11 papers · 1 filter
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…
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…
Structure-preserving approximation of the non-isothermal Cahn-Hilliard system based on the entropy equation
Aaron Brunk, Dennis Höhn, Mária LukáÄová-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…