We study a nonlinear, unsteady, moving boundary, fluid–structure interaction (FSI) problem in which the structure is composed of two layers: a thick layer, and a thin layer which serves as a fluid–structure interface with mass. The fluid flow, which is driven by the time-dependent dynamic pressure data, is modeled by the Navier–Stokes equations for an incompressible, viscous fluid, defined on a...

We study the local well-posedness for an interface with surface tension that separates a perfectly conducting inviscid fluid from vacuum. The flow is governed by equations of three-dimensional ideal compressible magnetohydrodynamics (MHD), while vacuum magnetic and electric fields are supposed to satisfy pre-Maxwell equations. tangential interface. This renders nonlinear hyperbolic-elliptic cou...

A problem of reflection and transmission of a plane shear wave incident at a corrugated interface between transversely isotropic inhomogeneous and visco-elastic half-spaces is investigated. Applying appropriate boundary conditions and using Rayleigh’s method of approximation expressions for reflection and transmission coefficients are obtained for the first and second order approximation of the...

In immiscible two-phase flows, the contact line denotes the intersection of the fluid– fluid interface with the solid wall. When one fluid displaces the other, the contact line moves along the wall. A classical problem in continuum hydrodynamics is the incompatibility between the moving contact line and the no-slip boundary condition, as the latter leads to a non-integrable singularity. The rec...

Abstract. In this work, an advanced numerical model, based on the cohesive zone approach and moving mesh technique, is proposed to simulate fracture propagation in quasi-brittle materials. particular, procedure consists of two stages. former one, according inter-element crack approach, once a suitable stress criterion for onset satisfied, boundary, representing segment, selected aligned along d...

This paper considers a class of one-dimensional solidification problem in which kinetic undercooling is incorporated into the temperature condition at the interface. A model problem with nonlinear kinetic law is considered. The main result is an existence theorem. The mathematical effects of the kinetic term are discussed

this paper deals with a theoretical mathematical analysis of one-dimensional solidification problem, in which kinetic undercooling is incorporated into the this temperature condition at the interface. a model problem with nonlinear kinetic law is considered. we prove a local result intimate for the uniqueness of solution of the corresponding free boundary problem.

Abstract We develop a family of cut finite element methods different orders based on the discontinuous Galerkin framework, for hyperbolic conservation laws with stationary interfaces in both one and two space dimensions, moving dimension. Interface conditions are imposed weakly so that stability ensured. A CutFEM elements is developed coupled to standard explicit time stepping schemes linear ad...