High-Order Adaptive Arbitrary-Lagrangian-Eulerian (ALE) Calculations of Solidification

Abstract

A high-order-accurate method for simulation of solidification is presented. The solidification front is tracked using an ALE method on an unstructured triangular mesh, and a high-order hp-finite element method is used to resolve the thermal and flow fields. This is combined with a mesh adaption algorithm to allow simulations of problems with large interfacial movement and an A-stable diagonally-implicit Runge-Kutta scheme for the temporal discretization. The method was demonstrated to give a temporal order of accuracy near 3 by comparing to a 1D analytic solution of melting. The spatial accuracy was calculated to be nearly 5th order for an approximation space of degree 4. Even for this simple case, the mesh adaption algorithm improved the accuracy over a simulation where the mesh only deformed. For a practical demonstration, the algorithm was used to simulate horizontal ribbon growth and was able to resolve solutions where the solid layer thickness decreased by a factor of 20 over the course of the simulation.© 2013 ASME