FLUID-PARTICLE FLOW - A SYMMETRICAL FORMULATION

In this Note, we present a numerical method to simulate the motion of solid particles in a moving viscous fluid. The fluid is supposed to be Newtonian and incompressible. The Arbitrary Lagrangian Eulerian formu lation of the Navier-Stokes equations is discretized at the first orde r in time, as are the equations for the solid bodies. The advection te rm is taken into account by a method of characteristics. The variation al formulation of the coupled problem is then established, and the bou ndary integrals expressing the hydrodynamical forces are eliminated. B y introduction of an appropriate Finite Element approximation, a symme tric linear system is obtained. This system is solved by an inexact Uz awa algorithm, preconditionned by a Laplace operator with Neumann boun dary conditions on the pressure. Numerical results are presented, for 2 and 100 particles: The Reynolds number in both cases is of the order of 100.