Numerical Modeling of Complex Fluids: State-of-the-Art, Recent Developments and New Challenges

International audience; Kinetic theory models involving the Fokker-Planck equation, can be accurately discretised using a mesh support (Finite Elements, Finite Differences, Finite Volumes, Spectral Techniques). However these techniques involve a high number of approximation functions. When the model involves high dimensional spaces (including physical and conformation spaces and time) standard discretisation techniques fail due to the excessive computation time required to perform accurate numerical simulations. Stochastic simulations have been widely used to bypass the difficulty just referred to. However accurate representations of molecular conformation distributions require simulation of an extremely large number of trajectories of the stochastic processes, as well as working with a very small time step. Some new appealing strategies that allow these limitations to be circumvented are based on the use of a reduced approximation basis within an adaptive procedure, some of them making use of an efficient separated representation of the solution. This paper explores the potential of these new advanced strategies.