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Authors: Berselli, L. C.* 
Cerminara, M.* 
Iliescu, T.* 
Title: Disperse Two-Phase Flows, with Applications to Geophysical Problems
Journal: Pure and Applied Geophysics 
Series/Report no.: 1/172(2014)
Publisher: Birkhauser Verlag AG
Issue Date: 2014
DOI: 10.1007/s00024-014-0889-5
Keywords: dam-break (lock-exchange) problem
Dilute suspensions
direct and large eddy simulations
Eulerian models
slightly compressible flows
Subject Classification04. Solid Earth::04.08. Volcanology::04.08.04. Thermodynamics 
04. Solid Earth::04.08. Volcanology::04.08.08. Volcanic risk 
05. General::05.05. Mathematical geophysics::05.05.99. General or miscellaneous 
Abstract: In this paper, we study the motion of a fluid with several dispersed particles whose concentration is very small (smaller than 10-3), with possible applications to problems coming from geophysics, meteorology, and oceanography. We consider a very dilute suspension of heavy particles in a quasi-incompressible fluid (low Mach number). In our case, the Stokes number is small and—as pointed out in the theory of multiphase turbulence—we can use an Eulerian model instead of a Lagrangian one. The assumption of low concentration allows us to disregard particle–particle interactions, but we take into account the effect of particles on the fluid (two-way coupling). In this way, we can study the physical effect of particles’ inertia (and not only passive tracers), with a model similar to the Boussinesq equations. The resulting model is used in both direct numerical simulations and large eddy simulations of a dam-break (lock-exchange) problem, which is a well-known academic test case. © 2014, Springer Basel.
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