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

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 5^th 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.