6 papers · 1 filter
Some new properties of an Active flux type scheme: PamPa
Rémi Abgrall, Philipp Ãffner, Yongle Liu
In this paper, we provide a few new properties of Active Flux (AF)/Point-Average-Moment PolynomiAl-interpreted (\pampa) schemes. First, we show, in full generality, that the AF/pam…
Why summation by parts is not enough
Jan Glaubitz, Armin Iske, Joshua Lampert +1
We investigate the construction and performance of summation-by-parts (SBP) operators, which offer a powerful framework for the systematic development of structure-preserving numer…
A Structure Preserving Finite Volume Scheme for the Navier-Stokes-Korteweg Equations
Jan Giesselmann, Philipp Ãffner, Robert Sauerborn
We present a semi-discrete finite volume scheme for the local NavierStokes-Korteweg and Euler-Korteweg systems. Our scheme is applicable for equidistant Cartesian meshes in one and…
Discontinuous Galerkin methods for the complete stochastic Euler equations
Dominic Breit, Thamsanqa Castern Moyo, Philipp Ãffner
In recent years, stochastic effects have become increasingly relevant for describing fluid behaviour, particularly in the context of turbulence. The most important model for invisc…
Locally energy-stable finite element schemes for incompressible flow problems: Design and analysis for equal-order interpolations
Hennes Hajduk, Dmitri Kuzmin, Gert Lube +1
We show that finite element discretizations of incompressible flow problems can be designed to ensure preservation/dissipation of kinetic energy not only globally but also locally.…
An optimization-based construction procedure for function space based summation-by-parts operators on arbitrary grids
Jan Glaubitz, Jan Nordström, Philipp Ãffner
We introduce a novel construction procedure for one-dimensional summation-by-parts (SBP) operators. Existing construction procedures for FSBP operators of the form p…