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...

We consider a viscous incompressible fluid filling an infinite horizontal domain bounded at the bottom by a plane wall and at the top by a rough wall. The latter is assumed to consist of a plane wall covered with periodically distributed asperities which size depends on a small parameter ε > 0. The assumption of sharp asperities is made, that is the height of the asperities does not vanish as ε...

The stability of viscous flow between rotating cylinders in the presence of a constant axial magnetic field is considered. The boundary conditions for general conductivities are examined. It is proved that the Principle of Exchange of Stabilities holds at zero magnetic Prandtl number, for all Chandrasekhar numbers, when the cylinders rotate in the same direction, the circulation decreases outwa...

We present a numerical scheme for viscoelastic flow based on a second-order central differencing method recently introduced in the context of incompressible newtonian flow; the incompressibility constraint is treated with the projection method. The result is a simple and efficient scheme that is readily adaptable to a wide class of differential constitutive equations and flow geometries. We imp...