Related papers: A Fully Parallelizable Loosely Coupled Scheme for …
We analyze a system of PDEs governing the interaction between two compressible mutually noninteracting fluids and a shell of Koiter type encompassing a time dependent 3D domain filled by the fluids. The dynamics of the fluids is modelled by…
In this work we consider a poroelastic flexible material that may deform largely which is situated in an incompressible fluid driven by the Navier-Stokes equations in two or three space dimensions. By a variational approach we show…
Modeling coupled systems of free flow adjacent to a porous medium by means of fully resolved Navier-Stokes equations is limited by the immense computational cost and is thus only feasible for relatively small domains. Model reduction allows…
In this work, we propose a fully discrete energy stable scheme for the phase-field moving contact line model with variable densities and viscosities. The mathematical model consists of a Cahn-Hilliard equation, a Navier-Stokes equation and…
In this paper, a parallel domain decomposition method is proposed for solving the fully-mixed Stokes-dual-permeability fluid flow model with Beavers-Joseph (BJ) interface conditions. Three Robin-type boundary conditions and a modified weak…
We present a new splitting method for time-dependent convection-dominated diffusion problems. The original convection diffusion system is split into two sub-systems: a pure convection system and a diffusion system. At each time step, a…
We show that, using the Crouzeix-Raviart scheme, a cheap algebraic transformation, applied to the coupled velocity-pressure linear systems issued from the transient or steady Stokes or Navier-Stokes problems, leads to a linear system only…
We study a novel approach for the existence of solutions to an incompressible fluid-rigid body interaction problem in three dimensions. Our approach introduces an iteration based on a sequence of related problems posed on domains with…
We address numerical solvers for a poromechanics model particularly adapted for soft materials, as it generally respects thermodynamics principles and energy balance. Considering the multi-physics nature of the problem, which involves solid…
This work proposes an efficient, linear, and fully decoupled pressure-correction scheme for the 2D stochastic Navier-Stokes equations with multiplicative noise and Dirichlet boundary condition. Leveraging the auxiliary variable approach,…
We consider a mathematical model for the interactions of an elastic body fully immersed in a viscous, incompressible fluid. The corresponding composite PDE system comprises a linearized Navier-Stokes system and a dynamic system of…
In this paper, we consider the numerical solution of some nonlinear poroelasticity problems that are of Biot type and develop a general algorithm for solving nonlinear coupled systems. We discuss the difficulties associated with flow and…
In this paper we consider a fluid-structure interaction problem given by the steady Navier Stokes equations coupled with linear elasticity taken from [Lasiecka, Szulc, and Zochoswki, Nonl. Anal.: Real World Appl., 44, 2018]. An elastic body…
We aim at the stability of time-dependent motions, such as time-periodic ones, of a rigid body in a viscous fluid filling the exterior to it in 3D. The fluid motion obeys the incompressible Navier-Stokes system, whereas the motion of the…
In many occurrences of fluid-structure interaction time-periodic motions are observed. We consider the interaction between a fluid driven by the three dimensional Navier-Stokes equation and a two dimensional linearized elastic Koiter shell…
In this article we address flow problems that carry a multiscale character in time. In particular we consider the Navier-Stokes flow in a channel on a fast scale that influences the movement of the boundary which undergoes a deformation on…
A filtration system, comprising a Biot poroelastic solid coupled to an incompressible Stokes free-flow, is considered in 3D. Across the flat 2D interface, the Beavers-Joseph-Saffman coupling conditions are taken. In the inertial, linear,…
The article is devoted to the mathematical analysis of a fluid-structure interaction system where the fluid is compressible and heat conducting and where the structure is deformable and located on a part of the boundary of the fluid domain.…
We propose an efficient numerical method for the simulation of multi-phase flows with moving contact lines in three dimensions. The mathematical model consists of the incompressible Navier-Stokes equations for the two immiscible fluids with…
Dispersion of low-density rigid particles with complex geometries is ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newton's equations…