Practical techniques for a three‐dimensional FEM analysis of incompressible fluid flow contained with slip walls and a downstream tube bundle

Two practical techniques are proposed in this paper to simulate a flow contained in a plenum with a downstream tube bundle under a PC environment. First, a technique to impose slip wall conditions on smooth‐faced planes and sharp edges is proposed to compensate for the mesh coarseness relative to boundary layer thickness. In particular, a new type of Poisson equation is formulated to simultaneously satisfy both such velocity boundary conditions on walls and the incompressibility constraint. Second, a numerical model for a downstream tube bundle is proposed, where hydraulic resistance in a tube is imposed as a traction boundary condition on a fluid surface contacting the tube bundle end. The effectiveness of the techniques is numerically demonstrated in the application to a flow in a condenser water box. Copyright © 2001 John Wiley & Sons, Ltd.     

A new positive‐definite regularization of incompressible Navier–Stokes equations discretized with Q1/P0 finite element

A new regularization method is proposed for the Galerkin approximation of the incompressible Navier–Stokes equations with Q1/P0 element, by newly introducing a square‐type linear form into the variational divergence‐free constraint regularized with the global pressure jump (GPJ) method. The addition of the square‐type linear form is intended to eliminate the hydrostatic pressure mode appearing in confined flows, and to make the discretized matrix positive definite and then non‐singular without the pressure pegging trick. Effects of the free parameters for the regularization on the solutions are numerically examined with a 2‐D driven cavity flow problem. Furthermore, the convergences in the conjugate gradient iteration for the solution of the pressure Poisson equation are compared among the mixed method, the GPJ method and the present method for both leaky and non‐leaky 3‐D driven cavity flows. Finally, the non‐leaky 3‐D cavity flows at different Re numbers are solved to compare with the literature data and to demonstrate the accuracy of the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.     

On streamline diffusion arising in Galerkin FEM with predictor/multi‐corrector time integration

In the present paper, the author shows that the predictor/multi‐corrector (PMC) time integration for the advection–diffusion equations induces numerical diffusivity acting only in the streamline direction, even though the equations are spatially discretized by the conventional Galerkin finite element method (GFEM). The transient 2‐D and 3‐D advection problems are solved with the PMC scheme using both the GFEM and the streamline upwind/Petrov Galerkin (SUPG) as the spatial discretization methods for comparison. The solutions of the SUPG‐PMC turned out to be overly diffusive due to the additional PMC streamline diffusion, while the solutions of the GFEM‐PMC were comparatively accurate without significant damping and phase error. A similar tendency was seen also in the quasi‐steady solutions to the incompressible viscous flow problems: 2‐D driven cavity flow and natural convection in a square cavity. Copyright © 2002 John Wiley & Sons, Ltd.     

A projection method of estimation for a subfamily of exponential families

Summary This paper is concerned with estimation for a subfamily of exponential-type, which is a parametric model with sufficient statistics. The family is associated with a surface in the domain of a sufficient statistic. A new estimator, termed a projection estimator, is introduced. The key idea of its derivation is to look for a one-to-one transformation of the sufficient statistic so that the subfamily can be associated with a flat subset in the transformed domain. The estimator is defined by the orthogonal projection of the transformed statistic onto the flat surface. Here the orthogonality is introduced by the inverse of the estimated variance matrix of the statistic on the analogy of Mahalanobis's notion (1936,Proc. Nat. Inst. Sci. Ind.,2, 49–55). Thus the projection estimator has an explicit representation with no iterations. On the other hand, the MLE and classical estimators have to be sought as numerical solutions by some algorithm with a choice of an initial value and a stopping rule. It is shown that the projection estimator is first-order efficient. The second-order property is also discussed. Some examples are presented to show the utility of the estimator.     

Data driven time scale in Gaussian quasi-likelihood inference

We study parametric estimation of ergodic diffusions observed at high frequency. Different from the previous studies, we suppose that sampling stepsize is unknown, thereby making the conventional Gaussian quasi-likelihood not directly applicable. In this situation, we construct estimators of both model parameters and sampling stepsize in a fully explicit way, and prove that they are jointly asymptotically normally distributed. High order uniform integrability of the obtained estimator is also derived. Further, we propose the Schwarz (BIC) type statistics for model selection and show its model-selection consistency. We conducted some numerical experiments and found that the observed finite-sample performance well supports our theoretical findings.

     

Railgun using plasma initiation separated from the projectile

Preacceleration of a projectile is important for reducing the erosion of the bore surface in a railgun. Gas guns, electrothermal guns, and other railguns are commonly used to preaccelerate the projectile. A new method, called the plasma initiation separated from the projectile (PISP) method is proposed, and its effectiveness is confirmed experimentally. A thin copper wire is placed near the edge of the railgun, and it explodes and forms a plasma that has a fast flow velocity due to the Lorentz force. This fast flowing plasma collides with the projectile, which obtains an initial velocity mainly by the momentum transfer. Since the current increases while only the plasma is accelerated, the driving force of the projectile just after the collision of the plasma with the projectile is large. The PISP method works as an inductive energy storage circuit with an opening switch     

Observation of micropores in hard-carbon using Xe NMR porosimetry

The existence of micropores and the change of surface structure in pitch-based hard-carbon in xenon atmosphere were demonstrated using ¹²⁹Xe NMR. For high-pressure (4.0 MPa) ¹²⁹Xe NMR measurements, the hard-carbon samples in Xe gas showed three peaks at 27, 34 and 210 ppm. The last was attributed to the xenon in micropores (<1 nm) in hard-carbon particles. The NMR spectrum of a sample evacuated at 773 K and exposed to 0.1 MPa Xe gas at 773 K for 24 h showed two peaks at 29 and 128 ppm, which were attributed, respectively, to the xenon atoms adsorbed in the large pores (probably mesopores) and micropores of hard-carbon. With increasing annealing time in Xe gas at 773 K, both peaks shifted and merged into one peak at 50 ppm. The diffusion of adsorbed xenon atoms is very slow, probably because the transfer of molecules or atoms among micropores in hard-carbon does not occur readily. Many micropores are isolated from the outer surface. For that reason, xenon atoms are thought to be adsorbed only by micropores near the surface, which are easily accessible from the surrounding space.     

23Na NMR study of ionic mesophases in molten sodium carboxylates

The ²³Na NMR lineshapes are reported for the ionic mesophase and isotropic phase of the melts of sodium n-butyrate and sodium isovalerate. The powder pattern for the central transition typical for the second-order quadrupole effect observed in the mesophase melts is of particular interest. Some analogies to ²³Na behavior in sodium β-alumina are pointed out.