On the multiple hyperbolic systems modeling phase transformation kinetics

TL;DR

This paper explores a reduction of Cahn's time cone integral model for phase transformation kinetics to multiple hyperbolic systems, and introduces an efficient numerical method for solving these equations, demonstrating practical applicability in 3D cases.

Contribution

It presents a novel reduction of the phase transformation model to multiple hyperbolic equations and develops a fast numerical solution method for these systems.

Findings

The reduced hyperbolic system accurately models phase transformation kinetics.

The proposed numerical method achieves satisfactory accuracy and efficiency.

In 3D, the method is particularly fast and effective.

Abstract

We discuss Cahn's time cone method modeling phase transformation kinetics. The model equation by the time cone method is an integral equation in the space-time region. First we reduce it to a system of hyperbolic equations, and in the case of odd spatial dimensions, the reduced system is a multiple hyperbolic equation. Next we propose a numerical method for such a hyperbolic system. By means of alternating direction implicit methods, numerical simulations for practical forward problems are implemented with satisfactory accuracy and efficiency. In particular, in the three dimensional case, our numerical method on basis of reduced multiple hyperbolic equation, is fast.