Efficient Stabilization of Advection Terms Involved in Separated Representations of Boltzmann and Fokker-Planck Equations
Article dans une revue avec comité de lecture
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.
Cette publication figure dans le(s) laboratoire(s) suivant(s)
Visualiser des documents liés par titre, auteur, créateur et sujet.
Article dans une revue avec comité de lectureSCHEUER, Adrien; AMMAR, Amine; ABISSET-CHAVANNE, Emmanuelle; CUETO, Elías; CHINESTA, Francisco; KEUNINGS, Roland; ADVANI, Suresh G. (Tech Science Press, 2018)Describing the orientation state of the particles is often critical in fibre suspension applications. Macroscopic descriptors, the so-called second-order orientation tensor (or moment) leading the way, are often preferred ...
Article dans une revue avec comité de lectureGHNATIOS, Chady; ABISSET-CHAVANNE, Emmanuelle; AMMAR, Amine; CUETO, Elías; DUVAL, Jean Louis; CHINESTA, Francisco (Elsevier, 2019)This work aims at proposing a new procedure for parametric problems whose separated representation has been considered difficult, or whose SVD compression impacted the results in terms of performance and accuracy. The ...
Some applications of compressed sensing in computational mechanics: model order reduction, manifold learning, data-driven applications and nonlinear dimensionality reduction Article dans une revue avec comité de lectureIBAÑEZ, R.; ABISSET-CHAVANNE, Emmanuelle; CUETO, Elías G.; AMMAR, Amine; DUVAL, Jean Louis; CHINESTA, Francisco (Springer Verlag, 2019)Compressed sensing is a signal compression technique with very remarkable properties. Among them, maybe the most salient one is its ability of overcoming the Shannon–Nyquist sampling theorem. In other words, it is able to ...
A Multidimensional Data-Driven Sparse Identification Technique: The Sparse Proper Generalized Decomposition Article dans une revue avec comité de lectureIBAÑEZ, Rubén; ABISSET-CHAVANNE, Emmanuelle; AMMAR, Amine; GONZALEZ, David; CUETO, Elias; HUERTA, Antonio; DUVAL, Jean-Louis; CHINESTA, Francisco (Wiley, 2018)Sparse model identification by means of data is especially cumbersome if the sought dynamics live in a high dimensional space. This usually involves the need for large amount of data, unfeasible in such a high dimensional ...
Article dans une revue avec comité de lectureANGEL, Leon; BARASINSKI, Anais; ABISSET-CHAVANNE, Emmanuelle; CUETO, Elias; CHINESTA, Francisco (Elsevier Masson, 2018)Separated representations at the heart of Proper Generalized Decomposition are constructed incrementally by minimizing the problem residual. However, the modes involved in the resulting decomposition do not exhibit a clear ...