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In this paper, we present a new computational framework to approximate a Cahn-Hilliard-Navier-Stokes model with variable density and degenerate mobility that preserves the mass of the mixture, the pointwise bounds of the density and the…

Numerical Analysis · Mathematics 2024-12-02 Daniel Acosta-Soba , Francisco Guillén-González , J. Rafael Rodríguez-Galván , Jin Wang

We propose and analyze a linearly stabilized semi-implicit diffusive Crank--Nicolson scheme for the Cahn--Hilliard gradient flow. In this scheme, the nonlinear bulk force is treated explicitly with two second-order stabilization terms. This…

Numerical Analysis · Mathematics 2020-04-14 Lin Wang , Haijun Yu

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 approach extends a previously proposed technique [1], which…

Numerical Analysis · Mathematics 2024-05-24 Aaron Brunk , Dennis Schumann

We propose a thermodynamically consistent phase-field model for the flow of a mixture of two different viscous incompressible fluids of equal density in a bounded domain. We prove the well-posedness of local-in-time strong solutions by…

Analysis of PDEs · Mathematics 2025-11-18 Helmut Abels , Alice Marveggio , Andrea Poiatti

Binary-fluid flows can be modeled using the Navier-Stokes-Cahn-Hilliard equations, which represent the boundary between the fluid constituents by a diffuse interface. The diffuse-interface model allows for complex geometries and topological…

We consider the numerical approximation of a sharp-interface model for two-phase flow, which is given by the incompressible Navier-Stokes equations in the bulk domain together with the classical interface conditions on the interface. We…

Numerical Analysis · Mathematics 2023-06-21 Harald Garcke , Robert Nürnberg , Quan Zhao

We present an energy-stable scheme for numerically approximating the governing equations for incompressible two-phase flows with different densities and dynamic viscosities for the two fluids. The proposed scheme employs a scalar-valued…

Computational Physics · Physics 2019-06-26 Z. Yang , S. Dong

In this paper, we consider a two-dimensional diffuse interface model for the phase separation of an incompressible and isothermal binary fluid mixture with matched densities. This model consists of the Navier--Stokes equations, nonlinearly…

Analysis of PDEs · Mathematics 2018-01-09 S. Frigeri , M. Grasselli , J. Sprekels

We propose a novel decoupled unconditionally stable numerical scheme for the simulation of two-phase flow in a Hele-Shaw cell which is governed by the Cahn-Hilliard-Hele-Shaw system (CHHS) with variable viscosity. The temporal…

Numerical Analysis · Mathematics 2014-11-03 Daozhi Han

We study a quasi-incompressible Navier--Stokes/Cahn--Hilliard coupled system which describes the motion of two macroscopically immiscible incompressible viscous fluids with partial mixing in a small interfacial region and long-range…

Analysis of PDEs · Mathematics 2025-08-12 Mingwen Fei , Xiang Fei , Daozhi Han , Yadong Liu

We propose and analyze unfitted finite element approximations for the two-phase incompressible Navier--Stokes flow in an axisymmetric setting. The discretized schemes are based on an Eulerian weak formulation for the Navier--Stokes equation…

Numerical Analysis · Mathematics 2023-09-12 Harald Garcke , Robert Nürnberg , Quan Zhao

A system of partial differential equations for a diffusion interface model is considered for the stationary motion of two macroscopically immiscible, viscous Newtonian fluids in a three-dimensional bounded domain. The governing equations…

Analysis of PDEs · Mathematics 2020-07-28 Zhilei Liang , Dehua Wang

In this paper, we consider numerical approximations for solving the nonlinear magneto-hydrodynamical system, that couples the Navier-Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is…

Numerical Analysis · Mathematics 2017-11-28 Guodong Zhang , Xiaoming He , Xiaofeng Yang

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

We consider a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids with matched constant densities. This model consists of the Navier-Stokes system coupled with a convective nonlocal Cahn-Hilliard equation…

Analysis of PDEs · Mathematics 2014-04-16 Sergio Frigeri , Maurizio Grasselli , Elisabetta Rocca

In this paper, we investigate a system coupled by nonhomogeneous incompressible Navier-Stokes equations and Allen-Cahn equations describing a diffuse interface for two-phase flow of viscous fluids with different densities in a bounded…

Analysis of PDEs · Mathematics 2025-03-06 Yinghua Li , Wenlin Ye

We have developed an efficient and unconditionally energy-stable method for simulating droplet formation dynamics. Our approach involves a novel time-marching scheme based on the scalar auxiliary variable technique, specifically designed…

Numerical Analysis · Mathematics 2024-02-08 Jinpeng Zhang , Changjuan Zhang , Xiaoping Wang

In this paper we construct new fully decoupled and high-order implicit-explicit (IMEX) schemes for the two-phase incompressible flows based on the new generalized scalar auxiliary variable approach with optimal energy approximation…

Numerical Analysis · Mathematics 2023-11-10 Xiaoli Li , Nan Zheng , Jie Shen , Zhengguang Liu

This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/Allen-Cahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the…

Analysis of PDEs · Mathematics 2021-10-28 Yazhou Chen , Hakho Hong , Xiaoding Shi

In this paper we describe two fully mass conservative, energy stable, finite difference methods on a staggered grid for the quasi-incompressible Navier-Stokes-Cahn-Hilliard (q-NSCH) system governing a binary incompressible fluid flow with…

Numerical Analysis · Mathematics 2017-10-11 Zhenlin Guo , Ping Lin , Steven Wise , John Lowengrub