@Article{CiCP-17-1,
author = {Vié, Aymeric and François, Doisneau and Massot, Marc},
title = {On the Anisotropic Gaussian Velocity Closure for Inertial-Particle Laden Flows},
journal = {Communications in Computational Physics},
year = {2015},
volume = {17},
number = {1},
pages = {1--46},
abstract = {<p style="text-align: justify;">The accurate simulation of disperse two-phase flows, where a discrete particulate
condensed phase is transported by a carrier gas, is crucial for many applications;
Eulerian approaches are well suited for high performance computations of such
flows. However, when the particles from the disperse phase have a significant inertia
compared to the time scales of the flow, particle trajectory crossing (PTC) occurs i.e. the
particle velocity distribution at a given location can become multi-valued. To properly
account for such a phenomenon many Eulerian moment methods have been recently
proposed in the literature. The resulting models hardly comply with a full set of desired
criteria involving: 1- ability to reproduce the physics of PTC, at least for a given
range of particle inertia, 2- well-posedness of the resulting set of PDEs on the chosen
moments as well as guaranteed realizability, 3- capability of the model to be associated
with a high order realizable numerical scheme for the accurate resolution of particle
segregation in turbulent flows. The purpose of the present contribution is to introduce
a multi-variate Anisotropic Gaussian closure for such particulate flows, in the spirit
of the closure that has been suggested for out-of-equilibrium gas dynamics and which
satisfies the three criteria. The novelty of the contribution is three-fold. First we derive
the related moment system of conservation laws with source terms, and justify the use
of such a model in the context of high Knudsen numbers, where collision operators
play no role. We exhibit the main features and advantages in terms of mathematical
structure and realizability. Then a second order accurate and realizable MUSCL/HLL
scheme is proposed and validated. Finally the behavior of the method for the description
of PTC is thoroughly investigated and its ability to account accurately for inertial
particulate flow dynamics in typical configurations is assessed.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.021213.140514a},
url = {https://global-sci.com/article/80370/on-the-anisotropic-gaussian-velocity-closure-for-inertial-particle-laden-flows}
}