Related papers: A consistent and conservative volume distribution …
In the present study, a consistent and conservative Phase-Field model is developed to study thermo-gas-liquid-solid flows with liquid-solid phase change. The proposed model is derived with the help of the consistency conditions and exactly…
Phase-field model is a powerful mathematical tool to study the dynamics of interface and morphology changes in fluid mechanics and material sciences. However, numerically solving a phase field model for a real problem is a challenge task…
We present a finite element based variational interface-preserving and conservative phase-field formulation for the modeling of incompressible two-phase flows with surface tension dynamics. The preservation of the hyperbolic tangent…
In order to prevent velocity, pressure, and temperature spikes at material discontinuities occurring when the interface-capturing schemes inconsistently simulate compressible multi-material flows(when the specific heats ratio is…
This paper focusses on finite volume schemes for solving multilayer diffusion problems. We develop a finite volume method that addresses a deficiency of recently proposed finite volume/difference methods, which consider only a limited…
The aim of this work is to propose a provably convergent finite volume scheme for the so-called Stefan-Maxwell model, which describes the evolution of the composition of a multi-component mixture and reads as a cross-diffusion system. The…
The aim of this contribution is to address the convergence study of a time and space approximation scheme for an Allen-Cahn problem with constraint and perturbed by a multiplicative noise of It\^o type. The problem is set in a bounded…
In this paper, we propose a local model reduction approach for subsurface flow problems in stochastic and highly heterogeneous media. To guarantee the mass conservation, we consider the mixed formulation of the flow problem and aim to solve…
In this paper, we present an efficient numerical algorithm for solving the time-dependent Cahn--Hilliard--Navier--Stokes equations that model the flow of two phases with different densities. The pressure-correction step in the projection…
In this paper, we consider the development and analysis of a new explicit compact high-order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic wave propagation…
We present a fast, unconditionally energy-stable numerical scheme for simulating vesicle deformation under osmotic pressure using a phase-field approach. The model couples an Allen-Cahn equation for the biomembrane interface with a…
In hydrodynamic problems involving wave impact on structures, air compressibility is crucial for accurate pressure prediction when an air bubble is entrapped. In this work, the consistent $\delta^{+}$-SPH model, originally developed for…
In this work, we study shape optimization problems in the Stokes flows. By phase-field approaches, the resulted total objective function consists of the dissipation energy of the fluids and the Ginzburg--Landau energy functional as a…
Volume-filling cross-diffusion equations for the components of a tissue structure are formally derived from mass conservation laws and force balances for the interphase pressures and viscous drag forces in a multiphase approach. The…
Reconstruction of an object from points cloud is essential in prosthetics, medical imaging, computer vision, etc. We present an effective algorithm for an Allen--Cahn-type model of reconstruction, employing the Lagrange multiplier approach.…
We present a new multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations. This scheme relies on relaxation and splitting techniques and can be easily used at high order. A fully conservative version is…
The Cahn-Hilliard equation with an externally-prescribed chaotic shear flow is studied in two and three dimensions. The main goal is to compare and contrast the phase separation in two and three dimensions, using high-resolution numerical…
Phase field lattice Boltzmann (LB) models have undergone continuous development, resulting in multiple variants widely used for simulating multiphase flows. However, direct performance comparisons remain limited, especially for…
We present an implicit-explicit finite volume scheme for isentropic two phase flow in all Mach number regimes. The underlying model belongs to the class of symmetric hyperbolic thermodynamically compatible models. The key element of the…
An emerging technique in image segmentation, semi-supervised learning, and general classification problems concerns the use of phase-separating flows defined on finite graphs. This technique was pioneered in Bertozzi and Flenner (2012),…