2002 -11 -29
10 :15 at ML J 21

Kinetic theory approach to the multiphase flow simulations

Santosh Ansumali

Institute of Polymers, ETH Zurich

A good understanding of the multiphase flows is needed both from the fundamental perspective, as well as, from the engineering perspective. A molecular simulation of the multiphase flows is not feasible, and a fully macroscopic description is difficult to formulate. Thus, it is natural to think of a mesoscopic scheme based on the kinetic theory. Recently, ways to obtain non-linearly stable and numerically efficient algorithms for hydrodynamic simulation from simplified BGK-like kinetic models have been proposed. However, such a simplified models for multiphase flows do not exist at present.

In this talk, I will review different approaches to simulate multiphase flows. Afterwards, I will present a simplified kinetic model to describe a multiphase fluid. The model is based on the fact that the Van der Waals' theory is not the unique mean field representation of short-range repulsive forces. Sanchez and Lacombe have shown that it is possible to get an equation of state similar to the Van der Waals' theory without resorting to the hard sphere picture. In particular, it is possible to get the excluded volume effect by considering a single non-ideal gas as a mixture of two ideal gases plus somegeometric constraints. Starting from the Grad's first equation, I will propose a systematic way to incorporate Sanchez and Lacombe description of the non-ideal fluid into the kinetic theory. Further, advantage of using such an approach for the numerical simulation will be discussed.