1 citations · 1 across the 5 of their papers we have counts for
5 papers
Convergence of a Finite Volume Scheme for the Navier-Stokes-Korteweg Model via Dissipative Solutions
Jan Giesselmann, Philipp Öffner, Robert Sauerborn
We propose a concept of dissipative weak (DW) solutions for the Navier-Stokes-Korteweg (NSK) system and prove conditional convergence of a structure-preserving finite volume scheme…
The Lax-Wendroff theorem for Patankar-type methods applied to hyperbolic conservation laws
Janina Bender, Thomas Izgin, Philipp Öffner +1
For hyperbolic conservation laws, the famous Lax-Wendroff theorem delivers sufficient conditions for the limit of a convergent numerical method to be a weak (entropy) solution. Thi…
A necessary condition for non oscillatory and positivity preserving time-integration schemes
Thomas Izgin, Philipp Öffner, Davide Torlo
Modified Patankar (MP) schemes are conservative, linear implicit and unconditionally positivity preserving time-integration schemes constructed for production-destruction systems.…
Entropy conservative high-order fluxes in the presence of boundaries
Simon-Christian Klein, Philipp Öffner
In this paper, we propose a novel development in the context of entropy stable finite-volume/finite-difference schemes. In the first part, we focus on the construction of high-orde…
Comparison to control oscillations in high-order Finite Volume schemes via physical constraint limiters, neural networks and polynomial annihilation
Dorian Hillebrand, Simon-Christian Klein, Philipp Öffner
The construction of high-order structure-preserving numerical schemes to solve hyperbolic conservation laws has attracted a lot of attention in the last decades and various differe…