arXiv subjects

Dennis Höhn

Publications and source records attributed to Dennis Höhn.

4 recordsLinked to original sources

arXiv2026

Entropy-stable and energy-conservative fully-discrete finite element method for non-isothermal phase-field models

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 preserves entropy production and total energy conservation exactly by variable transformations using entropy as main variable instead of temperature. Convergence tests in space are conducted, and representative examples are provided to demonstrate the scheme's effectiveness.

math.NA↗

arXiv2026

Structure-preserving approximation for non-isothermal phase-field models in melt flow

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 system comprises the incompressible Navier-Stokes equations coupled with the non-isothermal Allen-Cahn equation, which includes a non-conserved phase-field equation and a temperature equation. The proposed numerical scheme preserves entropy production exactly and maintains total energy conservation up to a negative numerical dissipation. Convergence tests in both space and time are conducted, and representative examples are provided to demonstrate the scheme's effectiveness.

math.NA↗

arXiv2026

Review of thermodynamic structures and structure-preserving discretisations of Cahn--Hilliard-type models

The Cahn-Hilliard equation and extensions, notably the Cahn-Hilliard-Darcy and Cahn-Hilliard-Navier-Stokes systems, provide widely used frameworks for coupling interfacial thermodynamics with flow. This review surveys the thermodynamic structures underlying these models, focusing on the formulation of free energy functionals, dissipation mechanisms, and variational principles. We compare structural properties, emphasizing how these models encode conservation laws and energy dissipation. A central theme is the translation of these thermodynamic structures into numerical practice by providing representative discretisation strategies that aim to preserve mass conservation, stability, and energy decay. Particular attention is paid to the trade-offs between accuracy, efficiency, and structure preservation in large-scale simulations.

math.NA↗

arXiv2026

Structure-preserving approximation of the non-isothermal Cahn-Hilliard system based on the entropy equation

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 problem-specific mixed explicit-implicit approach for the temporal discretization. To ensure the preservation of structural properties, i.e. conservation of mass and internal energy as well as entropy production, we introduce a suitable variational formulation for the continuous problem, based on the entropy equation. Analytical findings are supported by numerical tests, including convergence analysis.

math.NA↗