11 citations · 11 across the 7 of their papers we have counts for
19 papers · 1 filter
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…
A high-order, structure preserving scheme for the stochastic Galerkin shallow water equations -- unification and two-dimensional extension
Philipp Öffner, Per Pettersson, Andrew R. Winters
Recently, two independent research efforts have been made to study the stochastic Galerkin formulation of the shallow water equations. Bender and Öffner developed entropy-conservat…
Entropy analysis and entropy stable DG methods for the 1D shallow water moment equations
Julio Careaga, Patrick Ersing, Julian Koellermeier +1
We demonstrate that the one-dimensional shallow water moment equations satisfy an auxiliary entropy conservation law, where the entropy function corresponds to the total energy. Ad…
Boundary-optimized closures for diagonal-norm upwind SBP operators
Ken Mattsson, David Niemelä, Andrew R. Winters
By employing non-equispaced grid points near boundaries, boundary-optimized upwind finite-difference operators of orders up to nine are developed. The boundary closures are constru…
A new class of entropy stable fluctuations for the discontinuous Galerkin method with application to the Saint-Venant-Exner model
Patrick Ersing, Andrew R. Winters
In this work we consider entropy stable discontinuous Galerkin methods applied to nonconservative hyperbolic systems. We introduce a new class of entropy conservative fluctuations…
Numerical boundary flux functions that give provable bounds for nonlinear initial boundary value problems with open boundaries
Andrew R. Winters, David A. Kopriva, Jan Nordström
We present a strategy for interpreting nonlinear, characteristic-type penalty terms as numerical boundary flux functions that provide provable bounds for solutions to nonlinear hyp…