Numerical approximation for the phase-field transition system

Abstract

The ID phase-field transition system introduced by Caginalp to describe the moving boundary in melting problems is considered. It is discretized by finite differences and three algorithms are presented to solve the resulting nonlinear algebraic system: the Newton method, an improved Newton method with reduced system and a fractional step method. Numerical results are reported and a comparison between the algorithms is made.

Keywords:

• Phase-field transition system
• Newton method
• fractional step method

C.R. Categories:

• G.1.8
• G.1.5