-Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes
• A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes
• Numerical solutions of partial differential equations
• The numerical simulation of two-dimensional fluid flow with strong shocks
• 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
• Weighted essentially non-oscillatory schemes on triangular meshes
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Parallel, adaptive finite element methods for conservation laws
• Weighted essentially non-oscillatory schemes
• High-order accurate discontinuous finite element solution of the 2D Euler equations
• Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: One-dimensional case.
• Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws.
• Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids
• Efficient implementation of weighted ENO schemes
• A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids
• High-order accurate implementation of solid wall boundary conditions in curved geometries
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• On the computation of steady-state compressible flows using a discontinuous Galerkin method
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
• Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter
• A Comparison of Troubled-Cell Indicators for Runge--Kutta Discontinuous Galerkin Methods Using Weighted Essentially Nonoscillatory Limiters
• A problem-independent limiter for high-order Runge-Kutta discontinuous Galerkin methods

This page was built for publication: Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter on Unstructured Meshes