Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations

DOI10.1016/j.jcp.2021.110723OpenAlexW3200065707MaRDI QIDQ2134497

Jesse Chan, Yimin Lin, Timothy Warburton

Publication date: 3 May 2022

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

Full work available at URL: https://arxiv.org/abs/2011.11089

zbMATH Keywords

boundary conditionshigh orderdiscontinuous Galerkincompressible Navier-Stokessummation by partsentropy stable

Mathematics Subject Classification ID

Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Compressible fluids and gas dynamics (76Nxx)

Related Items (8)

Investigation of aspect ratio effects on flow characteristics and vorticity generation in shock-induced rectangular bubble ⋮ A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations ⋮ High order entropy stable discontinuous Galerkin spectral element methods through subcell limiting ⋮ Nonlinear boundary conditions for initial boundary value problems with applications in computational fluid dynamics ⋮ An entropy stable discontinuous Galerkin method for the two-layer shallow water equations on curvilinear meshes ⋮ Entropy stability for the compressible Navier-Stokes equations with strong imposition of the no-slip boundary condition ⋮ A skew-symmetric energy and entropy stable formulation of the compressible Euler equations ⋮ A simple and general framework for the construction of thermodynamically compatible schemes for computational fluid and solid mechanics

Uses Software

• Gmsh
• libParanumal

Cites Work

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• High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains
• Entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations
• A uniquely defined entropy stable matrix dissipation operator for high Mach number ideal MHD and compressible Euler simulations
• Dealiasing techniques for high-order spectral element methods on regular and irregular grids
• Affordable, entropy-consistent Euler flux functions. II: Entropy production at shocks
• A stable high-order finite difference scheme for the compressible Navier-Stokes equations: No-slip wall boundary conditions
• A new finite element formulation for computational fluid dynamics. I: Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics
• A family of embedded Runge-Kutta formulae
• On discretely entropy conservative and entropy stable discontinuous Galerkin methods
• A DPG method for steady viscous compressible flow
• High-order methods for computational fluid dynamics: a brief review of compact differential formulations on unstructured grids
• Interior penalties for summation-by-parts discretizations of linear second-order differential equations
• Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws
• Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements
• Shallow water equations: split-form, entropy stable, well-balanced, and positivity preserving numerical methods
• High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
• Second-order invariant domain preserving approximation of the compressible Navier-Stokes equations
• Stability of wall boundary condition procedures for discontinuous Galerkin spectral element approximations of the compressible Euler equations
• Entropy stable reduced order modeling of nonlinear conservation laws
• Entropy stable boundary conditions for the Euler equations
• Fully discrete explicit locally entropy-stable schemes for the compressible Euler and Navier-Stokes equations
• Entropy stable \(h/p\)-nonconforming discretization with the summation-by-parts property for the compressible Euler and Navier-Stokes equations
• Staggered-grid entropy-stable multidimensional summation-by-parts discretizations on curvilinear coordinates
• Conservative and entropy stable solid wall boundary conditions for the compressible Navier-Stokes equations: adiabatic wall and heat entropy transfer
• High-order entropy stable discontinuous Galerkin methods for the shallow water equations: curved triangular meshes and GPU acceleration
• Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting
• On discretely entropy stable weight-adjusted discontinuous Galerkin methods: curvilinear meshes
• Extension of tensor-product generalized and dense-norm summation-by-parts operators to curvilinear coordinates
• Skew-symmetric entropy stable modal discontinuous Galerkin formulations
• Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations
• Entropy-stable schemes for the Euler equations with far-field and wall boundary conditions
• Monolithic convex limiting in discontinuous Galerkin discretizations of hyperbolic conservation laws
• Mortar-based entropy-stable discontinuous Galerkin methods on non-conforming quadrilateral and hexahedral meshes
• Entropy Stable Staggered Grid Discontinuous Spectral Collocation Methods of any Order for the Compressible Navier--Stokes Equations
• Arbitrarily High-order Accurate Entropy Stable Essentially Nonoscillatory Schemes for Systems of Conservation Laws
• Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces
• Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
• The Numerical Viscosity of Entropy Stable Schemes for Systems of Conservation Laws. I
• Simplified Second-Order Godunov-Type Methods
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Entropy Stability and the No-Slip Wall Boundary Condition
• A Local Discontinuous Galerkin Method for Nonlinear Diffusion Problems with Mixed Boundary Conditions
• High‐order CFD methods: current status and perspective
• Relaxation Runge--Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier--Stokes Equations
• Efficient Entropy Stable Gauss Collocation Methods
• Kinetic Energy Preserving and Entropy Stable Finite Volume Schemes for Compressible Euler and Navier-Stokes Equations
• Analytical shock solutions at large and small Prandtl number
• Multidimensional Summation-by-Parts Operators: General Theory and Application to Simplex Elements

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