相关论文: Unfitted finite element modelling of surface-bulk …
Mechanochemical processes on surfaces such as the cellular cortex or epithelial sheets, play a key role in determining patterns and shape changes of biological systems. To understand the complex interplay of hydrodynamics and material flows…
Cellular morphodynamics requires solving systems of coupled partial differential equations on moving bulk and surface domains, where advection-dominant transport, structure preservation, and severe mesh distortions make robust simulation…
In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…
The finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid-fluid free surface and a liquid-solid interface, with the three-phase contact line moving across the…
We present a theoretical and computational model for the behavior of a porous solid undergoing two interdependent processes, the finite deformation of a solid and species migration through the solid, which are distinct in bulk and on…
Living soft tissues appear to promote the development and maintenance of a preferred mechanical state within a defined tolerance around a so-called set-point. This phenomenon is often referred to as mechanical homeostasis. In contradiction…
A novel finite element framework is proposed for the numerical simulation of two phase flows with surface tension. The Level-Set (LS) method with piece-wise quadratic (P2) interpolation for the liquid-gas interface is used in order to reach…
This paper studies a model of two-phase flow with an immersed material viscous interface and a finite element method for numerical solution of the resulting system of PDEs. The interaction between the bulk and surface media is characterized…
The dynamics of active viscoelastic surfaces plays an important role in biological systems. One prominent example is the actin cortex, a thin bio-polymer sheet underneath the outer membrane of biological cells which combines active…
We propose a new unfitted finite element method for simulation of two-phase flows in presence of insoluble surfactant. The key features of the method are 1) discrete conservation of surfactant mass; 2) the possibility of having meshes that…
In this paper we present a finite element method (FEM) for two-phase incompressible flows with moving contact lines. We use a sharp interface Navier-Stokes model for the bulk phase fluid dynamics. Surface tension forces, including Marangoni…
Animal morphogenesis often involves significant shape changes of epithelial tissue sheets. Great progress has been made in understanding the underlying cellular driving forces and their coordination through biomechanical feedback loops.…
The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…
The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk…
We present a finite element framework for the numerical prediction of cavitating turbulent flows interacting with flexible structures. The vapor-fluid phases are captured through a homogeneous mixture model, with a scalar transport equation…
The morphogenesis of cells and tissues involves an interplay between chemical signals and active forces on their surrounding surface layers. The complex interaction of hydrodynamics and material flows on such active surfaces leads to…
Interfacial energy plays an important role in equilibrium morphologies of nanosized microstructures of solid materials due to the high interface-to-volume ratio, and can no longer be neglected as it does in conventional mechanics analysis.…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
Unfitted finite element techniques are valuable tools in different applications where the generation of body-fitted meshes is difficult. However, these techniques are prone to severe ill conditioning problems that obstruct the efficient use…
In this article we present a goal-oriented adaptive finite element method for a class of subsurface flow problems in porous media, which exhibit seepage faces. We focus on a representative case of the steady state flows governed by a…