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Review on Discretization Techniques for Complex Fluid Flow Models: Past, Present and Future

By A. Ammar, Francisco Chinesta, Elías Cueto and T. Phillips

Abstract

In the last decades several new and advanced numerical strategies have been proposed for solving the flow models of complex fluids. Most of them were based in the classical discretization techniques (finite elements, finite volumes, finite differences, spectral methods, meshless approaches) applied on the macroscopic descriptions of such flows (differential and integral models) where special advances were introduced for accounting for the mixed character of the associated variational formulations as well as for stabilizing the advection terms in the motion and constitutive equations. Recently micro‐macro approaches are being the more and more applied. They allows to avoid closure relations and the microscopic physics are better described. These models are based on kinetic theory and their main difficulty concerns the curse of dimension. The microstructure conformation is defined in a multidimensional space where standard discretization techniques fail. To overcome this difficulty stochastic techniques were introduced (inspired in the Monte Carlo techniques) but the control of the statistical noise and the low convergence order are some of their main drawbacks. Other new strategies have been recently proposed, as for example the ones based on the sparse grid and the separated representation that allows circumventing the aforementioned difficulties. However the models are the more and more focused on the microscopic scale, where they are formulated in terms of Brownian or molecular dynamics. They allow describing very precisely the molecular dynamics, but the computing time remains its main drawback. Thus, in the next years new efforts must be paid to reduce the computing time involved in microscopic simulations and the definitions of bridges between the different descriptions scales

Topics: Complex flows, Micro-macro approaches, Meshless methods, [SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]
Publisher: 'AIP Publishing'
Year: 2007
DOI identifier: 10.1063/1.2729700
OAI identifier: oai:HAL:hal-00289749v1
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