Related papers: On discretizing sea-ice dynamics on triangular mes…
We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…
The dynamics of evolving fluid films in the viscous Stokes limit is relevant to various applications, such as the modeling of lipid bilayers in cells. While the governing equations were formulated by Scriven in 1960, solving for the flow of…
The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…
Continuum computational kinetic plasma models evolve the distribution function of a plasma species $f_s$ on a phase-space grid over time. In many problems of interest the distribution function has limited extent in velocity space; hence,…
Developing tissues often maintain mechanical coherence while continuously remodeling through cellular processes such as cell divisions and rearrangements. In this way, they are an example of amorphous solids. In passive amorphous solids,…
In this paper we analyze a virtual element method for the two dimensional elasticity problem allowing small edges. With this approach, the classic assumptions on the geometrical features of the polygonal meshes can be relaxed. In…
The hydrodynamics of viscoelastic materials (for example polymer melts and solutions) presents interesting and complex phenomena, for example instabilities and turbulent flow at very low Reynolds numbers due to normal stress effects and the…
Motivated by the elastic-viscous-plastic (EVP) sea-ice model [E. C. Hunke and J. K. Dukowicz, J. Phys. Oceanogr., 27, 9 (1997), 1849--1867], which is used in large-scale numerical climate simulations, we proposed in [D. W. Boutros, X. Liu,…
We develop a fourth order accurate finite difference method for the three dimensional elastic wave equation in isotropic media with the piecewise smooth material property. In our model, the material property can be discontinuous at curved…
We focus on the spatial discretization produced by the Variational Particle-Mesh (VPM) method for a prototype fluid equation the known as the EPDiff equation}, which is short for Euler-Poincar\'e equation associated with the diffeomorphism…
Recent applications (e.g. active gels and self-assembly of elastic sheets) motivate the need to efficiently simulate the dynamics of thin elastic sheets. We present semi-implicit time stepping algorithms to improve the time step constraints…
A framework for exponential time discretization of the multilayer rotating shallow water equations is developed in combination with a mimetic discretization in space. The method is based on a combination of existing exponential time…
Expressions for local discrete variance decay (DVD) rates are directly derived from discrete tracer equations without any assumptions on discrete fluxes of the second moment. Spurious mixing (SM) associated with numerical implementations of…
It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the…
The tractions that cells exert on a gel substrate from the observed displacements is an increasingly attractive and valuable information in biomedical experiments. The computation of these tractions requires in general the solution of an…
The accurate and efficient representation of atmospheric dynamics remains a central challenge in numerical weather prediction. A particular difficulty arises from the strong anisotropy of the atmosphere, in which horizontal and vertical…
The aim of this paper is twofold. On the one hand, we test numerically the performance of mixed virtual elements in three dimensions for the first time in the literature to solve the mixed formulation of three-dimensional elliptic equations…
The aim of this paper is to develop a virtual element method (VEM) for the vibration problem of thin plates on polygonal meshes. We consider a variational formulation relying only on the transverse displacement of the plate and propose an…
The shear-induced deformation of a capsule with a stiff nucleus, a model of eukaryotic cells, is studied numerically. The membrane of the cell and of its nucleus are modelled as a thin and impermeable elastic material obeying a Neo-Hookean…
We present a method for generating higher-order finite volume discretizations for Poisson's equation on Cartesian cut cell grids in two and three dimensions. The discretization is in flux-divergence form, and stencils for the flux are…