9 papers
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…
Well-Balanced Subcell Limiting for Discontinuous Galerkin Discretizations of the Shallow-Water Equations
Andrés M. Rueda-RamÃrez, 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 Ãffner, Philipp Öffner, Per Pettersson +1
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…
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…
Boundary-optimized closures for diagonal-norm upwind SBP operators
Ken Mattsson, David Niemelä, David Niemelä +1
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…