A stability condition is provided for a class of vorticity boundary formulas used with the second order finite-difference numerical scheme for the vorticity-stream function formulation of the unsteady incompressible Navier-Stokes equations. These local vorticity boundary formulas are derived using the no-slip boundary condition for the velocity. A new form of these long-stencil formulas is need...

We model and simulate numerically a droplet impact onto a solid substrate. The triple line dynamics modelling is implicit (as opposed to classical explicit mobility relations), it is based on the Shikhmurzaev equations. These equations include generalized Navier slip type boundary conditions with extra local surface tension gradient terms. Numerical results when spreading are presented. A parti...

We consider the system of Navier-Stokes equations as a model of the motion of compressible, viscous, “pressureless” fluids in the domain Ω = R+ with the no-slip boundary condition. We construct a global in time regular weak solution, provided that the initial density, ρ0, is bounded and the magnitude of the initial velocity u0 is suitably restricted in the semi-norm ‖ √ ρ0(·)u0(·)‖L2(Ω) + ‖∇u0(...

We show that molecular dynamics simulations can furnish useful boundary conditions at a solid surface bounding a two-component fluid. In contrast to some previous reports, convective-diffusive flow is consistent with continuum equations down to atomic scales. However, concentration gradients can produce flow without viscous dissipation that is inconsistent with the commonly used Navier slip con...

The authors establish error estimates for recently developed finite-element methods for incompressible viscous flow in domains with no-slip boundary conditions. The methods arise by discretization of a well-posed extended Navier-Stokes dynamics for which pressure is determined from current velocity and force fields. The methods use C elements for velocity and C elements for pressure. A stabilit...

Finite-volume procedure is presented for solving the natural convection of the laminar  nanofluid flow in a Γ shaped microchannel in this article. Modified Navier-Stokes equations for nanofluids are the basic equations for this problem. Slip flow region, including the effects of velocity slip and temperature jump at the wall, are the main characteristics of flow in the slip flow region. Steady ...

This paper is devoted to the existence of a weak solution system describing self-propelled motion rigid body in viscous fluid whole ℝ 3 . The modelled by incompressible nonhomogeneous Navier-Stokes with nonnegative density. described balance linear and angular momentum. We consider case where slip allowed at fluid-solid interface through Navier condition prove global solution.