We examine a heterogeneous alternating-direction method for the approximate solution of the FENE Fokker–Planck equation from polymer fluid dynamics and we use this method to solve a coupled (macro-micro) Navier–Stokes–Fokker–Planck system for dilute polymeric fluids. In this context the Fokker–Planck equation is posed on a high-dimensional domain and is therefore challenging from a computationa...

This survey paper reviews recent developments concerning the existence of global weak solutions to Fokker–Planck equations with unbounded drift terms, and coupled Navier–Stokes–Fokker–Planck systems of partial differential equations, that arise in finitely extensible nonlinear elastic (FENE) type kinetic models of incompressible dilute polymeric fluids in the case of general noncorotational flow.

Using branch continuation in the FENE-P model, we show that finite-amplitude travelling waves borne out of recently discovered linear instability viscoelastic channel flow (Khalid et al. , J. Fluid Mech. vol. 915, 2021, A43) are substantially subcritical reaching much lower Weissenberg ( $Wi$ ) numbers than on neutral curve at a given Reynolds $Re$ number over $Re \in [0,3000]$ . The surprising...

We prove global existence of weak solutions for the co-rotational FENE dumbbell model and the Doi model also called the Rod model. The proof is based on propagation of compactness, namely if we take a sequence of weak solutions which converges weakly and such that the initial data converges strongly then the weak limit is also a solution. To cite this article: A. Name1, A. Name2, C. R. Acad. Sc...

The problem of pure thermovibrational flow in a two-dimensional square cavity containing viscoelastic liquid is investigated the framework numerical approach based on governing balance equations for mass, momentum, and energy their complete non-linear time-dependent form. For closure, these are complemented with transport equation elastic stress formulated using finitely extensible nonlinear Ch...

We study translocation dynamics of a driven compressible semi-flexible chain consisting of alternate blocks of stiff (S) and flexible (F ) segments of size m and n respectively for different chain length N in two dimension (2D). The free parameters in the model are the bending rigidity κb which controls the three body interaction term, the elastic constant kF in the FENE (bond) potential betwee...