Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws

A Novel Robust Strategy for Discontinuous Galerkin Methods in Computational Fluid Mechanics: Why? When? What? Where?

(2021) Gregor J. Gassner et al.   Frontiers in Physics

Efficient Parallel 3D Computation of the Compressible Euler Equations with an Invariant-domain Preserving Second-order Finite-element Scheme

(2021) Matthias Maier et al.   ACM Transactions on Parallel Computing

An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part II: Subcell finite volume shock capturing

(2021) Andrés M. Rueda-Ramírez et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Entropy-Stable, High-Order Summation-by-Parts Discretizations Without Interface Penalties

(2020) Jason E. Hicken   JOURNAL OF SCIENTIFIC COMPUTING

FLEXI: A high order discontinuous Galerkin framework for hyperbolic–parabolic conservation laws

(2020) Nico Krais et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

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

(2020) Matteo Parsani et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Preventing spurious pressure oscillations in split convective form discretization for compressible flows

(2020) Nao Shima et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Encapsulated high order difference operators on curvilinear non-conforming grids

(2019) Oskar Ålund et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Skew-Symmetric Entropy Stable Modal Discontinuous Galerkin Formulations

(2019) Jesse Chan   JOURNAL OF SCIENTIFIC COMPUTING

High order entropy conservative central schemes for wide ranges of compressible gas dynamics and MHD flows

(2018) Björn Sjögreen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations

(2018) Andrew R. Winters et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Generalised summation-by-parts operators and variable coefficients

(2018) Hendrik Ranocha   JOURNAL OF COMPUTATIONAL PHYSICS

On discretely entropy conservative and entropy stable discontinuous Galerkin methods

(2018) Jesse Chan   JOURNAL OF COMPUTATIONAL PHYSICS

Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements

(2018) Jared Crean et al.   JOURNAL OF COMPUTATIONAL PHYSICS

On the use of kinetic energy preserving DG-schemes for large eddy simulation

(2017) David Flad et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws

(2017) Tianheng Chen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry

(2017) Niklas Wintermeyer et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Julia: A Fresh Approach to Numerical Computing

(2017) Jeff Bezanson et al.   SIAM REVIEW

Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations

(2016) Gregor J. Gassner et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Multidimensional Summation-by-Parts Operators: General Theory and Application to Simplex Elements

(2016) Jason E. Hicken et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

A comparison of two entropy stable discontinuous Galerkin spectral element approximations for the shallow water equations with non-constant topography

(2015) Andrew R. Winters et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations

(2014) David C. Del Rey Fernández et al.   COMPUTERS & FLUIDS

A kinetic energy preserving nodal discontinuous Galerkin spectral element method

(2014) Gregor J. Gassner   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS

Review of summation-by-parts schemes for initial–boundary-value problems

(2014) Magnus Svärd et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A generalized framework for nodal first derivative summation-by-parts operators

(2014) David C. Del Rey Fernández et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces

(2014) Mark H. Carpenter et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Kinetic Energy Preserving and Entropy Stable Finite Volume Schemes for Compressible Euler and Navier-Stokes Equations

(2013) Praveen Chandrashekar   Communications in Computational Physics

A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods

(2013) Gregor J. Gassner   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: Theory and boundary conditions

(2012) Travis C. Fisher et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Arbitrarily High-order Accurate Entropy Stable Essentially Nonoscillatory Schemes for Systems of Conservation Laws

(2012) Ulrik S. Fjordholm et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

A Comparison of the Dispersion and Dissipation Errors of Gauss and Gauss–Lobatto Discontinuous Galerkin Spectral Element Methods

(2011) Gregor Gassner et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

On the Quadrature and Weak Form Choices in Collocation Type Discontinuous Galerkin Spectral Element Methods

(2010) David A. Kopriva et al.   JOURNAL OF SCIENTIFIC COMPUTING

Roofline

(2009) Samuel Williams et al.   COMMUNICATIONS OF THE ACM

Affordable, entropy-consistent Euler flux functions II: Entropy production at shocks

(2009) Farzad Ismail et al.   JOURNAL OF COMPUTATIONAL PHYSICS