Energy-Stable Numerical Schemes for Multiscale Simulations of Polymer–Solvent Mixtures

Conference paper
Part of the Mathematics for Industry book series (MFI, volume 30)


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.


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of MainzMainzGermany
  2. 2.Max Planck Institute for Polymer ResearchMainzGermany

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