Abstract
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original formulation of this problem is restricted to transport by diffusion, we consider here the case of melt convection. Using an analysis of the coupled phase field-fluid dynamic equations, we show here that such a thin interface limit does also exist if transport contains both diffusion and convection. This prediction is tested by comparing simulation studies, which make use of the thin-interface condition, with an analytic sharp-interface theory for dendritic tip growth under convection.
Highlights
The European Physical Journal Special Topics (W → 0)
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model
Using an analysis of the coupled phase field-fluid dynamic equations, we show here that such a thin interface limit does exist if transport contains both diffusion and convection
Summary
The European Physical Journal Special Topics (W → 0). This ideal limit, is numerically quite expensive and often impractical. A major advancement was achieved in the mid 1990s by Karma and Rappel [4]. With the so-called thin-interface limit for problems involving diffusive transport. They found that instead of vanishing interface thickness, it is sufficient to have W small compared to the diffusion length of the solidification problem. This diffusion length is defined as Ld. D is the thermal diffusivity and V is the normal velocity of the interface
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