Abstract We present a numerical solution method for time-dependent viscoelastic fluid–structure interaction employing the arbitrary Lagrangian Eulerian framework. The derived monolithic variational formulation is discretized in time using shifted Crank–Nicolson scheme and space finite element method. For linearisation we employ Newton’s with exact Jacobians. fluid modelled either Oldroyd-B or B...

In this work a theoretical analysis is presented for the problem of peristaltic transport of an incompressible Oldroyd 3-constant fluid in an infinite channel with flexible walls. The flow is induced by an infinite sinusoidal wave train moving along the walls of the channel. The fluid is electrically conducting and a magnetic field has been applied transversely to the flow. This problem has num...

In this work, the exact analytic solutions for some unsteady oscillating flows of an incompressible Burgers' fluid in a duct of rectangular cross-section are considered. Here, two types of flows, namely, (1) flow due to the oscillating pressure gradient, and (2) flow due to the oscillation of duct parallel to its length, were considered. The exact analytical expressions for the velocity field a...

A coupled finite difference algorithm on rectangular grids is developed for viscoelastic ink ejection simulations. The ink is modeled by the Oldroyd-B viscoelastic fluid model. The coupled algorithm seamlessly incorporates several things: (1) a coupled level set-projection method for incompressible immiscible two-phase fluid flows; (2) a higher-order Godunov type algorithm for the convection te...

background: the airway surface liquid (asl), which is a fluid layer coating the interior epithelial surface of the bronchi and bronchiolesis, plays an important defensive role against foreign particles and chemicals entering lungs. objective: numerical investigation has been employed to solve two-layer model consisting of mucus layer as a viscoelastic fluid and periciliary liquid layer as a newt...

We prove an analogue of the Caffarelli–Kohn–Nirenberg theorem for weak solutions of a system of PDEs that model a viscoelastic fluid in the presence of an energy damping mechanism. The system was recently introduced as a possible method of establishing the global-in-time existence of weak solutions of the well-known Oldroyd system.