A Runge-Kutta–based WENO reconstruction on moving mesh for compressible fluids

In this paper, we construct a high-order moving mesh method based on total variation diminishing Runge-Kutta and weighted essential nonoscillatory reconstruction for compressible fluid system. Beginning with the integral form of fluid system, we get the semidiscrete system with an arbitrary mesh velocity. We use weighted essential nonoscillatory reconstruction to get the space accuracy on moving meshes, and the time accuracy is obtained by modified Runge-Kutta method; the mesh velocity is determined by moving mesh method. One- and two-dimensional numerical examples are presented to demonstrate the efficient and accurate performance of the scheme.     

Simulating bubble dynamics in a buoyant system

Multiphase flows are critical components of many physical systems; however, numerical models of multiphase flows with large parameter gradients can be challenging. Here, two different numerical methods, volume of fluid (VOF) and smoothed particle hydrodynamics (SPH), are used to model the buoyant rise of isolated gas bubbles through quiescent fluids for a range of Bond and Reynolds numbers. The VOF is an Eulerian grid–based method, whereas the SPH is Lagrangian and mesh free. Each method has unique strengths and weaknesses, and a comparison of the two approaches as applied to multiphase phenomena has not previously been performed. The VOF and SPH simulations are compared, verified, and validated. Results using two-dimensional VOF and SPH simulations are similar to each other and are able to reproduce numerical benchmarks and experimental results for sufficiently large Morton and Reynolds numbers. It is also shown that at low Reynolds numbers, the two methods, SPH and VOF, diverge in the transient regime of the bubble rise. Regimes that require simulations capable of representing three-dimensional drag are identified as well as regimes in which results from VOF and SPH diverge.     

A modified SPH method to model the coalescence of colliding non-Newtonian liquid droplets

This paper develops a modified smoothed particle hydrodynamics (SPH) method to model the coalescence of colliding non-Newtonian liquid droplets. In the present SPH, a van der Waals (vdW) equation of state is particularly used to represent the gas-to-liquid phase transition similar to that of a real fluid. To remove the unphysical behavior of the particle clustering, also known as tensile instability, an optimized particle shifting technique is implemented in the simulations. To validate the numerical method, the formation of a Newtonian vdW droplet is first tested, and it clearly demonstrates that the tensile instability can be effectively removed. The method is then extended to simulate the head-on binary collision of vdW liquid droplets. Both Newtonian and non-Newtonian fluid flows are considered. The effect of Reynolds number on the coalescence process of droplets is analyzed. It is observed that the time up to the completion of the first oscillation period does not always increase as the Reynolds number increases. Results for the off-center binary collision of non-Newtonian vdW liquid droplets are lastly presented. All the results enrich the simulations of the droplet dynamics and deepen understandings of flow physics. Also, the present SPH is able to model the coalescence of colliding non-Newtonian liquid droplets without tensile instability.     

Hall coefficient in solution for a simple dynamical model

A model Liouville equation is proposed for a system composed of an ion moving in a solvent fluid. Using this model, explicit results are obtained for the Ohmic conductivityL and the Hall conductivityh. These results are then used to calculate the Hall coefficientR = ehL^–2, which is a measure of the effect of non-Brownian motion, for several charge carriers of interest. Our results are in agreement with earlier findings based on a stochastic model which predictR > 1 for H⁺(aq). Our results also indicate thatR 1 for charge carriers such as Na⁺, Cl^–, and K⁺ which have a mass greater than that of a solvent molecule (here taken as 18 amu).This research was supported in part by grants from the National Science Foundation and by the Research Foundation of the State University of New York.     

改良干法压裂液摩擦阻力特性实验研究

对改良的干法压裂液这种非牛顿流体的摩擦阻力特性的正确认识,关系着干法压裂技术的有效实施.为此,本文在大型高压泡沫压裂液实验回路上,考察了在模拟实际施工条件下的改良干法压裂的摩擦阻力特性.实验表明:改良后的干法压裂液摩擦阻力系数随压力、温度的升高和泡沫质量的增加而增大,随流速的增加而减小.在实验范围内,温度对摩擦阻力系数的影响不大.实验得到了改良的干法压裂液摩擦阻力系数与广义雷诺数的关联式,平均计算误差为9.19%.     

Stationary Analysis of a Fluid Queue Driven by Some Countable State Space Markov Chain

Motivated by queueing systems playing a key role in the performance evaluation of telecommunication networks, we analyze in this paper the stationary behavior of a fluid queue, when the instantaneous input rate is driven by a continuous-time Markov chain with finite or infinite state space. In the case of an infinite state space and for particular classes of Markov chains with a countable state space, such as quasi birth and death processes or Markov chains of the G/M/1 type, we develop an algorithm to compute the stationary probability distribution function of the buffer level in the fluid queue. This algorithm relies on simple recurrence relations satisfied by key characteristics of an auxiliary queueing system with normalized input rates.      

Starting solutions for some unsteady unidirectional flows of Oldroyd-B fluids

Analytical expressions for the velocity fields corresponding to the motions of an Oldroyd-B fluid due to oscillations of an infinite flat plate as well as those induced by an oscillating pressure gradient and pressure jumps are determined by means of the Fourier sine transform. The corresponding solutions for a Maxwell and a Newtonian fluid appear as limiting cases of the solutions established here. Relevant physical properties of the flows and their dependence on material and geometry parameters are discussed. (Received: August 16, 2005; revised: December 19, 2005)     

两平行圆盘间或两圆球间存在二阶流体时的挤压流动

为了进行湿颗粒群的离散元模拟,研究两圆球颗粒间二阶流体在挤压流动时的法向粘性力．首先用小参数法对两平行圆盘间二阶流体挤压流动的速度场和正应力分布进行了近似分析,然后用类似的方法,分析任意两圆球间二阶流体的挤压流动,得到了压力分布和法向粘性力的解析解．     

Small angle x—ray scattering study on the conformation of polystyrene in toluene during adding anti—solvent CO2

The conformatiopn of polystyrene in the anti-solvent process of supercritical fluids(compressed CO2 polystyrene toluene)has been studied by small angle x-ray scattering with synchrotron radiation as an x-ray source.Coilto-globule transformation of the polystyrene chain was observed with the increase of the anti-solvent CO2 pressure;i.e.polystrene coiled at a prssure lower than the cloud point pressure(Pc)and turned into a globle with a uniform density at pressures higher than Pc.Fractal behaviour was also found in the chain contraction.and the mass fractal dimension increased with increasing CO2 pressure.     

A Particle-Mesh Method for the Shallow Water Equations Near Geostrophic Balance

In this paper we outline a new particle-mesh method for rapidly rotating shallow water flows based on a set of regularized equations of motion. The time-stepping method uses an operator splitting of the equations into an Eulerian gravity wave part and a Lagrangian advection part. An essential ingredient is the advection of absolute vorticity by means of translated radial basis functions. We show that this implies exact conservation of enstrophy. The method is tested on two model problems based on the qualitative features of the solutions obtained (i.e., dispersion or smoothness of potential vorticity contours) as well as on the increase in mean divergence level.