A question which has been open in the theory of stochastic equations with delay for around 25 years is: what conditions on the coefficients of a linear stochastic functional differential equations characterise the mean square stability of the solution? In this talk, a simple proof is supplied for a one-dimensional linear Volterra equation. The arguments extend to equations with finite memory or...

Turbulence equilibrium state is analyzed for the modeled Reynolds-stress transport equation, assuming most general formulation of pressure–strain correlation. In a two-dimensional mean flow at high-Reynolds number, an algebraic equation system obtained, providing anisotropies as functions model coefficients. Conversely, equations provide calibration conditions coefficients to predict specified ...

This paper presents a new finite-volume discretization of a generalised Lattice Boltzmann equation (LBE) on unstructured grids. This equation is the continuum LBE, with the addition of a second order time derivative term (memory), and is derived from a second-order differential form of the semi-discrete Boltzmann equation in its implicit form. The new scheme, named unstructured lattice Boltzman...

Last week we studied the key concepts of Finite Element Methods, in the context of solving the Laplace equation. We saw the …nite element method arise naturally as an instance of the Galerkin method, a discretization procedure for the corresponding weak formulation. Finally, we learned about error estimates, examples of elements and implementation practices. This week, our main objective is to ...

in general, the aerodynamic stability of long span bridges is evaluated based on the results of wind tunnel tests in the low reynolds number region, because in almost all wind tunnel tests, it is impracticable to satisfy reynolds number similitude. therefore, in order to correctly evaluate conventional wind tunnel test results, reynolds number effects on the aerodynamic force coefficients acting o...

S U M M A R Y The stationary Reynolds equation is solved over a rectangular region. The problem is linearized by Picard linearization. The ADI method is used to solve the resulting set of linear equations. A set of parameters is introduced to speed up convergence as well for the Picard linearization as for the ADI method. A comparison is made with Booy-Coleman's method. Results are given for be...

In this paper we extend the recently introduced edge stabilization method to the case of nonconforming finite element approximations of the linearized Navier-Stokes equation. To get stability also in the convective dominated regime we add a term giving L2-control of the jump in the gradient over element boundaries. An a priori error estimate that is uniform in the Reynolds number is proved and ...

We extend the numerical simulations of She et al. [Phys. Rev. Lett. 70, 3251 (1993)] of highly turbulent flow with 15 ≤ Taylor-Reynolds number Reλ ≤ 200 up to Reλ ≈ 45 000, employing a reduced wave vector set method (introduced earlier) to approximately solve the Navier-Stokes equation. First, also for these extremely high Reynolds numbers Reλ, the energy spectra as well as the higher moments –...

Efficient mixing, typically characterized by chaotic advection, is hard to achieve in low Reynolds number conditions because of the linear nature of the Stokes equation that governs the motion. Here we show that low-Reynolds-number swimmers moving on quasi-periodic orbits can result in considerable stretching and folding of fluid elements. We accurately follow packets of tracers within the flui...