In this article we discuss a methodology allowing the direct numerical simulation of the flow of mixtures of rigid solid particles and incompressible viscous fluids, possibly non-Newtonian. The simulation methods rest essentially on the combination of:
- (a) Lagrange multiplier based fictitious domain methods which allow the fluid flow computations to be done in a fixed flow region.
- (b) Finite element approximation of the Navier-Stokes equations occurring in the global model.
- (c) Time discretization by operator splitting schemes in order to treat optimally the various operators present in the model.
We conclude this article by the presentation of the results of various numerical experiments including the simulation of sedimentation and fluidization phenomena in two and three dimensions.
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Last updated October 16, 2000