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math.NA2022
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.…
math.NA2022
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…
math.NA2022
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…