Abstract. We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic fluid shell. The fluid motion is governed by the Navier-Stokes equations, while the fluid shell is modeled by a bending energy which extremizes the Willmore functional and a membrane energy that extremizes the surface area of the shell. The fluid flow a...

Abstract— The problem of vertical flow stability in an oil reservoir with a gas cap is considered, when the obeys Brinkman equation. Boundary conditions at moving boundary gas-oil interface are derived and basic solution obtained. normal mode method used to study gas–oil interface. obtained dispersion equation investigated. Conditions for found all values parameters, it shown that, linear appro...

The plane strain problem of determining strain energy release rate, crack energy, and crack-opening displacement (COD) for a moving Griffith crack at the interface of two dissimilar orthotropic half-planes is considered. The problem is reduced to a pair of singular integral equations of second kind which have finally been solved by using Jacobi polynomials. Graphical plots of the strain energy ...

A typical elliptic interface problem is casted as piecewise defined elliptic partial differential equations (PDE) in different regions which are coupled together with interface conditions, such as jumps in solution and flux across the interface. In many situations, such as the interface is moving, the challenge is how to solve such a problem accurately, robustly and efficiently without generati...

A moving, solidifying interface that grows by the instantaneous adsorption of a diffusing solute can be described by equations analogous to those of the classical one-sided Stefan problem for solidification. However, the behavior of precipitate growth by material deposition can depend on both surface kinetics and bulk drift of the depositing species. We generalize the Stefan problem and its int...

A moving, solidifying interface that grows by the instantaneous adsorption of a diffusing solute is described by the classic one-sided “Stefan problem” [15, 19]. More generally, the behavior of precipitate growth can depend on both surface kinetics and bulk drift of the depositing species. We generalize the Stefan problem and its interface boundary condition to explicitly account for both surfa...

Extending our previous work on 2D growth for the Laplace equation we study here multidimensional growth for arbitrary elliptic equations, describing inhomogeneous and anisotropic pattern formations processes. We find that these nonlinear processes are governed by an infinite number of conservation laws. Moreover, in many cases all dynamics of the interface can be reduced to the linear time–depe...

Fluid flow simulations that involve deforming domains, in the presence of one or more moving boundaries or fluidfluid interfaces, continue to present unique challenges, and form one of the frontiers of computational science. Freesurface flows in particular involve the motion of the fluid interface which is unknown at the outset of the simulation. Thus, both the domain and the flow field are par...

The paper describes the implementation of stress dependent boundary conditions in the FEMTOOL code developed for numerical solution of coupled problems. Moving interface flows including breaking waves are considered. The performance of the numerical technique is validated by solving the dam break problem in the confined domain. The code development issues and the detailed investigation of param...