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In the present manuscript, we consider the practical problem of wave interaction with a vertical wall. However, the novelty here consists in the fact that the wall can move horizontally due to a system of springs. The water wave evolution…
We introduce an Eulerian approach for problems involving one or more soft solids immersed in a fluid, which permits mechanical interactions between all phases. The reference map variable is exploited to simulate finite-deformation…
We derive a Nitsche-based formulation for fluid-structure interaction (FSI) problems with contact. The approach is based on the work of Chouly and Hild [SIAM Journal on Numerical Analysis. 2013;51(2):1295--1307] for contact problems in…
The proposed method aims to approximate a solution of a fluid-fluid interaction problem in case of low viscosities. The nonlinear interface condition on the joint boundary allows for this problem to be viewed as a simplified version of the…
Time modulation of the physical parameters offers interesting new possibilities for wave control. Examples include amplification of waves, harmonic generation and non-reciprocity, without resorting to non-linear mechanisms. Most of the…
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain…
Cartesian-grid methods with Adaptive Mesh Refinement (AMR) are ideally suited for simulating the breaking of waves, the formation of spray, and the entrainment of air around ships. As a result of the cartesian-grid formulation, minimal…
We develop a numerical a framework to study phoretic particle dynamics in two dimensions. The particles are modeled as chemically active rigid circles, which can emit or absorb a solute into surrounding fluid. The interaction between…
In this paper we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational…
Model-based computational elasticity imaging of tissues can be posed as solving an inverse problem over finite elements spanning the displacement image. As most existing quasi-static elastography methods count on deterministic formulations…
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 compare two high order finite-difference methods that solve the elastic wave equation in two dimensional domains with curved boundaries and material discontinuities. Two numerical experiments are designed with focus on wave boundary…
A main challenge in numerical simulations of moving contact line problems is that the adherence, or no-slip boundary condition leads to a non-integrable stress singularity at the contact line. In this report we perform the first steps in…
This paper is concerned with the study of interaction of waves originating from the Riemann problem centred at two different points for a system of equations modelling propagation of elastic waves. The system consists of two equations for…
Frictional sliding along an interface between two identical isotropic elastic plates under impact shear loading is investigated experimentally and numerically. The plates are held together by a compressive stress and one plate is subject to…
In the present article we consider the problem of wave interaction with a partially immersed, but floating body. We assume that the motion of the body is prescribed. The general mathematical formulation for this problem is presented in the…
Point masses connected by springs, or mass-spring systems, are widely used in computer animation to approximate the behavior of deformable objects. One of the restrictions imposed by these models is that points that are not topologically…
Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…
We introduce a contact law for the normal force generated between two contacting, elastically anisotropic bodies of arbitrary geometry. The only requirement is that their surfaces be smooth and frictionless. This anisotropic contact law is…
We revisit the classic problem of an elastic solid with a two-dimensional wavy surface squeezed against an elastic flat half-space from infinitesimal to full contact. Through extensive numerical calculations and analytic derivations, we…