A micromixer with unbalanced three-split rhombic sub-channels was proposed, and analyses of the mixing and flow characteristics of this micromixer were performed in this work. Three-dimensional Navier-Stokes equations in combination with an advection-diffusion model with two working fluids (water and ethanol) were solved for the analysis. The mixing index and pressure drop were evaluated and co...

In this paper, we perform an input-output analysis of the linearized Navier-Stokes equations by investigating their spatio-temporal ’impulse response’. Our first motivation for this problem comes from experimental work, where transition to turbulence is observed to occur either naturally, with so-called ’turbulent spots’, or when these spots are intentionally induced in the flow by deliberate e...

The tradition in Navier-Stokes analysis of finding estimates in terms of the Grashof number Gr , whose character depends on the ratio of the forcing to the viscosity ν, means that it is difficult to make comparisons with other results expressed in terms of Reynolds number Re, whose character depends on the fluid response to the forcing. The first task of this paper is to apply the approach of D...

A small parameter technique is used to derive Reynolds' lubrication equation from the Stokes equation. The error associated with the approximation is estimated in suitable norms.

We show that L3,∞-solutions to the three-dimensional NavierStokes equations near a flat part of the boundary are smooth. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 76D.

We prove the global existence of weak solutions for the 2-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient (λ = λ(ρ)). Initial data and solutions are small in energy-norm with nonnegative densities having arbitrarily large sup-norm. Then, we show that if there is a vacuum domain at the initial time, then the vacuum domain will retain for all time, and vanish...

In this work, the PGD method will be considered for solving some problems of fluid mechanics by looking for the solution as a sum of tensor product functions. In the first stage, the equations of Stokes and Burgers will be solved. Then, we will solve the Navier–Stokes problem in the case of the lid-driven cavity for different Reynolds numbers (Re = 100, 1000 and 10,000). Finally, the PGD method...

This paper presents an improved gas-kinetic scheme based on the Bhatnagar-Gross-Krook (BGK) model for the compressible Navier-Stokes equations. The current method extends the previous gaskinetic Navier-Stokes solver developed by Xu and Prendergast by implementing a general nonequilibrium state to represent the gas distribution function at the beginning of each time step. As a result, the requir...

We investigate the long-term dynamics of the three-dimensional NavierStokes-Voight model of viscoelastic incompressible fluid. Specifically, we derive upper bounds for the number of determining modes for the 3D Navier-Stokes-Voight equations and for the dimension of a global attractor of a semigroup generated by these equations. Viewed from the numerical analysis point of view we consider the N...

The Navier-Stokes equations describe a large class of fluid flows but are difficult to solve analytically because of their nonlinearity. We present in this paper a parallel solver for the 3-D Navier-Stokes equations of incompressible unsteady flows with constant coefficients, discretized by the finite difference method. We apply the prediction-projection method which transforms the Navier-Stoke...