arXiv subjects

Lars von Wolff

Publications and source records attributed to Lars von Wolff.

4 recordsLinked to original sources

arXiv2026

Thermodynamically consistent phase-field modeling and numerical simulation for reactive two-phase fluid-solid dynamics

We introduce a coupled Cahn-Hilliard Navier-Stokes model that governs the reactive two-phase dynamics of a system that consists of a fluid and a solid phase and prove its thermodynamic consistency. Moreover, we present an associated fully-discrete numerical method that relies on a continuous finite element approach and a semi-implicit time-stepping method. Our main theoretical result establishes that the fully discrete method satisfies an analog of the free energy dissipation inequality, provided that the phase-field variable remains within prescribed bounds. Numerical experiments confirm the theoretical findings and show the applicability of the method for realistic settings. In this context, we provide a preprocessing strategy that enables computing fluid flow in complex geometries given a sharp-interface formulation of the initial phase distribution. Moreover, we briefly introduce different solution strategies for the novel discretization based on the monolithic and partitioned solution paradigms and assess these in a comparative study.

math.NA↗

arXiv2021

Upscaling of a Cahn-Hilliard Navier-Stokes Model with Precipitation and Dissolution in a Thin Strip

We consider a phase-field model for the incompressible flow of two immiscible fluids. This model extends widespread models for two fluid phases by including a third, solid phase, which can evolve due to e.g. precipitation and dissolution. We consider a simple, two-dimensional geometry of a thin strip, which can still be seen as the representation of a single pore throat in a porous medium. Under moderate assumptions on the Peclet number and the capillary number, we investigate the limit case when the ratio between the width and the length of the strip is going to zero. In this way and employing transversal averaging, we derive an upscaled model. The result is a multi-scale model consisting of the upscaled equations for the total flux and the ion transport, while the phase-field equation has to be solved in cell-problems at the pore scale to determine the position of interfaces. We also investigate the sharp-interface limit of the multi-scale model, in which the phase-field parameter approaches 0. The resulting sharp-interface model consists only of Darcy-scale equations, as the cell-problems can be solved explicitly. Notably we find asymptotic consistency, that is the upscaling process and the sharp-interface limit commute. We use numerical results to investigate the validity of the upscaling when discontinuities are formed in the upscaled model.

math.AP↗

arXiv2019

A Ternary Cahn-Hilliard Navier-Stokes Model for Two Phase Flow with Precipitation and Dissolution

We consider the incompressible flow of two immiscible fluids in the presence of a solid phase that undergoes changes in time due to precipitation and dissolution effects. Based on a seminal sharp interface model a phase field approach is suggested that couples the Navier-Stokes equations and the solid's ion concentration transport equation with the Cahn-Hilliard evolution for the phase fields. The model is shown to preserve the fundamental conservation constraints and to obey the second law of thermodynamics for a novel free energy formulation. An extended analysis for vanishing interfacial width reveals that in this limit the sharp interface model is recovered, including all relevant transmission conditions. Notably, the new phase field model is able to realize Navier-slip conditions for solid-fluid interfaces in the limit.

math.AP↗

arXiv2019

Homogenization of Non-Local Navier-Stokes-Korteweg Equations for Compressible Liquid-Vapour Flow in Porous Media

We consider a nonlocal version of the quasi-static Navier-Stokes-Korteweg equations with a non-monotone pressure law. This system governs the low-Reynolds number dynamics of a compressible viscous fluid that may take either a liquid or a vapour state. For a porous domain that is perforated by cavities with diameter proportional to their mutual distance the homogenization limit is analyzed. We extend the results for compressible one-phase flow with polytropic pressure laws and prove that the effective motion is governed by a nonlocal version of the Cahn-Hilliard equation. Crucial for the analysis is the convolution-like structure of the nonlocal capillarity term that allows to equip the system with a generalized convex free energy. Moreover, the capillarity term accounts not only for the energetic interaction within the fluid but also for the interaction with a solid wall boundary.

math.AP↗