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A general diffuse interface model with a realistic equation of state (e.g. Peng-Robinson equation of state) is proposed to describe the multi-component two-phase fluid flow based on the principles of the NVT-based framework which is a…

Numerical Analysis · Mathematics 2016-11-29 Jisheng Kou , Shuyu Sun

This report summarises the results for the numerical simulation of thermocapillary convection in a two-fluid system with a deformable interface. An explicit technique with 3rd order Runge-Kutta method in time, 2nd order ENO for the…

Fluid Dynamics · Physics 2021-10-08 Swagat Kumar Nayak

In this paper, we introduce an interfacial profile-preserving approach for phase field modeling for simulating incompressible two-phase flows. While the advective Cahn-Hilliard equation effectively captures the topological evolution of…

Fluid Dynamics · Physics 2023-10-03 Haohao Hao , Xiangwei Li , Chenglin Jiang , Huanshu Tan

Solidification, coupled with melt flow, plays a critical role in determining the microstructure and properties of materials in several manufacturing processes. Phase-field models coupled with the Navier-Stokes equations are widely used to…

We present a thermodynamically consistent phase-field model for simulating fluid transport across semi-permeable membranes, with a particular focus on osmotic pressure effects. The model extends the classical Navier-Stokes-Cahn-Hilliard…

Fluid Dynamics · Physics 2025-06-16 Ruihan Guo , Jie Shen , Shixin Xu , Xianmin Xu

The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of fluid density on the phase-field order parameter. Driven by…

Numerical Analysis · Mathematics 2023-09-27 Yerbol Palzhanov , Alexander Zhiliakov , Annalisa Quaini , Maxim Olshanskii

In this paper we present numerical models for electrodynamical flows with time-dependent electrical fields with transport of bubbles. Such models are applied in e-jet printing, e.g., additive manufacturing (AM), and convective cooling,…

Computational Physics · Physics 2020-05-20 Jürgen Geiser , Paul Mertin

A phase-field crystal model based on the density-field approach incorporating high-order interparticle direct correlations is developed to study vapor-liquid-solid coexistence and transitions within a single continuum description.…

Materials Science · Physics 2020-10-21 Zi-Le Wang , Zhirong Liu , Zhi-Feng Huang , Wenhui Duan

We present a systematic derivation of thermodynamically consistent hydrodynamic phase field models for compressible viscous fluid mixtures using the generalized Onsager principle. By maintaining momentum conservation while enforcing mass…

Numerical Analysis · Mathematics 2018-09-25 Xueping Zhao , Tiezheng Qian , Qi Wang

We use direct numerical simulations to investigate the interaction between the temperature field of a fluid and the temperature of small particles suspended in the flow, employing both one and two-way thermal coupling, in a statistically…

Fluid Dynamics · Physics 2020-01-08 Maurizio Carbone , Andrew D. Bragg , Michele Iovieno

Thermal compositional multiphase flow in porous media with phase transitions involves complex nonlinear interactions among flow, transport, and phase equilibrium. This paper presents a persistent-variable formulation for thermal…

Computational Physics · Physics 2025-12-05 Veljko Lipovac , Omar Duran , Eirik Keilegavlen , Inga Berre

We present a new hydrodynamic model for incompressible binary fluids that is thermodynamically consistent and non-isothermal. This model follows the generalized Onsager principle and Boussinesq approximation and preserves the volume of each…

Fluid Dynamics · Physics 2023-08-14 Shouwen Sun , Liangliang Lei , Qi Wang

We study a diffuse-interface model for thermally driven phase separation in viscous incompressible mixtures. The system couples a convective Cahn-Hilliard equation for the order parameter with a Stokes subsystem for the velocity-pressure…

Analysis of PDEs · Mathematics 2026-04-24 Maria Deliyianni , Boris Muha , Andrej Novak

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…

Analysis of PDEs · Mathematics 2019-12-20 Christian Rohde , Lars von Wolff

An in-house numerical model has been developed to study the temperature destratification induced by bubble plumes in reservoirs. The mean flow of the mixed fluid phase is solved using the Reynolds-Averaged Navier-Stokes Equations, while the…

Fluid Dynamics · Physics 2024-11-06 Yiran Li , Dongming Liu

The rate of melting of a solid and the rate of deformation of the resulting melt due to capillary forces are comparable in additive manufacturing applications. This dynamic structural change of a melting solid is extremely challenging to…

Computational Physics · Physics 2018-04-18 Michael Blank , Prapanch Nair , Thorsten Pöschel

In this paper we report on 2D numerical simulations concerning linear and nonlinear evolution of surface-tension-driven instability in two-fluid systems heated from below using classical and phase-field models. In the phase-field formalism,…

Pattern Formation and Solitons · Physics 2015-06-26 Rodica Borcia , Domnic Merkt , Michael Bestehorn

We derive a thermodynamically consistent model, which describes the time evolution of a two-phase flow in an evolving domain. The movement of the free boundary of the domain is driven by the velocity field of the mixture in the bulk, which…

Analysis of PDEs · Mathematics 2026-04-29 Patrik Knopf , Yadong Liu

The paper addresses a two-temperature model for simulating compressible two-phase flow taking into account diffusion processes related to the heat conduction and viscosity of the phases. This model is reduced from the two-phase…

Numerical Analysis · Mathematics 2022-07-27 Chao Zhang , Igor Menshov , Lifeng Wang , Zhijun Shen

This work presents a unified numerical framework for simulating incompressible flows within the coupled fluid-porous-medium system and involving heat and solute transport and phase-changing process. A complete set of governing equations is…

Fluid Dynamics · Physics 2026-01-28 Rongfu Guo , Yantao Yang