2 citations · 8 across the 16 of their papers we have counts for
17 papers
Generalised dissipative solutions for a non-isothermal phase-field system: existence, weak-strong uniqueness, and long-time behaviour
Aaron Brunk, Marvin Fritz
We study a thermodynamically consistent non-isothermal phase-field system coupling two order parameters and the inverse temperature through a fully non-diagonal Onsager mobility. T…
Surface-tension calibration for N-phase mixtures
M. F. P. ten Eikelder, A. Brunk
Diffuse-interface (phase-field) models are a widely used framework for interfacial dynamics in complex fluids, in which sharp interfaces are replaced by smooth transition layers an…
Symmetric structure-preserving discretization of N-phase incompressible fluid mixtures with arbitrary density ratios
M. F. P. ten Eikelder, A. Brunk
Diffuse-interface models are a widely used framework for interfacial dynamics in complex fluids, in which interfaces are represented through smooth transition layers and capillary…
High-order conforming finite elements for the Cahn-Hilliard equation: Relative-energy stability and energy defects
Aaron Brunk, Marvin Fritz
We study a semidiscrete single-field Galerkin approximation of the Cahn-Hilliard equation using high-order conforming finite element spaces. More specifically, globally finit…
Entropy-stable and energy-conservative fully-discrete finite element method for non-isothermal phase-field models
Aaron Brunk, Dennis Höhn
This work presents a conforming finite-element scheme for non-isothermal phase-field systems coupled to the incompressible Navier-Stokes equations. The proposed numerical scheme pr…
Structure-preserving approximation for non-isothermal phase-field models in melt flow
Aaron Brunk, Dennis Höhn
This work presents a conforming finite-element scheme for the non-isothermal Allen-Cahn-Navier-Stokes system, incorporating periodic, closed, and thermal boundary conditions. The s…
Phase-field investigation of non-isothermal solidification coupled with melt flow dynamics
Timileyin David Oyedeji, Aaron Brunk, Yangyiwei Yang +3
Solidification, coupled with melt flow, plays a critical role in determining the microstructure and properties of materials in several manufacturing processes. Phase-field models c…
Review of thermodynamic structures and structure-preserving discretisations of Cahn--Hilliard-type models
Aaron Brunk, Marco F. P. ten Eikelder, Marvin Fritz +2
The Cahn-Hilliard equation and extensions, notably the Cahn-Hilliard-Darcy and Cahn-Hilliard-Navier-Stokes systems, provide widely used frameworks for coupling interfacial thermody…
A posteriori existence of strong solutions to the Navier-Stokes equations in 3D
Aaron Brunk, Jan Giesselmann, Tabea Tscherpel
Global existence of strong solutions to the three-dimensional incompressible Navier-Stokes equations remains an open problem. A posteriori existence results offer a way to rigorous…
Structure-preserving approximation of the non-isothermal Cahn-Hilliard system based on the entropy equation
Aaron Brunk, Dennis Höhn, Mária Lukáčová-Medvidová
We propose and analyze a structure-preserving approximation of the non-isothermal Cahn-Hilliard equation using conforming finite elements for the spatial discretization and a probl…
Analysis and structure-preserving approximation of a Cahn-Hilliard-Forchheimer system with solution-dependent mass and volume source
Aaron Brunk, Marvin Fritz
We analyze a coupled Cahn-Hilliard-Forchheimer system featuring concentration-dependent mobility, mass source and convective transport. The velocity field is governed by a generali…
A structure-preserving numerical method for quasi-incompressible Navier-Stokes-Maxwell-Stefan systems
Aaron Brunk, Ansgar Jüngel, Maria Lukáčová-Medvid'ová
A conforming finite element scheme with mixed explicit-implicit time discretization for quasi-incompressible Navier-Stokes-Maxwell-Stefan systems in a bounded domain with periodic…
A simple, fully-discrete, unconditionally energy-stable method for the two-phase Navier-Stokes Cahn-Hilliard model with arbitrary density ratios
Aaron Brunk, Marco F. P. ten Eikelder
The two-phase Navier-Stokes Cahn-Hilliard (NSCH) mixture model is a key framework for simulating multiphase flows with non-matching densities. Developing fully discrete, energy-sta…
Analysis and discretization of the Ohta-Kawasaki equation with forcing and degenerate mobility
Aaron Brunk, Marvin Fritz
The Ohta-Kawasaki equation models the mesoscopic phase separation of immiscible polymer chains that form diblock copolymers, with applications in directed self-assembly for lithogr…
Structure-preserving approximation of the Cahn-Hilliard-Biot system
Aaron Brunk, Marvin Fritz
In this work, we propose a structure-preserving discretisation for the recently studied Cahn-Hilliard-Biot system using conforming finite elements in space and problem-adapted expl…
Nonisothermal Cahn-Hilliard Navier-Stokes system
Aaron Brunk, Dennis Schumann
In this research, we introduce and investigate an approximation method that preserves the structural integrity of the non-isothermal Cahn-Hilliard-Navier-Stokes system. Our approac…
Structure-preserving approximation for the non-isothermal Cahn-Hilliard-Navier-Stokes system
Aaron Brunk, Dennis Schumann
In this work we propose and analyse a structure-preserving approximation of the non-isothermal Cahn-Hilliard-Navier-Stokes system using conforming finite elements in space and impl…