Energy-stable linear schemes for polymer-solvent phase field models
Paul J. Strasser, Giordano Tierra, Burkhard D\"unweg, M\'aria, Luk\'a\v{c}ov\'a-Medvid'ov\'a
TL;DR
This paper introduces new linear, energy-stable numerical schemes for simulating polymer-solvent mixtures, ensuring thermodynamic consistency and computational efficiency in modeling complex phase behaviors.
Contribution
The paper develops novel linear schemes that are energy dissipative for the polymer-solvent phase field model, improving stability and efficiency over existing methods.
Findings
Schemes are proven to be energy dissipative.
Numerical experiments demonstrate stability and efficiency.
Applicable to complex polymer-solvent systems.
Abstract
We present new linear energy-stable numerical schemes for numerical simulation of complex polymer-solvent mixtures. The mathematical model proposed by Zhou, Zhang and E (Physical Review E 73, 2006) consists of the Cahn-Hilliard equation which describes dynamics of the interface that separates polymer and solvent and the Oldroyd-B equations for the hydrodynamics of polymeric mixtures. The model is thermodynamically consistent and dissipates free energy. Our main goal in this paper is to derive numerical schemes for the polymer-solvent mixture model that are energy dissipative and efficient in time. To this end we will propose several problem-suited time discretizations yielding linear schemes and discuss their properties.
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