Related papers: A numerical scheme for a multi-scale model of thro…
The Galerkin method is used to derive a realistic model of plane Couette flow in terms of partial differential equations governing the space-time dependence of the amplitude of a few cross-stream modes. Numerical simulations show that it…
In this paper, we study a model for the transport of an external component, e.g., a surfactant, in variably saturated porous media. We discretize the model in time and space by combining a backward Euler method with the linear Galerkin…
The semi-implicit (partly decoupled, also called staggered or fraction-step) time discretization is applied to compressible nonlinear dynamical models of viscoelastic solids in the Eulerian description, i.e.\ in the actual deforming…
We study a model describing the slow flow of a fluid through a deformable, porous, elastic solid undergoing small deformations. The stress-strain relationship of the solid incorporates nonlinear effects, formulated as a perturbation of the…
In this paper we investigate the interaction of fluid flow with a thin porous elastic layer. We consider two fluid-filled bulk domains which are separated by a thin periodically perforated layer consisting of a fluid and an elastic solid…
We consider the interaction between a poroelastic structure, described using the Biot model in primal form, and a free-flowing fluid, modelled with the time-dependent incompressible Stokes equations. We propose a diffuse interface model in…
The immersed boundary method is a mathematical framework for modeling fluid-structure interaction. This formulation describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form, and it uses…
Biological cells utilize membranes and liquid-like droplets, known as biomolecular condensates, to structure their interior. The interaction of droplets and membranes, despite being involved in several key biological processes, is so far…
In this work, we present a localized form of the dynamic eddy viscosity model for computationally efficient and accurate simulation of the turbulent flows governed by Euler equations. In our framework, we determine the dynamic model…
Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…
We study a recent formulation for fluid-structure interaction problems based on the use of a distributed Lagrange multiplier in the spirit of the fictitious domain approach. In this paper, we focus our attention on a crucial computational…
As a first step towards the numerical analysis of the stochastic primitive equations of the atmosphere and oceans, we study their time discretization by an implicit Euler scheme. From deterministic viewpoint the 3D Primitive Equations are…
Motivated by the phenomenon of transport barriers in fusion plasma devices, we write a mathematical model of heat dispersion in a turbulent fluid with a transport barrier, properly idealized; in a scaling limit of the turbulence model with…
A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…
We present a flexible discretization technique for computational models of thin tubular networks embedded in a bulk domain, for example a porous medium. These systems occur in the simulation of fluid flow in vascularized biological tissue,…
We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are…
This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of…
We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different…
We present a complete numerical analysis for a general discretization of a coupled flow-mechanics model in fractured porous media, considering single-phase flows and including frictionless contact at matrix-fracture interfaces, as well as…
A numerical model was developed for flows involving an interface between a homogenous fluid and a porous medium. The numerical model is based on the finite volume method with body-fitted and multi-block grids. The Darcy-Forchheimer extended…