A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids. Part II: Transient simulation using space-time separated representations

Amine Ammar (1) , Béchir Mokdad (1) , Francisco Chinesta (2) , Roland Keunings (3)

1 LR - Laboratoire de rhéologie
2 LMSP - Laboratoire de Mécanique des Systèmes et des Procédés
3 CESAME - Centre for systems engineering and applied mechanics [Louvain]

Kinetic theory models described within the Fokker–Planck formalism involve high-dimensional spaces (including physical and conformation spaces and time). One appealing strategy for treating this kind of problems lies in the use of separated representations and tensor product approximations basis. This technique that was introduced in a former work for treating steady state kinetic theory models is extended here for treating transient models.

Mots clés: Multidimensional problems; Complex fluids; Numerical modeling; Separation of variables; Model reduction; Kinetic theory; Fokker–Planck equation

Domaines: Mécanique des structures [physics.class-ph]

Amine Ammar, Béchir Mokdad, Francisco Chinesta, Roland Keunings. A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids. Part II: Transient simulation using space-time separated representations. Journal of Non-Newtonian Fluid Mechanics, 2007, 144 (2-3), pp.98-121. ⟨10.1016/j.jnnfm.2007.03.009⟩. ⟨hal-01633241⟩