350 citations · 1.2k across the 53 of their papers we have counts for
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A Discontinuous Galerkin Method for the Intrinsic Beam Model with Kelvin-Voigt Damping
Shivam Sundriyal, Christian Bleffert, Lukas Dreyer +3
We present an energy-stable discontinuous Galerkin (DG) spatial discretization of the intrinsic beam equations with Kelvin-Voigt damping. We reformulate the governing equations by…
Invariant-domain-preserving limiting with Adaptive Mesh Refinement for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral Element Methods
Benjamin Bolm, Andrés M. Rueda-Ramírez, Dmitri Kuzmin +1
We present an invariant-domain-preserving (IDP) treatment of nonconforming interfaces for Legendre--Gauss--Lobatto Discontinuous Galerkin Spectral Element Methods (LGL-DGSEM) with…
Well-Balanced Subcell Limiting for Discontinuous Galerkin Discretizations of the Shallow-Water Equations
Andrés M. Rueda-Ramírez, Patrick Ersing, Andrew R. Winters +1
High-order discontinuous Galerkin (DG) methods equipped with subcell finite-volume (FV) limiters provide an efficient framework for the simulation of nonlinear hyperbolic balance l…
SBP-FDEC: Summation-by-Parts Finite Difference Exterior Calculus
Daniel Bach, Andrés M. Rueda-Ramírez, Eric Sonnendrücker +2
We demonstrate that we can carry over the strategy of Finite Element Exterior Calculus (FEEC) to Summation-by-Parts (SBP) Finite Difference (FD) methods to achieve divergence- and…
Entropy-Stable Discontinuous Spectral-Element Methods for the Spherical Shallow Water Equations in Covariant Form
Tristan Montoya, Andrés M. Rueda-Ramírez, Gregor J. Gassner
We introduce discontinuous spectral-element methods of arbitrary order that are well balanced, conservative of mass, and conservative or dissipative of total energy (i.e., a mathem…
An Entropy-Stable Discontinuous Galerkin Discretization of the Ideal Multi-Ion Magnetohydrodynamics System
Andrés M Rueda-Ramírez, Aleksey Sikstel, Gregor J Gassner
In this paper, we present an entropy-stable (ES) discretization using a nodal discontinuous Galerkin (DG) method for the ideal multi-ion magneto-hydrodynamics (MHD) equations. We s…
On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws
Hendrik Ranocha, Andrew R. Winters, Michael Schlottke-Lakemper +3
We use the framework of upwind summation-by-parts (SBP) operators developed by Mattsson (2017, doi:10.1016/j.jcp.2017.01.042) and study different flux vector splittings in this con…
Monolithic Convex Limiting for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral Element Methods
Andrés M Rueda-Ramírez, Benjamin Bolm, Dmitri Kuzmin +1
We extend the monolithic convex limiting (MCL) methodology to nodal discontinuous Galerkin spectral element methods (DGSEM). The use of Legendre-Gauss-Lobatto (LGL) quadrature endo…
A Flux-Differencing Formula for Split-Form Summation By Parts Discretizations of Non-Conservative Systems: Applications to Subcell Limiting for magneto-hydrodynamics
Andrés M Rueda-Ramírez, Gregor J Gassner
In this paper, we show that diagonal-norm summation by parts (SBP) discretizations of general non-conservative systems of hyperbolic balance laws can be rewritten as a finite-volum…
On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics
Hendrik Ranocha, Andrew R. Winters, Hugo Guillermo Castro +4
We study temporal step size control of explicit Runge-Kutta methods for compressible computational fluid dynamics (CFD), including the Navier-Stokes equations and hyperbolic system…
On the entropy projection and the robustness of high order entropy stable discontinuous Galerkin schemes for under-resolved flows
Jesse Chan, Hendrik Ranocha, Andres Rueda-Ramirez +2
High order entropy stable schemes provide improved robustness for computational simulations of fluid flows. However, additional stabilization and positivity preserving limiting can…
Entropy-Stable Gauss Collocation Methods for Ideal Magneto-Hydrodynamics
Andrés M Rueda-Ramírez, Florian J Hindenlang, Jesse Chan +1
In this paper, we present an entropy-stable Gauss collocation discontinuous Galerkin (DG) method on 3D curvilinear meshes for the GLM-MHD equations: the single-fluid magneto-hydrod…
On the Theoretical Foundation of Overset Grid Methods for Hyperbolic Problems II: Entropy Bounded Formulations for Nonlinear Conservation Laws
David A. Kopriva, Gregor J. Gassner, Jan Nordstrom
We derive entropy conserving and entropy dissipative overlapping domain formulations for systems of nonlinear hyperbolic equations in conservation form, such as would be approximat…
Subcell limiting strategies for discontinuous Galerkin spectral element methods
Andrés M. Rueda-Ramírez, Will Pazner, Gregor J. Gassner
We present a general family of subcell limiting strategies to construct robust high-order accurate nodal discontinuous Galerkin (DG) schemes. The main strategy is to construct comp…
Local Fourier Analysis of a Space-Time Multigrid Method for DG-SEM for the Linear Advection Equation
Lea M. Versbach, Philipp Birken, Viktor Linders +1
In this paper we present a Local Fourier Analysis of a space-time multigrid solver for a hyperbolic test problem. The space-time discretization is based on arbitrarily high order d…
On the Theoretical Foundation of Overset Grid Methods for Hyperbolic Problems: Well-Posedness and Conservation
David A. Kopriva, Jan Nordström, Gregor J. Gassner
We use the energy method to study the well-posedness of initial-boundary value problems approximated by overset mesh methods in one and two space dimensions for linear constant-coe…
A Subcell Finite Volume Positivity-Preserving Limiter for DGSEM Discretizations of the Euler Equations
Andrés M. Rueda-Ramírez, Gregor J. Gassner
In this paper, we present a positivity-preserving limiter for nodal Discontinuous Galerkin disctretizations of the compressible Euler equations. We use a Legendre-Gauss-Lobatto (LG…
An Entropy Stable Nodal Discontinuous Galerkin Method for the resistive MHD Equations. Part II: Subcell Finite Volume Shock Capturing
Andrés M Rueda-Ramírez, Sebastian Hennemann, Florian J Hindenlang +2
The second paper of this series presents two robust entropy stable shock-capturing methods for discontinuous Galerkin spectral element (DGSEM) discretizations of the compressible m…
Stability of Discontinuous Galerkin Spectral Element Schemes for Wave Propagation when the Coefficient Matrices have Jumps
David A. Kopriva, Gregor J. Gassner, Jan Nordström
We use the behavior of the norm of the solutions of linear hyperbolic equations with discontinuous coefficient matrices as a surrogate to infer stability of discontinuous G…
A Sub-Element Adaptive Shock Capturing Approach for Discontinuous Galerkin Methods
Johannes Markert, Gregor Gassner, Stefanie Walch
In this paper, a new strategy for a sub-element based shock capturing for discontinuous Galerkin (DG) approximations is presented. The idea is to interpret a DG element as a collec…
A Split-Form, Stable CG/DG-SEM for Wave Propagation Modeled by Linear Hyperbolic Systems
David A. Kopriva, Gregor J. Gassner
We present a hybrid continuous and discontinuous Galerkin spectral element approximation that leverages the advantages of each approach. The continuous Galerkin approximation is us…
Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes
Hendrik Ranocha, Gregor J Gassner
Recently, it was discovered that the entropy-conserving/dissipative high-order split-form discontinuous Galerkin discretizations have robustness issues when trying to solve the sim…
A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics
Michael Schlottke-Lakemper, Andrew R. Winters, Hendrik Ranocha +1
One of the challenges when simulating astrophysical flows with self-gravity is to compute the gravitational forces. In contrast to the hyperbolic hydrodynamic equations, the gravit…
Stability issues of entropy-stable and/or split-form high-order schemes
Gregor J. Gassner, Magnus Svärd, Florian J. Hindenlang
The focus of the present research is on the analysis of local energy stability of high-order (including split-form) summation-by-parts methods, with e.g. two-point entropy-conservi…