Both the particle based Direct Simulation Monte Carlo (DSMC) method and a compressible Navier-Stokes based continuum method are used to investigate the flow inside micronozzles and to predict the performance of such devices. For the Navier-Stokes approach, both slip and no-slip boundary conditions are applied. Moreover, the two methods have been coupled to be used together in a hybrid particle-...

In this paper we propose the analysis of the incompressible nonhomogeneous Navier-Stokes equations with nonlinear outflow boundary condition. This kind of boundary condition appears to be, in some situations, a useful way to perform numerical computations of the solution to the unsteady Navier-Stokes equations when the Dirichlet data are not given explicitly by the physical context on a part of...

Numerical prediction of flow physics involves the specification of boundary conditions to close the problem. Whether all or part of the boundary needs consideration depends on the nature of the investigated partial differential equations. Taking as an example, closure boundary conditions for Navier-Stokes equations at an incompressible limit take different forms because a time-dependent problem...

We consider the lubrication model for a thin film driven by competing gravitational forces and thermal gradients on an inclined plane. We are interested in the general traveling wave problem when the Navier slip boundary condition is used. We contrast (1) gravity dominated flow, (2) Marangoni dominated flow, and (3) flow in which the two driving effects balance. For a “singular slip” model we s...

A sufficient condition of regularity for solutions to the Navier-Stokes equations is proved. It generalizes the so-called L 3,∞-case.

We use the biorthogonal multiwavelets related by differentiation constructed in previous work to construct compactly supported biorthogonal multiwavelet bases for the space of vector fields on the upper half plane R+ such that the reconstruction wavelets are divergence-free and have vanishing normal components on the boundary of R+. Such wavelets are suitable to study the Navier–Stokes equation...