Efficient entropy-stable discontinuous spectral-element methods using tensor-product summation-by-parts operators on triangles and tetrahedra

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains
Review of summation-by-parts schemes for initial-boundary-value problems
A generalized framework for nodal first derivative summation-by-parts operators
A uniquely defined entropy stable matrix dissipation operator for high Mach number ideal MHD and compressible Euler simulations
Nodal discontinuous Galerkin methods on graphics processors
Affordable, entropy-consistent Euler flux functions. II: Entropy production at shocks
A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions
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
Approximate Riemann solvers, parameter vectors, and difference schemes
Spectral methods for problems in complex geometries
On the symmetric form of systems of conservation laws with entropy
Spectral methods on triangles and other domains
A triangular spectral element method; applications to the incompressible Navier-Stokes equations.
On discretely entropy conservative and entropy stable discontinuous Galerkin methods
Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
Comparison of some entropy conservative numerical fluxes for the Euler 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
Simultaneous approximation terms for multi-dimensional summation-by-parts operators
Tetrahedral \(hp\) finite elements: Algorithms and flow simulations
Efficient implementation of weighted ENO schemes
A discontinuous Galerkin spectral/\(hp\) method on hybrid grids
Entropy conserving and kinetic energy preserving numerical methods for the Euler equations using summation-by-parts operators
Subcell limiting strategies for discontinuous Galerkin spectral element methods
A p-adaptive discontinuous Galerkin method with hp-shock capturing
High-order accurate entropy-stable discontinuous collocated Galerkin methods with the summation-by-parts property for compressible CFD frameworks: scalable SSDC algorithms and flow solver
A unifying algebraic framework for discontinuous Galerkin and flux reconstruction methods based on the summation-by-parts property
Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes
On discretely entropy stable weight-adjusted discontinuous Galerkin methods: curvilinear meshes
Analysis and entropy stability of the line-based discontinuous Galerkin method
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 shock capturing space-time discontinuous Galerkin schemes for systems of conservation laws
Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: theory and boundary conditions
Metric identities and the discontinuous spectral element method on curvilinear meshes
Mortar-based entropy-stable discontinuous Galerkin methods on non-conforming quadrilateral and hexahedral meshes
A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations
A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods
An Energy Stable Discontinuous Galerkin Spectral Element Discretization for Variable Coefficient Advection Problems
Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces
A Comparison of High Order Interpolation Nodes for the Pyramid
Solving Ordinary Differential Equations I
Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
Implementing Spectral Methods for Partial Differential Equations
The Numerical Viscosity of Entropy Stable Schemes for Systems of Conservation Laws. I
Simplified Second-Order Godunov-Type Methods
Geometric Conservation Law and Its Application to Flow Computations on Moving Grids
A discontinuous Galerkin method for the Navier-Stokes equations
Turbulent Flows
Weight-Adjusted Discontinuous Galerkin Methods: Curvilinear Meshes
Fully Discrete, Entropy Conservative Schemes of ArbitraryOrder
Efficient Matrix-Free High-Order Finite Element Evaluation for Simplicial Elements
Efficient Entropy Stable Gauss Collocation Methods
Kinetic Energy Preserving and Entropy Stable Finite Volume Schemes for Compressible Euler and Navier-Stokes Equations
FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
Systems of Conservation Equations with a Convex Extension
Spectral/hp Element Methods for Computational Fluid Dynamics
Multidimensional Summation-by-Parts Operators: General Theory and Application to Simplex Elements
Hyperbolic Conservation Laws in Continuum Physics
High-order positivity-preserving entropy stable schemes for the 3-D compressible Navier-Stokes equations
High-order symmetric cubature rules for tetrahedra and pyramids
Efficient tensor-product spectral-element operators with the summation-by-parts property on curved triangles and tetrahedra
Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws

This page was built for publication: Efficient entropy-stable discontinuous spectral-element methods using tensor-product summation-by-parts operators on triangles and tetrahedra