Direct numerical simulation of microstructured uids : Numerical aspects

Direct Numerical Simulations (DNS) of the distribution function of conformation of small axisymmetric particles is considered from a numerical point of view. The mathematical modelling of microstructured uid has to take into account (i) the e ect of the surrounding uid onto the microstructure and (ii) the e ect of the microstructures on the uid. We consider (i) the simulation of the conformation distribution function by using a Fokker-Planck equation in an Eulerian framework (ii) a full Lagrangian technique to track individual particles,(stochastic simulation) (iii) the double Lagrangian technique for the solution of the Fokker-Planck equation of Szeri and Leal [20]. Finally a method is proposed which combines the advantages of the stochastic simulation with those of the double Lagrangian method by clustering particles within the framework of stochastic simulation.