Construction of modern robust nodal discontinuous Galerkin spectral element methods for the compressible Navier-Stokes equations
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Publication:2230452
DOI10.1007/978-3-030-60610-7_3zbMath1472.76066arXiv2005.02317OpenAlexW3023375590MaRDI QIDQ2230452
David A. Kopriva, Gregor J. Gassner, Andrew R. Winters, Florian J. Hindenlang
Publication date: 17 September 2021
Full work available at URL: https://arxiv.org/abs/2005.02317
Spectral methods applied to problems in fluid mechanics (76M22) Compressible Navier-Stokes equations (76N06)
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Cites Work
- Unnamed Item
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- Perfect derivatives, conservative differences and entropy stable computation of hyperbolic conservation laws
- High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains
- Review of summation-by-parts schemes for initial-boundary-value problems
- Entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations
- Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography
- A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media
- A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations
- A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
- A uniquely defined entropy stable matrix dissipation operator for high Mach number ideal MHD and compressible Euler simulations
- Affordable, entropy-consistent Euler flux functions. II: Entropy production at shocks
- Numerical simulation of optical coupling and light propagation in coupled optical resonators with size disorder
- Skew-selfadjoint form for systems of conservation laws
- Smoothing and the second law
- Entropy functions for symmetric systems of conservation laws
- Optimal time splitting for two- and three-dimensional Navier-Stokes equations with mixed derivatives
- On the symmetric form of systems of conservation laws with entropy
- The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
- An analysis of the discontinuous Galerkin method for wave propagation problems
- Summation by parts for finite difference approximations for \(d/dx\)
- Approximate Riemann solvers, parameter vectors, and difference schemes. (Reprint)
- High-order fluxes for conservative skew-symmetric-like schemes in structured meshes: Application to compressible flows
- An entropy stable \(h/p\) non-conforming discontinuous Galerkin method with the summation-by-parts property
- The BR1 scheme is stable for the compressible Navier-Stokes equations
- On discretely entropy conservative and entropy stable discontinuous Galerkin methods
- Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction
- A provably stable discontinuous Galerkin spectral element approximation for moving hexahedral meshes
- Comparison of some entropy conservative numerical fluxes for the Euler equations
- An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry
- Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws
- On the use of kinetic energy preserving DG-schemes for large eddy simulation
- Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes
- Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements
- Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
- Spectral element approximation of convection-diffusion type problems
- A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations
- An entropy stable discontinuous Galerkin method for the shallow water equations on curvilinear meshes with wet/dry fronts accelerated by GPUs
- An entropy-stable discontinuous Galerkin approximation for the incompressible Navier-Stokes equations with variable density and artificial compressibility
- A large eddy simulation method for DGSEM using non-linearly optimized relaxation filters
- Design of a Smagorinsky spectral vanishing viscosity turbulence model for discontinuous Galerkin methods
- Entropy stable discontinuous Galerkin schemes on moving meshes for hyperbolic conservation laws
- Entropy stable numerical approximations for the isothermal and polytropic Euler equations
- Entropy stable DGSEM for nonlinear hyperbolic systems in nonconservative form with application to two-phase flows
- Conservative and entropy stable solid wall boundary conditions for the compressible Navier-Stokes equations: adiabatic wall and heat entropy transfer
- A free-energy stable nodal discontinuous Galerkin approximation with summation-by-parts property for the Cahn-Hilliard equation
- Free-stream preservation for curved geometrically non-conforming discontinuous Galerkin spectral elements
- Entropy stable space-time discontinuous Galerkin schemes with summation-by-parts property for hyperbolic conservation laws
- Analysis and entropy stability of the line-based discontinuous Galerkin method
- Explicit discontinuous Galerkin methods for unsteady problems
- Affordable, entropy conserving and entropy stable flux functions for the ideal MHD equations
- Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations
- A study of spectral element and discontinuous Galerkin methods for the Navier-Stokes equations in nonhydrostatic mesoscale atmospheric modeling: equation sets and test cases
- Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: theory and boundary conditions
- Reduced aliasing formulations of the convective terms within the Navier-Stokes equations for a compressible fluid
- Metric identities and the discontinuous spectral element method on curvilinear meshes
- Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
- Generalized conservative approximations of split convective derivative operators
- 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
- A Comparison of the Dispersion and Dissipation Errors of Gauss and Gauss–Lobatto Discontinuous Galerkin Spectral Element Methods
- Construction of curvilinear co-ordinate systems and applications to mesh generation
- The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
- The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
- Stable Boundary Conditions and Difference Schemes for Navier–Stokes Equations
- A Conservative Discontinuous Galerkin Semi-Implicit Formulation for the Navier–Stokes Equations in Nonhydrostatic Mesoscale Modeling
- Implementing Spectral Methods for Partial Differential Equations
- Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
- Approximation Results for Orthogonal Polynomials in Sobolev Spaces
- The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
- Computation of electromagnetic scattering with a non‐conforming discontinuous spectral element method
- Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems
- High-Order Schemes, Entropy Inequalities, and Nonclassical Shocks
- Finite Volume Methods for Hyperbolic Problems
- Weight-Adjusted Discontinuous Galerkin Methods: Wave Propagation in Heterogeneous Media
- On exponential convergence of Gegenbauer interpolation and spectral differentiation
- 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
- Spectral Methods
- Kinetic Energy Preserving and Entropy Stable Finite Volume Schemes for Compressible Euler and Navier-Stokes Equations
- ENTROPY STABLE APPROXIMATIONS OF NAVIER–STOKES EQUATIONS WITH NO ARTIFICIAL NUMERICAL VISCOSITY
- Hyperbolic Difference Equations: A Review of the Courant-Friedrichs-Lewy Paper in the Light of Recent Developments
- The Logarithmic Mean
- Well-Posed Boundary Conditions for the Navier--Stokes Equations
- Spectral/hp Element Methods for Computational Fluid Dynamics
- Multidimensional Summation-by-Parts Operators: General Theory and Application to Simplex Elements
- Weak solutions of nonlinear hyperbolic equations and their numerical computation
- An efficient implicit discontinuous spectral Galerkin method
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