4 papers
Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions
Jan Giesselmann, Hendrik Ranocha
We prove the convergence of hyperbolic approximations for several classes of higher-order PDEs, including the Benjamin-Bona-Mahony, Korteweg-de Vries, Gardner, Kawahara, and Kuramo…
Justification of a Relaxation Approximation for the Navier-Stokes-Cahn-Hilliard System
Jan Giesselmann, Jens Keim, Fabio Leotta +1
The Navier-Stokes-Cahn-Hilliard (NSCH) system governs the diffuse-interface dynamics of two incompressible and immiscible fluids. We consider a relaxation approximation of the NSCH…
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…
Extending relative entropy for Korteweg-Type models with non-monotone pressure:large friction limit and weak-strong uniqueness
Giada Cianfarani Carnevale, Jan Giesselmann
In this paper we study weak-strong uniqueness and singular relaxation limits for the Euler--Korteweg and Navier--Stokes--Korteweg systems with non monotone pressure. Both weak-stro…