Finite element discretization of non-linear diffusion equations with thermal fluctuations

The Journal of Chemical Physics
J A de la TorreAleksandar Donev

Abstract

We present a finite element discretization of a non-linear diffusion equation used in the field of critical phenomena and, more recently, in the context of dynamic density functional theory. The discretized equation preserves the structure of the continuum equation. Specifically, it conserves the total number of particles and fulfills an H-theorem as the original partial differential equation. The discretization proposed suggests a particular definition of the discrete hydrodynamic variables in microscopic terms. These variables are then used to obtain, with the theory of coarse-graining, their dynamic equations for both averages and fluctuations. The hydrodynamic variables defined in this way lead to microscopically derived hydrodynamic equations that have a natural interpretation in terms of discretization of continuum equations. Also, the theory of coarse-graining allows to discuss the introduction of thermal fluctuations in a physically sensible way. The methodology proposed for the introduction of thermal fluctuations in finite element methods is general and valid for both regular and irregular grids in arbitrary dimensions. We focus here on simulations of the Ginzburg-Landau free energy functional using both regular and i...Continue Reading

References

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Jan 24, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Steven DelongAleksandar Donev

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Citations

Jun 15, 2015·The Journal of Chemical Physics·Amit Kumar BhattacharjeeAleksandar Donev
Apr 15, 2016·The Journal of Physical Chemistry. B·Frédéric PoitevinHenri Orland
Apr 8, 2017·The Journal of Chemical Physics·Changho KimAleksandar Donev
May 10, 2020·The Journal of Chemical Physics·D Duque-ZumajoPep Español
Jan 18, 2020·Physical Review Letters·J A de la TorrePep Español
Jun 20, 2019·Physical Review. E·D Duque-ZumajoPep Español
May 26, 2021·Chemical Reviews·Marcus Müller, Volker Abetz

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