Extended separated representation of micro-macro models related to complex fluid flows

International audienceRecently, we proposed a new discretization technique (fully deterministic and based on a separated representation of the unknown fields) was applied for solving efficiently highly dimensional partial differential equation, some of them never until now solved. In particular we addressed the models related to polymer solutions (FENE, bead-spring-chains, …) and melts (Doi-Edwars or Ottinger models), associative polymers, fiber suspensions, …. The interested reader can refer to [1]-[2] and the references therein. All the models considered in our former publications concerned rheological flows, where a homogeneous microstructure evolution was assumed. In the present work we focus on the solution of complex flows, where an extended separated representation involving physical space, time and the conformational coordinates is proposed and successfully applied. Two benchmark problems are here considered: (i) the converging flow of an associative polymer, where the flow kinematics is solved by using the stream-tubes method technique; and (ii) the driven cavity flow, involving a short fiber suspension, where the flow kinematics is solved by using a stabilized finite element method. In both cases the microscopic model is solved by applying the extended separated representation technique. [1] A. Ammar, B. Mokdad, F. Chinesta, R. Keunings, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids, J. Non-Newtonian Fluid Mech., 139, 2006, pp. 153-176. [2] A. Ammar, B. Mokdad, F. Chinesta et R. Keunings, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. Part II: transient simulation using space-time separated representations, 144, 2007, pp. 98-121. [no pdf