In this paper, we prove the uniform nonlinear structural stability of Hagen–Poiseuille flows with arbitrary fluxes in axisymmetric case an infinitely long pipe. This is first step to study Liouville type property for steady solutions Navier–Stokes system a pipe, which may play important role proving existence flux nozzle Poiseuille as far field asymptotic states (Leray’s problem). A key priori ...

Exact coherent structures are three-dimensional, nonlinear traveling wave solutions of the Navier-Stokes equations. These solutions are typically unstable from onset, yet they capture the basic statistical and structural features of low Reynolds number turbulent shear flows remarkably well. These exact coherent structures have now been found in all canonical shear flows: plane Couette, Poiseuil...

A thermal lattice Boltzmann method (TLBM) is used for analysis of flow and heat transfer in two-dimensional channels. Simulation results are presented for thermal Couette and thermal Poiseuille channel flows. Analytical solution for temperature field in hydraulically and thermally developed flows are used to verify the current TLBM results. The method is further applied to study the forced conv...

Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time τ and the lattice spacing. The analytic solutions are the exact representation of these two flows without an...

An H theorem for the linearized Grad 13 moment equations leads to regularizing constitutive equations for higher fluxes and to a complete set of boundary conditions. Solutions for Couette and Poiseuille flows show good agreement with direct simulation Monte Carlo calculations. The Knudsen minimum for the relative mass flow rate is reproduced.

To evaluate a lattice Boltzmann method (LBM) for the three dimensional continuum to non-continuum transitional flow regimes, the results are compared with those of the molecular dynamics (MD) simulations by the Leonard-Jones potential. The flow field considered is in a modeled nanoporous medium whose porosity is 0.88 and consists of square cylinder rods. The equations used in the LBM are modifi...