This paper concerns the vanishing viscosity limit of the two-dimensional degenerate viscous lake equations when the Navier slip conditions are prescribed on the impermeable boundary of a simply connected bounded regular domain. When the initial vorticity is in the Lebesgue spaceL with 2 < q ∞, we show that the degenerate viscous lake equations possess a unique global solution and the solution c...

This paper deals with the Rayleigh-Taylor Instability (RTI) at the interface between heavy poorly conducting fluid supported by a lighter poorly conducting fluid in the presence of transverse electric field, thermal radiation and roughness with slip boundary condition at bottom rough wall and no-shear condition at the top interface. Analytical solutions are obtained for modified Navier-Stokes a...

We study the influence of different implementations of no-slip solid wall boundary conditions on the convergence to steady-state of the Navier-Stokes equations. The various approaches are investigated using the energy method and an eigenvalue analysis. It is shown that the weak implementation is superior and enhances the convergence to steady-state for coarse meshes. It is also demonstrated tha...

Differences between Navier-Stokes-Fourier (NSF) slip/jump solutions and direct simulation Monte-Carlo (DSMC) computations are highlighted for a micro lid-driven cavity problem. The results indicate a need for better modelling techniques which at the same time retain low computational cost of NSF models. We also highlight the fact that many micro-flows that have been considered are simple planar...

The conventional Navier-Stokes-Fourier equations with no-slip boundary conditions are unable to capture the phenomenon of gas thermal transpiration. While kinetic approaches such as the direct simulation Monte Carlo method and direct solution of the Boltzmann equation can predict thermal transpiration, these methods are often beyond the reach of current computer technology, especially for compl...

Abstract We present a survey concerning the convergence, as viscosity goes to zero, of solutions three-dimensional evolutionary Navier-Stokes equations Euler equations. After considering Cauchy problem, particular attention is given convergence under Navier slip-type boundary conditions. show that, in presence flat boundaries (typically, half-space case), holds, uniformly time, with respect ini...

We consider 3D Navier-Stokes flows with no-slip boundary condition in an infinitely long pipe with circular cross section. The velocity fields we consider are independent of the variable parametrizing the axis of the pipe, and the component of the velocity normal to the axis is arranged to be circularly symmetric, though we impose no such symmetry on the component of velocity parallel to the ax...

We apply lattice Boltzmann method to study the phase separation of a two-dimensional binary fluid mixture in shear flow. The algorithm can simulate systems described by the Navier-Stokes and convection-diffusion equations. We propose a new scheme for imposing the shear flow which has the advantage of preserving mass and momentum conservation on the boundary walls without introducing slip veloci...