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Differential Equations

, Volume 55, Issue 7, pp 929–939 | Cite as

Stability Analysis of Solution Methods for a Phase Transition Problem

  • A. O. GusevEmail author
  • O. V. ShcheritsaEmail author
  • O. S. MazhorovaEmail author
Numerical Methods
  • 5 Downloads

Abstract

We consider a model of crystallization process in a binary compound taking into account heat and mass transfer in the solid and liquid phases. Stability of various methods for the numerical implementation of nonlinear conditions on a moving internal boundary is analyzed. For a group of methods based on the successive solution of governing equations, the stability domains determined by the system thermodynamic parameters are indicated. A coupled algorithm for solving the problem is proposed. Nonlinear equations at the phase interface are solved by the Newton method. The coupled algorithm has a significant stability margin and provides reliable results in a broad range of parameters of practical interest.

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Keldysh Institute of Applied MathematicsRussian Academy of SciencesMoscowRussia

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