From kinetic theory to dissipative fluid dynamics

We present the results of deriving the Israel-Stewart equations of relativistic dissipative fluid dynamics from kinetic theory via Grad’s 14-moment expansion. Working consistently to second order in the Knudsen number, these equations contain several new terms which are absent in previous treatments.     

Influence of cubic nonlinearity on the dispersion relation for long waves on a water surface

The influence of cubic nonlinearity on the dispersion relation for long waves on a water surface is analyzed. In the long wavelength limit, it is shown that the dispersion relation is not affected by the cubic terms. The results are compared with the dispersion relation for stationary solutions to the Korteweg—de Vries equation.     

Non-adiabatic gravitational collapse of charged radiating fluid spheres

Dynamical equations governing the non-adiabatic collapse of a shear-free spherical distribution of unisotropic matter in the presence of charge are obtained. A brief outline of constructing a model describing collapse of a charged radiating fluid sphere in the set up developed is given.     

Time-dependent quantum fluid density functional theory of hydrogen molecule under intense laser fields

A time-dependent generalized non-linear Schr?dinger equation (GNLSE) of motion was earlier derived in our laboratory by combining density functional theory and quantum fluid dynamics in three-dimensional space. In continuation of the work reported previously, the GNLSE is applied to provide additional knowledge on the femtosecond dynamics of the electron density in the hydrogen molecule interacting with high-intensity laser fields. For this purpose, the GNLSE is solved numerically for many time-steps over a total interaction time of 100 fs, by employing a finite-difference scheme. Various time-dependent (TD) quantities, namely, electron density, ground-state survival probability and dipole moment have been obtained for two laser wavelengths and four different intensities. The high-order harmonics generation (HHG) is also examined. The present approach goes beyond the linear response formalism and, in principle, calculates the TD electron density to all orders of change. Dedicated to Prof. D Mukherjee on his 60th birthday     

Validation of adaptive unstructured hexahedral mesh computations of flow around a wind turbine airfoil

In this paper we investigate local adaptive refinement of unstructured hexahedral meshes for computations of the flow around the DU91 wind turbine airfoil. This is a 25% thick airfoil, found at the mid‐span section of a wind turbine blade. Wind turbine applications typically involve unsteady flows due to changes in the angle of attack and to unsteady flow separation at high angles of attack. In order to obtain reasonably accurate results for all these conditions one should use a mesh which is refined in many regions, which is not computationally efficient. Our solution is to apply an automated mesh adaptation technique. In this paper we test an adaptive refinement strategy developed for unstructured hexahedral meshes for steady flow conditions. The automated mesh adaptation is based on local flow sensors for pressure, velocity, density or a combination of these flow variables. This way the mesh is refined only in those regions necessary for high accuracy, retaining computational efficiency. A validation study is performed for two cases: attached flow at an angle of 6° and separated flow at 12°. The results obtained using our adaptive mesh strategy are compared with experimental data and with results obtained with an equally sized non‐adapted mesh. From these computations it can be concluded that for a given computing time, adapted meshes result in solutions closer to the experimental data compared to non‐adapted meshes for attached flow. Finally, we show results for unsteady computations. Copyright © 2005 John Wiley & Sons, Ltd.     

Bianchi Type VI1 Cosmological Model in Scale-Invariant Theory

An attempt has been taken to study the feasibility of scale-invariant theory in Bianchi type VI _h space-time with a time dependent gauge function (Dirac gauge) and a matter field in the form of a perfect fluid with isotropic matter pressure. It is found that Bianchi type VI _h (h = 1) space-time is feasible in this theory whereas Bianchi type VI _h (h = -1) and VI _h (h = 0) space-times are not feasible. In the feasible case a non-singular model for the universe filled with disorder radiation is constructed and some of its physical behaviors are studied.     

Numerical calculations of three-dimensional turbulent vortex breakdown

Numerical solutions to the three-dimensional, unsteady, incompressible Reynolds-averaged Navier-Stokes equations have been obtained for bubble-type vortex breakdown. Two different turbulence models were employed: (1) standard K-ε and (2) an explicit, regularized algebraic Reynolds stress model. Results are computed at a Reynolds number of 10,000. The algebraic Reynolds stress model produced a breakdown bubble with a larger length-to-diameter ratio than did the K-ε model. Breakdown also occurred at lower levels of adverse pressure gradient for the algebraic stress model than for the K-ε model. In each case single-cell breakdown structures resulted. This is contrasted with numerical calculations for laminar breakdown which reveal the existence of complex multicell bubble breakdown structures.     

A novel finite point method for flow simulation

A novel finite point method is developed to simulate flow problems. The mashes in the traditional numerical methods are supplanted by the distribution of points in the calculation domain. A local interpolation based on the properties of Taylor series expansion is used to construct an approximation for unknown functions and their derivatives. An upwind‐dominated scheme is proposed to efficiently handle the non‐linear convection. Comparison with the finite difference solutions for the two‐dimensional driven cavity flow and the experimental results for flow around a cylinder shows that the present method is capable of satisfactorily predicting the flow separation characteristic. The present algorithm is simple and flexible for complex geometric boundary. The influence of the point distribution on computation time and accuracy of results is included. Copyright © 2002 John Wiley & Sons, Ltd.     

离轴受限圆射流的三维湍流流场分析

利用原始变量,交叉网格的方法,以及采用κ-ε湍流模型,计算了离轴受限射流三维湍流流场,计算结果与用LDV测量结果作了比较,结果是满意的。计算结果提供了这样一个复杂的三维流场的清晰图象,为研究具有离轴射流的预燃室的稳燃机理提供了很多有用的信息,对计算结果作了详细的分析和讨论后,指出这样一个流场的重要三维特征是在θ方向梳线有大角度的扭曲。     

The dynamic performance of the Weissenberg Rheogoniometer

The dynamic performance of a standard Model R18 Weissenberg Rheogoniometer has been studied in detail. The Rheogoniometer was carefully calibrated and used to measure accurately the rheological behaviour of a highly nonlinear viscoelastic polymer solution (1% polyacrylamide in 50% glycerol/water).In this paper the elaborate procedures that were used to calibrate the electronic signal processing equipment are described. The various static and dynamic calibration/correction factors are defined and incorporated into a computer implemented calculation scheme for evaluating the linear dynamic properties from the raw digital transfer function analyser readings.The linear dynamic properties of the polymer solution are presented together with the corresponding steady shearing properties. Both cone and plate and parallel plates geometries were used and good agreement was obtained over the wide range (six decades) of frequencies and shear rates employed.Fluid inertia effects were found to become important when the modified Reynolds number,Re _c ² orRe(H/R)², exceeded a value of about 0.1. These effects had a strong influence on the phase angle() which could readily be detected by varying the gap angle/width. The Walters-Kemp equations were found to give consistently accurate values for the linear dynamic properties for modified Reynolds numbers up to 11.6 which was the highest reached.