We perform a linear stability analysis of viscoelastic plane Couette and Poiseuille flows with free-slip boundary conditions. The fluid is described by the Oldroyd-B constitutive model, are driven suitable body force. find that both types flow become linearly unstable, we characterise spatial structure unstable modes. By performing condition homotopy from to no-slip boundaries, demonstrate mode...

This paper reports the results of direct numerical simulation of the motion of a two-dimensional circular cylinder in Couette flow and in Poiseuille flow of an Oldroyd-B fluid. Both neutrally buoyant and nonneutrally buoyant cylinders are considered. The cylinder's motion and the mechanisms which cause the cylinders to migrate are studied. The stable equilibrium position of neutrally buoyant pa...

The simulation of flows of viscoelastic fluids is a very challenging domain from the theoretical as well as the numerical modelling point of view. In particular, all the existing methods have failed to solve the high Weissenberg number problem (HWNP). It is therefore clear that new tools are necessary. In this thesis we propose to tackle the problem of the simulation of viscoelastic fluids pres...

The Boltzmann equation describes the dynamics of rarefied gas flows, but the multidimensional nature of its collision operator poses a real challenge for its numerical solution. In this paper, the fast spectral method [36], originally developed by Mouhot and Pareschi for the numerical approximation of the collision operator, is extended to deal with other collision kernels, such as those corres...

Abstract. In this paper we present a fully deterministic method for the numerical solution to the Boltzmann equation of rarefied gas dynamics in a bounded domain for multi-scale problems. Periodic, specular reflection and diffusive boundary conditions are discussed and investigated numerically. The collision operator is treated by a Fourier approximation of the collision integral, which guarant...

Fluid flow through porous media is of great importance for many natural systems, such as transport of groundwater flow, pollution transport and mineral processing. In this paper, we propose and validate a novel finite volume formulation of the lattice Boltzmann method for porous flows, based on the Brinkman–Forchheimer equation. The porous media effect is incorporated as a force term in the lat...

A theoretical analysis is presented of viscous incompressible laminar flow in a pipe which rotates around an axis held at small angle with respect to its symmetry-axis. Analogous to the results of Barua and Benton [1, 2], solutions in closed-form are given for circulatory flows in the crosssectional plane of the pipe due to Coriolis forces in combination with Hagen-Poiseuille flow through the p...

In the present paper, we provide an analytical expression for the first- and second-order velocity slip coefficients by means of a variational technique that applies to the integrodifferential form of the Boltzmann equation based on the true linearized collision operator and the Cercignani-Lampis scattering kernel of the gas-surface interaction. The polynomial form of the Knudsen number obtaine...

The most important property of a fluid is its viscosity, it determines the flow properties. If one simulates a fluid using a particle model, calculating the viscosity accurately is difficult because it is a collective property. In this article we describe a new method that has a better signal to noise ratio than existing methods. It is based on using periodic boundary conditions to simulate cou...