On the modeling of the transport of particles in turbulent flows

We investigate different asymptotic regimes for Vlasov equations modeling the evolution of a cloud of particles in a turbulent flow. In one case we obtain a convection or a convection-diffusion effective equation on the concentration of particles. In the second case, the effective model relies on a Vlasov-Fokker-Planck equation.

[1]  Henar Herrero,et al.  On The Motion of Dispersed Balls in a Potential Flow: A Kinetic Description of the Added Mass Effect , 1999, SIAM J. Appl. Math..

[2]  Pierre Berthonnaud.  Limites fluides pour des modles cintiques de brouillards de gouttes monodisperss , 2000 .

[3]  Giovanni Russo,et al.  Kinetic Theory for Bubbly Flow II: Fluid Dynamic Limit , 1996, SIAM J. Appl. Math..

[4]  Sergey Gavrilyuk,et al.  Kinetic model for the motion of compressible bubbles in a perfect fluid , 2002 .

[5]  Matthieu Brassart.  Limite semi-classique de transformées de Wigner dans des milieux périodiques ou aléatoires , 2002 .

[6]  K. Domelevo,et al.  Solution of a Kinetic Stochastic Equation Modeling a Spray in a Turbulent Gas Flow , 1997 .

[7]  M. Vignal,et al.  Limites visqueuses pour des systèmes de type Fokker–Planck–Burgers unidimensionnels , 2001 .

[8]  George Papanicolaou,et al.  Dynamic Theory of Suspensions with Brownian Effects , 1983 .

[9]  P. Jabin.  Macroscopic limit of Vlasov type equations with friction , 2000 .

[10]  P. Jabin,et al.  Large time concentrations for solutions to kinetic equations with energy dissipation , 2000 .

[11]  Ryogo Kubo,et al.  STOCHASTIC LIOUVILLE EQUATIONS , 1963 .

[12]  Alexis Vasseur,et al.  Classical and quantum transport in random media , 2003 .

[13]  Pierre-Emmanuel Jabin,et al.  Notes on Mathematical Problems on the Dynamics of Dispersed Particles Interacting through a Fluid , 2000 .

[14]  Kamel Hamdache,et al.  Global existence and large time behaviour of solutions for the Vlasov-Stokes equations , 1998 .

[15]  François Golse,et al.  From Kinetic To Macroscopic Models , 1998 .

[16]  A. Majda,et al.  SIMPLIFIED MODELS FOR TURBULENT DIFFUSION : THEORY, NUMERICAL MODELLING, AND PHYSICAL PHENOMENA , 1999 .

[17]  P. J. O'rourke,et al.  Statistical properties and numerical implementation of a model for droplet dispersion in a turbulent gas , 1989 .

[18]  Leonid I. Zaichik,et al.  A statistical model of particle transport and heat transfer in turbulent shear flows , 1999 .

[19]  Giovanni Russo,et al.  Kinetic Theory for Bubbly Flow I: Collisionless case , 1996, SIAM J. Appl. Math..

[20]  C. Villani.  Chapter 2 – A Review of Mathematical Topics in Collisional Kinetic Theory , 2002 .

[21]  F. Spellman.  Combustion Theory , 2020 .

[22]  G. Hidy,et al.  The dynamics of aerocolloidal systems , 1970 .

[23]  T. Goudon.  Asymptotic problems for a kinetic model of two-phase flow , 2001, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.