A Numerical Method for Sharp-Interface Simulations of Multicomponent Alloy Solidification

TL;DR

This paper introduces a novel numerical method for simulating multicomponent alloy solidification with sharp interfaces, combining Newton-type solvers, adaptive grids, and level-set techniques for high accuracy and efficiency.

Contribution

It presents the first sharp-interface simulation approach for multicomponent alloys using a Newton-type method and adaptive spatial discretization, advancing computational capabilities in alloy solidification modeling.

Findings

Method achieves near second-order accuracy.

Validated on axisymmetric solidification with analytical solution.

Analyzed solutal segregation in ternary alloy simulations.

Abstract

We present a computational method for the simulation of the solidification of multicomponent alloys in the sharp-interface limit. Contrary to the case of binary alloys where a fixed point iteration is adequate, we hereby propose a Newton-type approach to solve the non-linear system of coupled PDEs arising from the time discretization of the governing equations, allowing for the first time sharp-interface simulations of the multialloy solidification. A combination of spatially adaptive quadtree grids, Level-Set Method, and sharp-interface numerical methods for imposing boundary conditions is used to accurately and efficiently resolve the complex behavior of the solidification front. The convergence behavior of the Newton-type iteration is theoretically analyzed in a one-dimensional setting and further investigated numerically in multiple spatial dimensions. We validate the overall computational method on the case of axisymmetric radial solidification admitting an analytical solution and show that the overall method's accuracy is close to second order. Finally, we perform numerical experiments for the directional solidification of a Co-Al-W ternary alloy with a phase diagram obtained from the PANDAT database and analyze the solutal segregation dependence on the processing conditions and alloy properties.