Modelling of free boundary problems for phase change with diffuse interfaces

Phase-field models for free-boundary problems

Phase-field models are very attractive in view of their numerical simplicity. With only a few lines of code, one can model complex physical situations such as dendritic growth. From this point of view, they constitute very interesting tools for teaching purposes at graduate level. The main difficulty with these models is in their formulation, which incorporates the physical ingredients in a sub...

Diffuse-Interface Approximations of Osmosis Free Boundary Problems

Free boundary problems based on mass conservation and surface tension with application in osmotic swelling are the topic of this contribution. Phase-field approximations of such models are introduced, in order to numerically investigate properties of the solutions. Formal justification of the proposed approximations is provided by matched asymptotic expansions supported by numerical tests repro...

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

Boundary conditions for free interfaces with the lattice Boltzmann method

In this paper we analyze the boundary treatment of the Lattice Boltzmann method for simulating 3D flows with free surfaces. The widely used free surface boundary condition of Körner is shown to be first order accurate. The article presents new free surface boundary schemes that are suitable for the lattice Boltzmann method and that have second order spatial accuracy. The new method takes the fr...

On Free Boundary Problems