Abstract
We present a new second-order energy dissipative numerical scheme to treat macroscopic equations aiming at the modeling of the dynamics of complex polymer–solvent mixtures. These partial differential equations are the Cahn-Hilliard equation for diffuse interface phase fields and the Oldroyd-B equations for the hydrodynamics of the polymeric mixture. A second-order combined finite volume/finite difference method is applied for the spatial discretization. A complementary approach to study the same physical system is realized by simulations of a microscopic model based on a hybrid Lattice Boltzmann/Molecular Dynamics scheme. These latter simulations provide initial conditions for the numerical solution of the macroscopic equations. This procedure is intended as a first step toward the development of a multiscale method that aims at combining the two models.
The present paper has been supported by the German Science Foundation (DFG) under the grant TRR 146.
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Lukáčová-Medvid’ová, M., Dünweg, B., Strasser, P., Tretyakov, N. (2018). Energy-Stable Numerical Schemes for Multiscale Simulations of Polymer–Solvent Mixtures. In: van Meurs, P., Kimura, M., Notsu, H. (eds) Mathematical Analysis of Continuum Mechanics and Industrial Applications II. CoMFoS 2016. Mathematics for Industry, vol 30. Springer, Singapore. https://doi.org/10.1007/978-981-10-6283-4_13
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DOI: https://doi.org/10.1007/978-981-10-6283-4_13
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