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On the efficient numerical simulation of kinetic theory models of complex fluids and flows

On the efficient numerical simulation of kinetic theory models of complex fluids and flows. Francisco (Paco) Chinesta & Amine Ammar. LMSP UMR CNRS – ENSAM PARIS, France. Laboratoire de Rhéologie GRENOBLE, France. francisco.chinesta@paris.ensam.fr. In collaboration with:

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On the efficient numerical simulation of kinetic theory models of complex fluids and flows

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  1. On the efficient numerical simulation of kinetic theory models of complex fluids and flows Francisco (Paco) Chinesta & Amine Ammar LMSP UMR CNRS – ENSAM PARIS, France Laboratoire de Rhéologie GRENOBLE, France francisco.chinesta@paris.ensam.fr In collaboration with: R. Keunings Polymer solutions and melts M. Laso LCP M. Mackley & A. Ma Suspensions of CNT

  2. q1 q2 r1 r2 rN+1 qN Molecular dynamics R Brownian dynamics The different scales: Kinetic theory: Fokker-Planck Eq. Deterministic, Stochastic & BCF solvers Constitutive Eq.

  3. General Micro-Macro approach

  4. Solving the deterministic Fokker-Planck equation New efficient solvers for: • Reducing the simulation time of grid discretizations. • Computing multidimensional solutions where grid methods don’t run.

  5. I. Reducing the simulation time The idea … Model: PDE Model: PDE + Karhunen-Loève decomposition

  6. 1. FENE Model 1D 300.000FEM dof ~10dof 3D ~10 functions (1D, 2D or 3D)

  7. 2. Non-Linear Models: Doi LCP With only 6 d.o.f. !! Larson & Ottinger (Macromolecules, 1991)

  8. q1 q2 r1 r2 rN+1 qN II. Computing multidimensional solutions • It is time for dreaming! For N springs, the model is defined in a 3N+3+1 dimensional space !! ~ 10 approximation functions are enough

  9. BUT How defining those high-dimensional functions ? Natural answer: with a nodal description 10 nodes = 10 function values 1D

  10. q1 q2 r1 r2 rN+1 1080 ~ presumed number ofelementary particles in the universe !! qN 1D 10 dof 10x10 dof 2D 1080 dof 80D >1000D No function can be defined in a such space from a computational point of view !! F.E.M.

  11. Computing multidimensional solutions The idea … Model: PDE FEM GRID

  12. Solution EF q2 q1 F G q2 q1 1. MBS-FENE q2 q1

  13. Solution EF q2 q1 F G q2 q1

  14. Solution EF q2 q1 F G q2 q1

  15. Solution EF q2 q1 F G q2 q1

  16. Solution EF q2 q1 F G q2 q1

  17. Solution EF q2 q1 F G q2 q1

  18. Solution EF q2 q1 F G q2 q1

  19. Solution EF q2 q1 F G q2 q1

  20. Solution EF q2 q1 F G q2 q1

  21. Solution EF q2 q1 F G q2 q1

  22. Solution EF q2 q1 F G q2 q1

  23. 1D/9D q1 q2 q9 809 ~ 1016 FEM dof 80x9 RM dof 1040 FEM dof 100.000 RM dof 2D/10D

  24. 2. Complex Flows Example: Flow involving short fiber suspensions Kinematics: FEM-DVESS

  25. 3. Entangled polymer models based on reptation motion s = 0 s = 1 Doi-Edwards Model Ottinger Model: double reptation, CCR, chain stretching, …

  26. Ongoing works : (I) Stochastic models can be also reduced ! y=1

  27. Reduced Brownian Configurations Fields Discretization 4x4 1000x1000 • Solve i=1 and computed the reduced approximation basis • Solve for all i>1 the reduced problem:

  28. Ongoing works: (II) Suspensions of CNT: Aggregation/Orientation model Enhanced modeling: + The associated Fokker-Planck equation

  29. Perspectives • Enhanced kinetic model for CNT suspensions taking into account orientation and aggregation effects: FP & BD simulations. Collaboration with M. Mackley • Reduction of Stochastic, Brownian and molecular dynamics simulations. • Fast micro-macro simulations of complex flows: Lattice-Boltzmann & Reduced-FP; and many others mathematical topics (stabilization, wavelet bases, mixed formulations, enhanced particles methods, …). Collaboration with T. Phillips.

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