Computation of head–disk interface gap micro flowfields using DSMC and continuum–atomistic hybrid methods

This paper discusses computational modeling of micro flow in the head–disk interface (HDI) gap using the direct simulation Monte Carlo (DSMC) method. Modeling considerations are discussed in detail both for a stand‐alone DSMC computation and for the case of a hybrid continuum–atomistic simulation that couples the Navier–Stokes (NS) equation to a DSMC solver. The impact of the number of particles and number of cells on the accuracy of a DSMC simulation of the HDI gap is investigated both for two‐ and three‐dimensional configurations. An appropriate implicit boundary treatment method for modeling inflow and outflow boundaries is used in this work for a three‐dimensional DSMC micro flow simulation. As the flow outside the slider is in the continuum regime, a hybrid continuum–atomistic method based on the Schwarz alternating method is used to couple the DSMC model in the slider bearing region to the flow outside the slider modeled by NS equation. Schwarz coupling is done in two dimensions by taking overlap regions along two directions and the Chapman–Enskog distribution is employed for imposing the boundary condition from the continuum region to the DSMC region. Converged hybrid flow solutions are obtained in about five iterations and the hybrid DSMC–NS solutions show good agreement with the exact solutions in the entire domain considered. An investigation on the impact of the size of the overlap region on the convergence behavior of the Schwarz method indicates that the hybrid coupling by the Schwarz method is weakly dependent on the size of the overlap region. However, the use of a finite overlap region will facilitate the exchange of boundary conditions as the hybrid solution has been found to diverge in the absence of an overlap region for coupling the two models. Copyright © 2009 John Wiley & Sons, Ltd.     

A Gibbs-Like Measure for Single-Time, Multi-Scale Energy Transfer in Stochastic Signals and Shell Model of Turbulence

A Gibbs-like approach for simultaneous multi-scale correlation functions in random, time-dependent, multiplicative processes for the turbulent energy cascade is investigated. We study the optimal log-normal Gibbs-like distribution able to describe the subtle effects induced by non-trivial time dependency on both single-scale (structure functions) and multi-scale correlation functions. We provide analytical expression for the general multi-scale correlation functions in terms of the two-point correlations between multipliers and we show that the log-normal distribution is already accurate enough to reproduce quantitatively many of the observed behavior. The main result is that non-trivial time effects renormalize the Gibbs-like effective potential necessary to describe single-time statistics. We also present a generalization of this approach to more general, non log-normal, potentials. In the latter case one obtains a formal expansion of both structure functions and multi-scale correlations in terms of cumulants of all orders.     

Approximate Inverse Preconditioning for Shifted Linear Systems

In this paper we consider the problem of preconditioning symmetric positive definite matrices of the form A =A+I where >0. We discuss how to cheaply modify an existing sparse approximate inverse preconditioner for A in order to obtain a preconditioner for A . Numerical experiments illustrating the performance of the proposed approaches are presented.     

On the scaling of three-dimensional homogeneous and isotropic turbulence

In this paper we investigate the scaling properties of three-dimensional isotropic and homogeneous turbulence. We analyze a new form of scaling (extended self-similarity) recently introduced in the literature. We found that anomalous scaling of the velocity structure functions is clearly detectable even at a moderate and low Reynolds number and it extends over a much wider range of scales with respect to the inertial range.     

On the energy dissipation in a convective well-mixed layer

Summary Energy dissipation in a convective atmospheric mixed layer and its parametrization are discussed. A formulation of energy dissipation based on the results of Zeman and Tennekes and Kitaigoroskii is proposed.

---

Riassunto In questo lavoro si discutono il ruolo e la parametrizzazione dell'energia dissipata nei moti convettivi che generano lo strato rimescolato in atmosfera. Si propone una possibile parametrizzazione basata sui precedenti lavori di Kitaigoroskii e di Zeman e Tennekes.

---

Резюме Обсуждается диссипация энергии в конвективном атмосферном перемешанном слое и параметризация диссипации. Предлагается формулировка диссипации энергии, основанная на результатах Земана и Тенекеса (1976) и Китайгородского (1978).

     

A Relaxed Dimensional Factorization preconditioner for the incompressible Navier–Stokes equations

In this paper we introduce a Relaxed Dimensional Factorization (RDF) preconditioner for saddle point problems. Properties of the preconditioned matrix are analyzed and compared with those of the closely related Dimensional Splitting (DS) preconditioner recently introduced by Benzi and Guo [7]. Numerical results for a variety of finite element discretizations of both steady and unsteady incompressible flow problems indicate very good behavior of the RDF preconditioner with respect to both mesh size and viscosity.