Dendritic Solidification with Triangular Finite Elements

Abstract

The use of triangular elements in simulations of dendritic solidification of binary alloys is examined. The simulations require the solution of the diffusion equation for the solute concentration in very distorted geometries that change continuously with time, therefore a new mesh of triangular elements is generated at each time step and data from the previous mesh interpolated to the new one. It is shown that because of the exponential nature of the solute concentration field and the large number of time steps/interpolations, linear triangles suffer from excessive interpolation error that leads to unacceptable error in the total mass conservation unless unreasonably fine meshes are used. The problem is greatly alleviated by the use of quadratic triangles, which introduce the curvature needed to obtain better accuracy in the interpolation of the exponential fields. Examples of simulations of dendritic growth in binary alloys are given.