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03/01/2023
Monolithic Convex Limiting for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral Element Methods
We extend the monolithic convex limiting (MCL) methodology to nodal disc...
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11/25/2022
A Flux-Differencing Formula for Split-Form Summation By Parts Discretizations of Non-Conservative Systems: Applications to Subcell Limiting for magneto-hydrodynamics
In this paper, we show that diagonal-norm summation by parts (SBP) discr...
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09/15/2022
On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics
We study temporal step size control of explicit Runge-Kutta methods for ...
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03/21/2022
On the Theoretical Foundation of Overset Grid Methods for Hyperbolic Problems II: Entropy Bounded Formulations for Nonlinear Conservation Laws
We derive entropy conserving and entropy dissipative overlapping domain ...
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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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02/01/2022
Subcell limiting strategies for discontinuous Galerkin spectral element methods
We present a general family of subcell limiting strategies to construct ...
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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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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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05/10/2021
On the Theoretical Foundation of Overset Grid Methods for Hyperbolic Problems: Well-Posedness and Conservation
We use the energy method to study the well-posedness of initial-boundary...
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02/11/2021
A Subcell Finite Volume Positivity-Preserving Limiter for DGSEM Discretizations of the Euler Equations
In this paper, we present a positivity-preserving limiter for nodal Disc...
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12/11/2020
A Split-Form, Stable CG/DG-SEM for Wave Propagation Modeled by Linear Hyperbolic Systems
We present a hybrid continuous and discontinuous Galerkin spectral eleme...
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11/23/2020
Stability of Discontinuous Galerkin Spectral Element Schemes for Wave Propagation when the Coefficient Matrices have Jumps
We use the behavior of the L_2 norm of the solutions of linear hyperboli...
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09/28/2020
Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes
Recently, it was discovered that the entropy-conserving/dissipative high...
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08/24/2020
A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics
One of the challenges when simulating astrophysical flows with self-grav...
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07/17/2020
Stability issues of entropy-stable and/or split-form high-order schemes
The focus of the present research is on the analysis of local linear sta...
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05/05/2020
Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations
Discontinuous Galerkin (DG) methods have a long history in computational...
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09/27/2019
Entropy Stable p-Nonconforming Discretizations with the Summation-by-Parts Property for the Compressible Navier-Stokes Equations
The entropy conservative, curvilinear, nonconforming, p-refinement algor...
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07/10/2019
Multi-element SIAC filter for shock capturing applied to high-order discontinuous Galerkin spectral element methods
We build a multi-element variant of the smoothness increasing accuracy c...
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07/07/2019