用Level Set方法求解具有自由面的流动问题

为采用Ｌｅｖｅｌ Ｓｅｔ方法来计算有自由的流动问题提出了一种方案,把自由水面视为水和空气的交界面,两种介质用统一的Ｎ－Ｓ方法求解,在自由面两侧分别采用各自的密度和粘性,并在自由面上给以适当的光滑;采用边界元法求解双调和方程来确定距离函数;Ｎ－Ｓ方程用投影法求解,文中给出了二维水池水面振荡和瞬时溃坝问题的算例,可以看出用ＬｅｖｅｌＳｅｔ方法求解有自由面流动问题是有效的。     

三维溃坝流的光滑粒子动力学方法模拟

采用光滑粒子动力学SPH(Smoothed Particle Hydrodynamics)方法对三维溃坝流问题进行了数值模拟。为了逼真地模拟出坝内水体与壁面间相互作用而产生的水花飞溅、融合以及近壁面流动等现象,加入了混合长度形式的湍流模型。为了有效地防止粒子穿透固壁,提出了一种新型的适合三维数值模拟的固壁边界处理方法。应用SPH方法对三维溃坝流进行了数值模拟,并分别考虑了未添加障碍物和添加圆柱障碍物两种情形。计算结果表明,改进SPH方法能够精细地捕捉溃坝流在不同时刻的自由液面,并获得稳定而精确的数值结果。     

一维溃坝洪水波的高精度数值模拟

将ENO(Essentially Non-Oscillatory)格式和Runge-Kutta时间离散的思想应用于一维Saint-Venant方程组的求解,数值模拟溃坝洪水,得出了水位和流速的沿程分布。经与理论解比较可见,数值解在间断波附近没有出现数值振荡,水位和流速大小均符合较好,表明ENO格式是一类新的高精度无振荡差分格式,采用ENO格式所建立的高分辨率模型能够很好地模拟溃坝波的演进过程。     

Lattice Boltzmann method with the cell-population equilibrium

The central problem of the lattice Boltzmann method （LBM） is to construct a discrete equilibrium. In this paper, a multi-speed 1D cell-model of Boltzmann equation is proposed, in which the cell-population equilibrium, a direct non- negative approximation to the continuous Maxwellian distribution, plays an important part. By applying the explicit one-order Chapman-Enskog distribution, the model reduces the transportation and collision, two basic evolution steps in LBM, to the transportation of the non-equilibrium distribution. Furthermore, 1D dam-break problem is performed and the numerical results agree well with the analytic solutions.     

带有障碍物溃坝流动问题的有限元数值模拟研究

针对下游带有障碍物的溃坝流动问题,本文基于两相流动模型,在有限元算法框架下对其进行数值模拟研究。依据水平集(Level Set)方法追踪运动界面,并引入了一个简单的修正技术,保证较好的质量守恒性。为了精确表示运动界面,采用稳定和有效的间断有限元方法求解双曲型Level Set及其重新初始化方程。对于两相统一Navier-Stokes方程,首先利用分裂格式对其解耦,然后通过SUPG (Streamline Upwind Petrov Galerkin)方法进行数值求解。模拟研究了下游带有障碍物的牛顿流体溃坝流动问题,得到的数值结果与文献已有模拟结果及实验结果均吻合较好。此外,还考虑了幂律型非牛顿流体,并分析了不同特性非牛顿流体对于溃坝流动过程和界面形态等的影响。     

Waves resulting from partial dam break with the formation of a breach in the form of a cut to the channel bottom

This paper gives experimental data on the propagation speed and height of a dam-break wave arising in the tailwater region during a partial dam break event. These data were used to confirm the Khristianovich calculation method. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 97–103, May–June, 2009.     

Block-based adaptive mesh refinement scheme using numerical density of entropy production for three-dimensional two-fluid flows

In this work, we present a fast and parallel finite volume scheme on unstructured meshes applied to complex fluid flow. The mathematical model is based on a three-dimensional compressible low Mach two-phase flows model, combined with a linearised ‘artificial pressure’ law. This hyperbolic system of conservation laws allows an explicit scheme, improved by a block-based adaptive mesh refinement scheme. Following a previous one-dimensional work, the useful numerical density of entropy production is used as mesh refinement criterion. Moreover, the computational time is preserved using a local time-stepping method. Finally, we show through several test cases the efficiency of the present scheme on two- and three-dimensional dam-break problems over an obstacle.     

Discharge and energy-loss coefficients in flow through a breach in a trapezoidal dam

The paper presents experimental data on the discharge and energy-loss coefficients for two weirs of polygonal profiles with lateral contraction, which are required, in particular, in simulations of partial dam-break waves. It is shown that the values of these coefficients for a trapezoidal weir with a slope ratio of 1: 3 differ insignificantly from their values for a rectangular weir. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 68–73, January–February, 2008.     

Experimental verification of methods for calculating partial dam-break waves

This paper presents results of an experimental study of waves generated by partial break of two model dams. The previously proposed calculation methods are extended and compared with the experimental data obtained. It is shown that the wave propagation speed in the tailwater is significantly influenced by the energy losses due to flow through the breach. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 61–69, September–October, 2008     

非牛顿流体二维溃坝问题的数值模拟

移动粒子半隐式法(Moving Particle Semi-implicit,MPS)是一种广泛应用于不可压缩自由表面流动的粒子方法。本文通过把非牛顿流体转化为变黏度牛顿流体的处理方法将MPS方法拓展至非牛顿自由表面流动,以Casson流体和Cross流体为例计算了非牛顿流体的二维溃坝问题。将计算结果与前人数据进行了对比,结果吻合较好。同时对比了非牛顿流体与牛顿流体的计算结果,发现非牛顿流体的溃坝前端发展速度较慢。