We review the use of phase field methods in solidification modeling, describing their
fundamental connection to the physics of phase transformations. The inherent challenges …

We study the effect of fluid flow on three-dimensional (3D) dendrite growth using a phase-
field model on an adaptive finite-element grid. In order to simulate 3D fluid flow, we use an …

A method for optimising a pre-existing mesh of tetrahedral finite elements is described. It is
based on a series of mesh connectivity and node position searches of the landscape …

Many inhomogeneous systems involve domains of well-de? ned phases se-rated by a
distinct interface. If they are driven out of equilibrium one phase will grow at the cost of the …

The objective of this paper is to analyze the pressure stability of fractional step finite element
methods for incompressible flows that use a pressure Poisson equation. For the classical …

We study how the dendritic evolution of an initially small nucleus is affected by a mean
external flow. The nucleus is considered to be attached to a solid wall, and it grows away …

Surface wave instabilities in a two-dimensional thin draining film are studied by a direct
numerical simulation of the full nonlinear system. A finite element method is used with an …

A numerical study of the effect of an external mean flow on dendritic growth has been
performed. All simulations are 2D phase-field computations using an adaptive finite element …

Geodynamical simulations over the past decades have widely been built on quadrilateral
and hexahedral finite elements. For the discretization of the key Stokes equation describing …

We study the growth of a single dendrite from a small initial seed in an undercooled melt in
the presence of a forced flow. Three-dimensional models are constructed in which the …