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07/22/2023
High order entropy stable schemes for the quasi-one-dimensional shallow water and compressible Euler equations
High order schemes are known to be unstable in the presence of shock dis...
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06/22/2023
High order entropy stable discontinuous Galerkin spectral element methods through subcell limiting
Subcell limiting strategies for discontinuous Galerkin spectral element ...
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11/22/2022
High-Order Methods for Hypersonic Flows with Strong Shocks and Real Chemistry
We compare high-order methods including spectral difference (SD), flux r...
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03/19/2022
On the entropy projection and the robustness of high order entropy stable discontinuous Galerkin schemes for under-resolved flows
High order entropy stable schemes provide improved robustness for comput...
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03/11/2022
Entropy-Stable Gauss Collocation Methods for Ideal Magneto-Hydrodynamics
In this paper, we present an entropy-stable Gauss collocation discontinu...
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01/27/2022
A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations
High-order entropy-stable discontinuous Galerkin methods for the compres...
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12/20/2021
Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws
Many modern discontinuous Galerkin (DG) methods for conservation laws ma...
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12/14/2021
Entropy stable discontinuous Galerkin methods for the shallow water equations with subcell positivity preservation
High order schemes are known to be unstable in the presence of shock dis...
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09/23/2021
Provably Stable Flux Reconstruction High-Order Methods on Curvilinear Elements
Provably stable flux reconstruction (FR) schemes are derived for partial...
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08/14/2021
Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing
We present Trixi.jl, a Julia package for adaptive high-order numerical s...
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07/23/2021
Discrete adjoint computations for relaxation Runge-Kutta methods
Relaxation Runge-Kutta methods reproduce a fully discrete dissipation (o...
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11/22/2020
Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations
Entropy stable schemes ensure that physically meaningful numerical solut...
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10/31/2020
A high order discontinuous Galerkin method for the symmetric form of the anisotropic viscoelastic wave equation
Wave propagation in real media is affected by various non-trivial physic...
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10/20/2020
Entropy stable discontinuous Galerkin methods for nonlinear conservation laws on networks and multi-dimensional domains
We present a high-order entropy stable discontinuous Galerkin (ESDG) met...
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09/27/2020
High order weight-adjusted discontinuous Galerkin methods for wave propagation on moving curved meshes
This paper presents high order accurate discontinuous Galerkin (DG) meth...
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06/12/2020
Efficient computation of Jacobian matrices for entropy stable summation-by-parts schemes
Entropy stable schemes replicate an entropy inequality at the semi-discr...
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06/12/2020
Explicit Jacobian matrix formulas for entropy stable summation-by-parts schemes
Entropy stable schemes replicate an entropy inequality at the semi-discr...
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05/07/2020
Mortar-based entropy-stable discontinuous Galerkin methods on non-conforming quadrilateral and hexahedral meshes
High-order entropy-stable discontinuous Galerkin (DG) methods for nonlin...
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05/05/2020
High-order entropy stable discontinuous Galerkin methods for the shallow water equations: curved triangular meshes and GPU acceleration
We present a high-order entropy stable discontinuous Galerkin (ESDG) met...
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09/19/2019
Entropy stable reduced order modeling of nonlinear conservation laws
Reduced order models of nonlinear conservation laws in fluid dynamics do...
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09/30/2016