We present modeling of an incompressible viscous flow through a fracture adjacent to a porous medium. A fast stationary flow, predominantly tangential to the porous medium is considered. Slow flow in such setting can be described by the Beavers-Joseph-Saffman slip. For fast flows, a nonlinear filtration law in the porous medium and a nonlinear interface law are expected. In this paper we rigoro...

The stability of an infinitely long, inviscid but compressible liquid jet under sinusoidal disturbances of the surface, still assumed to be sharp, is considered. This extends Rayleigh's theory. We show that despite compressibility the unstable region is /.> kc = 2na (/. wavelength, a radius) as Rayleigh's criterion for incompressible liquids states. The character of the unstable long wavelength...

Using a very high precision spectral calculation applied to the incompressible and inviscid flow with initial condition ψ0(x1, x2) = cos x1 + cos 2x2, we find that the width δ(t) of its analyticity strip follows a ln(1/t) law at short times over eight decades. The asymptotic equation governing the structure of spatial complex-space singularities at short times (Frisch, Matsumoto and Bec 2003, J...

In this paper we consider the problem of boundary observer design for one-dimensional first order linear and quasi-linear strict hyperbolic systems with n rightward convecting transport PDEs. By means of Lyapunov based techniques, we derive some sufficient conditions for exponential boundary observer design using only the information from the boundary control and the boundary conditions. We con...

The flow field of an infinitely bladed propeller of disk loading proportional to (r/R) • (l-r/R) in an incompressible, inviscid fluid is expressed in terms of a series of Legendre functions. Numerical calculations have been carried out for the case n = 5« The radial velocity at r = R, and the shape of the stream surface passing through the periphery of the propeller disk are determined and comp...

The flux-vector and flux-difference splittings of Steger-Warming, Van Leer and Roe are tested in all possible combinations in the implicit and explicit operators that can be distinguished in implicit relaxation methods for the steady Euler and Navier-Stokes equations. The tests include one-dimensional inviscid nozzle flow, and two-dimensional inviscid and viscous shock reflection. Roe’s splitti...

We review and extend to the compressible regime an earlier parallelization of an implicit incompressible unstructured Euler code [9], and solve for ow over an M6 wing in subsonic, transonic, and supersonic regimes. While the parallelization philosophy of the compressible case is identical to the incompressible, we focus here on the nonlinear and linear convergence rates, which vary in di erent ...

We review and extend to the compressible regime an earlier parallelization of an implicit incompressible unstructured Euler code [9], and soIve for ffow over an M6 wing in subsonic, transonic, and supersonic regimes. While the parallelization philosophy of the compressible case is identical to the incompressible, we focus here on the nonlinear and linear convergence rates, which vary in dMerent...

Research in convective heat transfer using suspensions of nanometer-sized solid particles in base liquids started only over the past decade. Recent investigations on nanofluid, as such suspensions are often called, indicate that the suspended nanoparticles remarkably change the transport properties and heat transfer characteristics of the suspension. Bending walls can also improve heat transfer...

A new fourth order compact formulation for the steady 2-D incompressible Navier-Stokes equations is presented. The formulation is in the same form of the Navier-Stokes equations such that any numerical method that solve the Navier-Stokes equations can easily be applied to this fourth order compact formulation. In particular in this work the formulation is solved with an efficient numerical meth...