@Article{CiCP-17-975,
author = {F. Chinesta, E. Abisset-Chavanne, A. Ammar and E. Cueto},
title = {Efficient Stabilization of Advection Terms Involved in Separated Representations of Boltzmann and Fokker-Planck Equations},
journal = {Communications in Computational Physics},
year = {2018},
volume = {17},
number = {4},
pages = {975--1006},
abstract = {<p style="text-align: justify;">The fine description of complex fluids can be carried out by describing the
evolution of each individual constituent (e.g. each particle, each macromolecule, etc.).
This procedure, despite its conceptual simplicity, involves many numerical issues, the
most challenging one being that related to the computing time required to update the
system configuration by describing all the interactions between the different individuals.
Coarse grained approaches allow alleviating the just referred issue: the system
is described by a distribution function providing the fraction of entities that at certain
time and position have a particular conformation. Thus, mesoscale models involve
many different coordinates, standard space and time, and different conformational
coordinates whose number and nature depend on the particular system considered.
Balance equation describing the evolution of such distribution function consists of an
advection-diffusion partial differential equation defined in a high dimensional space.
Standard mesh-based discretization techniques fail at solving high-dimensional models
because of the curse of dimensionality. Recently the authors proposed an alternative
route based on the use of separated representations. However, until now these
approaches were unable to address the case of advection dominated models due to stabilization
issues. In this paper this issue is revisited and efficient procedures for stabilizing
the advection operators involved in the Boltzmann and Fokker-Planck equation
within the PGD framework are proposed.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.2014.m326},
url = {http://global-sci.org/intro/article_detail/cicp/10989.html}
}