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Published on: October 24, 2017
Unconditionally gradient-stable computational schemes in problems of fast phase transitions.
Vladimir Lebedev1, Alena Sysoeva, Peter Galenko
1Department of Theoretical Physics, Udmurt State University, 426034 Izhevsk, Russia.
Summary
Computational schemes for fast phase transitions are stabilized by extending the Eyre theorem. This ensures numerical stability and monotonic free energy decrease in modeling rapid material changes.
Area of Science:
- Materials Science
- Computational Physics
- Chemical Engineering
Background:
- Phase transitions describe material state changes.
- Fast phase transitions involve rapid boundary movement.
- Existing models face computational stability challenges.
Purpose of the Study:
- Analyze equations for fast phase transitions.
- Develop unconditionally stable computational schemes.
- Extend the Eyre theorem for non-equilibrium systems.
Main Methods:
- Analysis of singular perturbation in phase transition equations.
- Extension of the Eyre theorem to fast phase transitions.
- Free energy expansion into contractive and expansive parts.
- Grid approximation for numerical modeling.
Main Results:
- The Eyre theorem is extended to fast phase transitions.
- Free energy expansion is valid for these rapid transitions.
- Grid approximations yield gradient-stable algorithms.
- Algorithms ensure monotonic free energy non-increase with arbitrary time steps.
Conclusions:
- The extended Eyre theorem provides a foundation for stable numerical modeling of fast phase transitions.
- Developed algorithms enable accurate simulation of rapid material changes.
- This work advances computational methods in materials science and physics.
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