International Conference «Mathematical and Information Technologies, MIT-2016»

28 August – 5 September 2016

Vrnjacka Banja, Serbia – Budva, Montenegro

Esipov D.V.   Popenov A.  

The simulation of viscous flows with disperse particles in the flat channel

Reporter: Popenov A.

There is a large class of problems involve the interaction of a viscous incompressible fluid with immersed
bodies. One of the challenges is to determine nonstationary influence of dispersed particles on the flow. Some
examples of such fluid-particles systems are: the proppant transport in hydraulic fractures, slurry pipes systems,
nanofluids flow in microchannels, transfer and absorption of medicines in the blood vessels. To avoid dificulties
with complicated remeshing procedures, we chose the immersed boundary method as main simulation tool.
In our proposed numerical method, the Navier-Stokes equations are dicretized using standard finite
difference scheme on a staggered Cartesian grid. Force field is calculated in a feedback way such that the fluid
velocity on the boundary satisfy the no-slip boundary condition. The force values are then spread to the
Cartesian grid points by a discrete representation of the delta function. The Navier-Stokes equations with the
forcing terms are then solved for pressure and velocity using SIMPLE method or MacCormack method. The
motion of the particles is governed by Newton's equations. Evaluating the hydrodynamic forces acting upon a
particles we calculate their positions and velocities. Three cases including driven cavity flow, steady and
unsteady flows past a circular cylinder are conducted to verificate the method.
A numerical simulation of fluid flow in a flat channel with relatively large number of rigid circular and
triangular particles has been performed. The influence of disperse particles on the flow has been investigated.

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