粘性流基于特征线的四阶Runge-Kutta有限元法

对于二维不可压缩粘性流,通过沿流线方向的坐标变换,推导了无对流项的二维N-S(Navier-Stokes)方程。采用四阶Runge-Kutta法对N-S方程进行时间离散,并沿流线进行Taylor展开,得到显式的时间离散格式,然后利用Galerkin法对其进行空间离散,得到了高精度的有限元算法。利用本文算法对方腔驱动流和圆柱绕流进行了数值计算,通过对时间步长、网格尺寸和流场区域的计算分析,进一步验证了本文算法相比经典CBS法在时间步长、收敛性、耗散性和计算精度方面更具有优势。     

基于S-A湍流模型的Runge-Kutta有限元算法

采用一方程S-A模型(Spalart-Allmaras模型)封闭雷诺时均N-S方程(RANS方程)进行湍流数值计算,可以减少方程求解数量,节约计算时间。本文对其进行了有限元数值算法研究,首先通过沿流线坐标变换,得到无对流项RANS方程,并引入三阶Runge-Kutta法对其进行时间离散;然后利用沿流线的Taylor展开解决坐标变换带来的网格更新的困难;最后采用Galerkin法进行空间离散,得到湍流模型的有限元算法。基于方柱绕流和覆冰输电线绕流模型,与试验结果进行对比,验证了该算法的有效性,与一阶数值算法相比,该算法在精度和收敛性方面更具优势。     

非定常不可压N-S方程的最小二乘算子分裂有限元法数值求解

采用最小二乘算子分裂有限元法求解非定常不可压N-S(Navier-Stokes)方程,即在每个时间层上采用算子分裂法将N-S方程分裂成扩散项和对流项,这样既能考虑对流占优特点又能顾及方程的扩散性质。扩散项是一个抛物型方程,时间离散采用向后差分格式,空间离散采用标准Galerkin有限元法。对流项的时间项采用后向差分格式,非线性部分用牛顿法进行线性化处理,再用最小二乘有限元法进行空间离散,得到对称正定的代数方程组系数矩阵。采用Re=1000的方腔流对该算法的有效性进行检验,表明其具有较高的精度,能够很好地捕捉流场中的涡结构。同时,对圆柱层流绕流进行了数值研究,通过流线图、压力场、阻力系数、升力系数及斯特劳哈数等结果的分析与对比,表明本文算法对于模拟圆柱层流绕流是准确和可靠的。     

高黏性流动有限元模拟的迭代稳定分步算法

分步算法已被广泛应用于数值求解不可压缩N-S方程. Guermond等认为时间步长必须大于 某个临界值方能使算法稳定. 然而在高黏性流动模拟中，已有的显式和半隐式分步算法由于 其显式本质，必须采用小时间步长计算，不但降低了计算效率，同时也常与为使分步算法稳 分步算法已被广泛应用于数值求解不可压缩N-S方程. Guermond等认为时间步长必须大于 某个临界值方能使算法稳定. 然而在高黏性流动模拟中，已有的显式和半隐式分步算法由于 其显式本质，必须采用小时间步长计算，不但降低了计算效率，同时也常与为使分步算法稳 定必须满足的最小时间步长要求冲突. 本文目的是构造一种含迭代格式的分步算法，它能在 保证精度的前提下大幅度地增大时间步长. 方腔流和平面Poisseuille流数值计算结果证实 了此特点，该方法被有效应用于充填流动过程的数值模拟.     

基于非结构化同位网格的SIMPLE算法

通过基于非结构化网格的有限体积法对二维稳态Navier—Stokes方程进行了数值求解。其中对流项采用延迟修正的二阶格式进行离散；扩散项的离散采用二阶中心差分格式；对于压力-速度耦合利用SIMPLE算法进行处理；计算节点的布置采用同位网格技术，界面流速通过动量插值确定。本文对方腔驱动流、倾斜腔驱动流和圆柱外部绕流问题进行了计算，讨论了非结构化同位网格有限体积法在实现SIMPLE算法时，迭代次数与欠松弛系数的关系、不同网格情况的收敛性、同结构化网格的对比以及流场尾迹结构。通过和以往结果比较可知，本文的方法是准确和可信的。     

非流线体分离流动态载荷的数值模拟方法研究

以圆柱绕流为研究对象,针对圆形边界,采用O型网格对流场进行离散,用二阶精度的中心差分有限体积法作空间离散,用二阶精度的中心差分处理时间问题,用双时间方法求解了二维非定常Navier-Stokes方程,系统研究了计算方法对收敛精度、时间步长和网格数量的依赖性.计算结果表明,对于长时间历程的非定常问题,虽然双时间方法收敛性很好,但对于分离流而言,时间步长的选取并非没有限制;每一步伪时间的推进中,收敛精度也有要求;而要模拟圆柱分离流的非线性气动力现象,计算网格至少要达到260×80的数量.     

基于Boltzmann模型方程的气体运动论统一算法研究

模型方程出发,研究确立含流态控制参数可描述不同流域气体流动特征的气体分子速度分布函数方程; 研究发展气体运动论离散速度坐标法, 借助非定常时间分裂数值计算方法和NND差分格式, 结合DSMC方法关于分子运动与碰撞去耦技术, 发展直接求解速度分布函数的气体运动论耦合迭代数值格式; 研制可用于物理空间各点宏观流动取矩的离散速度数值积分方法, 由此提出一套能有效模拟稀薄流到连续流不同流域气体流动问题统一算法. 通过对不同Knudsen数下一维激波内流动、二维圆柱、三维球体绕流数值计算表明, 计算结果与有关实验数据及其它途径研究结果(如DSMC模拟值、N-S数值解)吻合较好, 证实气体运动论统一算法求解各流域气体流动问题的可行性. 尝试将统一算法进行HPF并行化程序设计, 基于对球体绕流及类``神舟'返回舱外形绕流问题进行HPF初步并行试算, 显示出统一算法具有很好的并行可扩展性, 可望建立起新型的能有效模拟各流域飞行器绕流HPF并行算法研究方向. 通过将气体运动论统一算法推广应用于微槽道流动计算研究, 已初步发展起可靠模拟二维短微槽道流动数值算法; 通过对Couette流、Poiseuille流、压力驱动的二维短槽道流数值模拟, 证实该算法对微槽道气体流动问题具有较强的模拟能力, 可望发展起基于Boltzmann模型方程能可靠模拟MEMS微流动问题气体运动论数值计算方法研究途径.      

N-S方程基于投影法的特征线算子分裂有限元求解

提出了一种求解非定常不可压缩纳维-斯托克斯方程（N-S方程）的新型有限元法:基于投影法的特征线算子分裂有限元法.在每一个时间层上将N-S方程分裂成扩散项、对流项、压力修正项.对流项采用多步显式格式,且在每一个对流子时间步内采用更加精确的显式特征线-伽辽金法进行时间离散,空间离散采用标准伽辽金法.应用此算法对平面泊肃叶流、方腔流和圆柱绕流进行数值模拟,所得结果与基准解符合良好.尤其对于Re=10000的方腔流,给出了方腔中分离涡发展和运动的计算结果,并发现在该雷诺数下存在周期解,表明该算法能较好地模拟流体流动中的小尺度物理量以及流场中分离涡的运动.      

绕侧滑翼三维可压缩湍流边界层计算

本文从广义曲线坐标运动方程出发,以及根据Head的二维牵引理论(entrainment theory)模型导出沿侧滑翼法向翼剖面表面曲线的三维可压缩湍流边界层运动方程组。通过矩阵变换得到具有初值问题的常微分方程组的典型形式,用数值方法求解。 利用Thompson和MacDonaId关于侧滑翼前缘附着线(attachment linc)上的绕流计算结果作为求解微分方程组的初值。 本文方法可计算出边界层分离位置,各种边界层厚度,壁面摩擦应力,描绘出壁面流线与边界层边缘流线间的差异。 典型算例表明本文方法与实验结果符合得很好。     

NUMERICAL SIMULATION FOR NAVIER-STOKES EQUATIONS BY PROJECTION/CHARACTERISTIC-BASED OPERATOR-SPLITTING FINITE ELEMENT METHOD

提出了一种求解非定常不可压缩纳维-斯托克斯方程（N-S方程）的新型有限元法：基于投影法的特征线算子分裂有限元法.在每一个时间层上将N-S方程分裂成扩散项、对流项、压力修正项.对流项采用多步显式格式,且在每一个对流子时间步内采用更加精确的显式特征线-伽辽金法进行时间离散,空间离散采用标准伽辽金法.应用此算法对平面泊肃叶流、方腔流和圆柱绕流进行数值模拟,所得结果与基准解符合良好.尤其对于Re=10000的方腔流,给出了方腔中分离涡发展和运动的计算结果,并发现在该雷诺数下存在周期解,表明该算法能较好地模拟流体流动中的小尺度物理量以及流场中分离涡的运动.     

A Galerkin finite element algorithm based on third-order Runge-Kutta temporal discretization along the uniform streamline for unsteady incompressible flows

In this paper, for two-dimensional unsteady incompressible flow, the Navier-Stokes equations without convection term are derived by the coordinate transformation along the streamline characteristic. The third-order Runge-Kutta method along the streamline is introduced to discrete the alternative Navier-Stokes equations in time, and spacial discretization is carried out by the Galerkin method, and then, the third-order accuracy finite element method is obtained. Meanwhile, the streamline velocity is uniformly approximated by initial velocity in each time step in order to reduce update frequency of total element matrix and improve calculation efficiency. Finally, some classic unsteady flow examples are calculated and analyzed by different calculation methods, which further demonstrate that the present method has more advantages in stability, permissible time step, dissipation, computational cost, and accuracy. The code can be downloaded at https://doi.org/10.13140/RG.2.2.27706.44484 .     

Compositional Streamline Simulation: A Parallel Implementation

Compositional reservoir simulators are needed to model oil recovery from petroleum reservoirs by miscible gas injection. This article describes the development and application of a parallel version of a compositional streamline simulator. A compositional streamline module is developed and integrated with an existing finite-difference simulator. Finite-difference calculations including pressure solution are performed on a single processor. The movement of fluids (which includes streamline tracing, mappings, flux calculations, and one-dimensional solver) is done along streamlines in the streamline module. The streamline module is parallelized by distributing streamlines among different processors because computations along any streamline are independent of other streamlines and no communication is required. Flux calculation along streamlines is computationally expensive primarily due to flash calculations that are performed to distribute components among the hydrocarbon phases. Simultaneous solution of this time-consuming step results in reduction of total CPU time. Communication (gathering) across the streamlines or processors is achieved by using message passing interface (MPI). Test runs are conducted for different examples to investigate the performance of the parallel streamline simulator. Results indicate that significant reduction in CPU time can be obtained by distributing streamlines on different processors.     

Two-phase flow for a horizontal well penetrating a naturally fractured reservoir with edge water injection

This paper examines the two-phase flow for a horizontal well penetrating a naturally fractured reservoir with edge water injection by means of a fixed streamline model. The mathematical model of the vertical two-dimensional flow or oil-water for a horizontal well in a medium with double-porosity is established, and whose accurate solutions are obtained by using the characteristic method. The saturation distributions in the fractured system and the matrix system as well as the formula of the time of water free production are presented. All these results provide a theoretical basis and a computing method for oil displacement by edge water from naturally fractured reservoirs.     

EFFICIENT COMPUTATIONS USING UPWIND BIASED SCHEMES

A new multiblock unfactored implicit upwind scheme for inviscid two-dimensional flow calculations is presented. Spatial discretization is carried out by means of an upwind first-order method; an original extension to higher accuracy is also presented. The integration algorithm is constructed in a ‘δ’ form that provides a direct derivation of the scheme and leads to an efficient computational method. Fast solutions of the linear systems arising at each time step are obtained by means of the bi-conjugate gradient stabilized technique. The computational results for super/hypersonic steady state flows illustrate the efficiency and accuracy of the algorithm.     

Extension of Bernoulli's theorem on steady flows of inviscid fluids to steady flows of plastic solids

A differential equation is derived which is valid along any streamline in a steady flow of a general continuum where the streamline is also a trajectory of principal stress. For special materials and flow conditions this equation can be integrated to give algebraic relations between variables along the streamline. For inviscid fluids this leads to Bernoulli's famous theorem relating pressure and velocity along any streamline. For three-dimensional ideal flows of Tresca plastic solids and planar ideal flows of general rigid/perfectly plastic solids, it also leads to known results along any streamline. For other special constitutive materials in rigid/plastic solids additional streamline relations are obtained.     

圆柱尾流雷诺应力与平均运动变形率的空间弛豫效应

针对圆柱尾流中沿流向存在的Karman涡街周期性涡旋结构,对湍流雷诺应力与平均运动变形率之间的空间弛豫效应进行了实验研究.在回流式水槽中,放入不同直径的圆柱模型,获得不同雷诺数下的圆柱尾流,利用二维高时间分辨率粒子图像测速(TRPIV)技术测量圆柱尾流二维瞬时速度空间分布图像的时间序列.经过数字图像处理,获得二维雷诺应...     

考虑边界层影响时溢流坝动水压强分布规律的研究

根据溢流坝反弧段水流运动的基本方程,考虑水流边界层的影响,在流线曲率同心圆假设条件下,得到了溢流坝反弧段水流压强计算的表达式。通过引入近壁薄流层要领和缓和过渡流线假设,在水工模型试验的基础上,得到了溢流坝反弧段水流流线曲率半径的计算公式,使反弧段离心力影响范围内的水流流线曲率光滑连续,从而得到反弧段水流压强分布规律的统一表达式,该表达式能够反映水流压强沿反弧法线方向及切线方向的变化规律。     

A parallel gas-kinetic Bhatnagar–Gross–Krook method for the solution of viscous flows on two-dimensional hybrid grids

In this study, a parallel implementation of gas-kinetic Bhatnagar–Gross–Krook method on two-dimensional hybrid grids is presented. Boundary layer regions in wall bounded viscous flows are discretised with quadrilateral grid cells stretched in the direction normal to the solid surface while the rest of the flow domain is discretised by triangular cells. The parallel solution algorithm on hybrid grids is based on the domain decomposition using METIS, a graph partitioning software. The flow solutions obtained in parallel significantly improve the computation time, a significant deficiency of gas-kinetic methods. Several validation test cases presented show the accuracy and robustness of the method developed.     

COMPARISON OF ACCURACY AND PERFORMANCE FOR LATTICE BOLTZMANN AND FINITE DIFFERENCE SIMULATIONS OF STEADY VISCOUS FLOW

The lattice Boltzmann method (LBM) is used to simulate flow in an infinite periodic array of octagonal cylinders. Results are compared with those obtained by a finite difference (FD) simulation solved in terms of streamfunction and vorticity using an alternating direction implicit scheme. Computed velocity profiles are compared along lines common to both the lattice Boltzmann and finite difference grids. Along all such slices, both streamwise and transverse velocity predictions agree to within 0ċ5% of the average streamwise velocity. The local shear on the surface of the cylinders also compares well, with the only deviations occurring in the vicinity of the corners of the cylinders, where the slope of the shear is discontinuous. When a constant dimensionless relaxation time is maintained, LBM exhibits the same convergence behaviour as the FD algorithm, with the time step increasing as the square of the grid size. By adjusting the relaxation time such that a constant Mach number is achieved, the time step of LBM varies linearly with the grid size. The efficiency of LBM on the CM-5 parallel computer at the National Center for Supercomputing Applications (NCSA) is evaluated by examining each part of the algorithm. Overall, a speed of 13ċ9 GFLOPS is obtained using 512 processors for a domain size of 2176×2176.