arXiv subjects

Andreas Schömer

Publications and source records attributed to Andreas Schömer.

4 recordsLinked to original sources

arXiv2025

Hybrid multiscale method for polymer melts: analysis and simulations

We model the flow behaviour of dense melts of flexible and semiflexible ring polymers in the presence of walls using a hybrid multiscale approach. Specifically, we perform molecular dynamics simulations and apply the Irving-Kirkwood formula to determine an averaged stress tensor for a macroscopic model. For the latter, we choose a Cahn-Hilliard-Navier-Stokes system with dynamic and no-slip boundary conditions. We present numerical simulations of the macroscopic flow that are based on a finite element method. In particular, we present detailed proofs of the solvability and the energy stability of our numerical scheme. Phase segregation under flow between flexible and semiflexible rings, as observed in the microscopic simulations, can be replicated in the macroscopic model by introducing effective attractive forces.

math.NA↗

arXiv2024

Conditional regularity for the compressible Navier-Stokes equations with potential temperature transport

We study conditional regularity for the compressible Navier-Stokes equations with potential temperature transport in a bounded domain $Ω\subset\mathbb{R}^d$, $d\in\{2,3\}$, with no-slip boundary conditions. We first prove the existence and uniqueness of local-in-time strong solutions. Further, we prove a blow-up criterion for the strong solution in terms of $L^\infty$-norms for the density and the velocity.

math.AP↗

arXiv2022

Existence of dissipative solutions to the compressible Navier-Stokes system with potential temperature transport

We introduce dissipative solutions to the compressible Navier-Stokes system with potential temperature transport motivated by the concept of Young measures. We prove their global-in-time existence by means of convergence analysis of a mixed finite element-finite volume method. If a classical solution to the compressible Navier-Stokes system with potential temperature transport exists, we prove the strong convergence of numerical solutions. Our results hold for the full range of adiabatic indices including the physically relevant cases in which the existence of global-in-time weak solutions is open.

math.NA↗

arXiv2021

DMV-strong uniqueness principle for the compressible Navier-Stokes system with potential temperature transport

We establish a DMV-strong uniqueness result for the compressible Navier-Stokes system with potential temperature transport. The concept of generalized, the so-called dissipative measure-valued (DMV), solutions was proposed in [7], where their global-in-time existence was proved. Here we show that strong solutions are stable in the class of DMV solutions. More precisely, a DMV solution coincides with a strong solution emanating from the same initial data as long as the strong solution exists.

math.AP↗