基于子网格边界近似Riemann解的人为粘性方法

在交错网格型Lagrange(拉格朗日)流体力学算法中,通常采用人为粘性捕捉激波,人为粘性的好坏对于计算结果至关重要.研究了一种基于子网格边界处近似Riemann解的新型人为粘性.新人为粘性能够满足动量守恒和熵不等式.利用子网格边界速度差中引入的限制器,新人为粘性能够区分激波和等熵压缩,并能满足球对称问题中的波面不变性.新人为粘性在典型模型数值模拟及惯性约束聚变黑腔整体数值模拟中取得了较好的结果.     

四个对激波与涡旋有高分辨率的计算格式的比较*

近十年来,计算非定常无粘可压气体力学Euler方程组的高分辨率差分格式有显着进展.本文选择四个近年受到重视的格式,用一较复杂的二维不定常问题作进一步的考验.所选算例为平面激波遇矩形障碍物初始阶段的绕射与反射.在挡板头部有两个尖角点,角点附近流场参量变化剧烈,会有中心稀疏波和集中涡的出现,要模拟好它们,就要求格式有较好的适应性.本文选择特殊的激波马赫数M_s=2.068,使静止坐标系下激波后流速恰为声速,并沿中心稀疏波区从角点发出的一条曲线也有这一现象,以考察各格式在方程组某一特征值恰为零时的计算特点,因零特征值可以使某些格式局部受损.计算结果的图形显示可表明四个格式在激波分辨率,格式粘性、膨胀波的计算、模拟非定常集中涡产生过程的能力等方面的性质.     

膛口流场动力学过程数值研究

采用基于ALE方法的动网格及嵌入网格技术,运用有限体积方法,结合二阶精度Roe格式,对弹丸由高压气体驱动从静止状态加速至超音速,射出膛口到完全飞离初始流场的整个过程进行了数值模拟．根据数值结果,详细讨论了初始流场、火药燃气流场的形成与发展以及与弹丸的耦合和相互作用过程,揭示了在这一变化过程中激波与激波、激波与漩涡、激波与弹丸等的相互作用以及激波衍射、聚焦等对弹丸加速的影响．     

数值求解Euler方程的UCGVC差分格式的注记

１．引言 近年来高精度差分格式的研究引起国内外的普遍重视,目的是更准确地模拟复杂流场的流动．众所周知,传统的二阶ＴＶＤ类格式虽然能较好地捕捉激波,但却存在局部极值点降阶的问题,而且由于一些格式的数值粘性过大,当用该格式计算粘性流特别是高雷诺数问题时,格式本身的数值粘性可能掩盖了流场的物理粘性,从而降低了格式对边界层的分辨率,因而无法正确计算热流值。文献［３］指出,采用高精度格式可适当放松对网格雷诺数的要求,因此发展三阶或三阶以上的格式是需要的。近年来,人们已经发展了一些无伪振荡的高阶格式,如ＥＮ…     

基于第二粘性用局部微分求积法计算激波

考虑第二粘性效应,采用局部微分求积法数值求解激波问题．首先解释了在激波计算时,有必要考虑第二粘性,然后基于粘性模型,对一维和二维激波进行了数值模拟,还分别考察了剪切粘性力和第二粘性力对数值结果的影响．结果表明,采用粘性模型加上局部微分求积法能够模拟出激波特征,具有客观、简单的优点．     

基于三维CFD-DEM的多孔介质流场数值模拟

将多孔介质局部细观流动与基于Darcy定律的宏观物理模型相结合，应用三维CFD-DEM对多孔介质流场进行局部细观数值模拟，得到多孔介质的惯性阻力系数和粘性阻力系数.并将其作为参数提供给基于Darcy定律的CFD多孔介质模型，从而可用于更大规模的多孔介质流场计算.应用Voronoi多面体作为网格单元，解决了CFD DEM中网格孔隙率精确计算的困难.文中发展的多尺度结合应用的研究方法，在计算精度和计算效率的矛盾中找到了较好的平衡，对于工程应用而言，有节约实验成本、提高计算结果可靠性的功效.     

有限体积法与多重网格法用于提高激波捕捉质量及加速收敛

多重网格技术是一种非常有效的数值计算方法，本文采用多重网格的ＦＡＳ格式进行数值实验，计算加速效果十分明显，同时，结合矢通量分裂用有限体积法，大大提高了主激波的质量。     

一种抑制激波计算中数值振荡现象的双重小波收缩方法

在激波数值计算中,容易出现数值振荡的问题,振荡激烈时会掩盖真实解,为此提出了许多高精度复杂计算格式或采用人工粘性抑制数值振荡.从信号处理的角度,提出双重小波收缩方法,它能自适应提取激波数值振荡解中的真实物理解.先用局部微分求积法求解浅水波方程和理想流体Euler运动方程中的激波问题,发现其数值振荡现象严重,然后采用双重小波收缩方法对其处理,获得了无数值振荡解,它能准确捕捉激波的位置并且保持激波结构.相比于复杂的Riemann(黎曼)求解格式,借助小波收缩方法,可以采用相对简单的计算格式如微分求积法求解激波问题.     

超声速流场中6自由度物体运动的模拟研究

物体在流场中自由运动的模拟有很广泛的应用,文章描述计算6自由度(6DOF)刚体在超声速流场中自由运动的一种方法.流体部分求解LES方程,亚网格模型为拉伸涡模型.激波和刚体边界周围区域采用迎风型WENO格式,湍流区域采用低数值耗散的TCD格式.时间推进采用三阶的SSP R-K法.刚体采用6自由度模型,刚体姿态用四元数来表示,控制方程为常微分方程,采用四阶Runge-Kutta法求解.文章给出若干算例来验证程序的有效性,结果理想.     

群速度直接控制四阶迎风紧致格式

为求解多尺度复杂流动在有限网格点的情况下高精度方法是可供选择的方法之一,其中紧致型格式数值解的分辨率更好.用迎风型紧致格式计算激波时,数值解中仍有数值振荡产生,这是由于对应于不同波数之群速度不均一所致.采用群速度直接控制方法重构紧致型格式以提高捕捉激波的能力.该方法简单,精度高,网格基架点少.算例表明,这一新的方法是可行的.     

超音速探测器-刚性盘-缝-带型降落伞系统的大涡模拟研究

研究了Mach数为2时,流场不同块结构自适应网格加密精度对探测器-刚性盘-缝-带型降落伞系统的气动减速性能以及流场结构特性的影响.对于非定常可压缩流体流动,采用了兼顾激波与湍流的WENO(weighted essen-tially non-oscillatory)和TCD(tuned center difference...     

Unsteady rarefied gas flow in a microchannel driven by a pressure difference

The kinetic S-model is used to study the unsteady rarefied gas flow through a plane channel between two parallel infinite plates. Initially, the gas is at rest and is separated by the plane x = 0 with different pressure values on opposite sides. The gas deceleration effect of the channel walls is studied depending on the degree of gas rarefaction and the initial pressure drop, assuming that the molecules are diffusely reflected from the boundary. The decay of the shock wave and the disappearance of the uniform flow region behind the shock wave are monitored. Special attention is given to the gas mass flux through the cross section at x = 0, which is computed as a function of time. The asymptotic behavior of the solution at unboundedly increasing time is analyzed. The kinetic equation is solved numerically by applying a conservative finite-difference method of second-order accuracy in space.     

Numerical study of unsteady rarefied diatomic gas flows in a plane microchannel

The numerical solution of a kinetic equation for a diatomic gas (nitrogen) is used to study two-dimensional unsteady gas flows in a plane microchannel caused by discontinuous in the initial distributions of macroscopic gas parameters. The plane discontinuity fronts are perpendicular to the walls of the channel. The arising flows are model ones for gas flows in a shock tube and a microchannel. The reflection of an incident shock wave from a flat end face is studied. It is found that the gas piles up at the cold wall, which slows down the shock wave detachment. The numerical results are in qualitative agreement with experimental data.     

Mach configuration in pseudo-stationary compressible flow

This paper is devoted to studying the local structure of Mach reflection, which occurs in the problem of the shock front hitting a ramp. The compressible flow is described by the full unsteady Euler system of gas dynamics. Because of the special geometry, the motion of the fluid can be described by self-similar coordinates, so that the unsteady flow becomes a pseudo-stationary flow in this coordinate system. When the slope of the ramp is less than a critical value, the Mach reflection occurs. The wave configuration in Mach reflection is composed of three shock fronts and a slip line bearing contact discontinuity. The local existence of a flow field with such a configuration under some assumptions is proved in this paper. Our result confirms the reasonableness of the corresponding physical observations and numerical computations in Mach reflection.

In order to prove the result, we formulate the problem to a free boundary value problem of a pseudo-stationary Euler system. In this problem two unknown shock fronts are the free boundary, and the slip line is also an unknown curve inside the flow field. The proof contains some crucial ingredients. The slip line will be transformed to a fixed straight line by a generalized Lagrange transformation. The whole free boundary value problem will be decomposed to a fixed boundary value problem of the Euler system and a problem to updating the location of the shock front. The Euler system in the subsonic region is an elliptic-hyperbolic composite system, which will be decoupled to the elliptic part and the hyperbolic part at the level of principal parts. Then some sophisticated estimates and a suitable iterative scheme are established. The proof leads to the existence and stability of the local structure of Mach reflection.

     

Exact solutions for the flow of an Oldroyd-B fluid due to an infinite flat plate

The unsteady flow of an Oldroyd-B fluid due to an infinite flat plate, subject to a translation motion of linear time-dependent velocity in its plane, is studied by means of the Laplace transform. The velocity field and the associated tangential stress corresponding to the flow induced by the constantly accelerating plate as well as those produced by the impulsive motion of the plate are obtained as special cases. The solutions that have been determined, in all accordance with the solutions established using the Fourier transform, reduce to those for a Newtonian fluid as a limiting case. The similar solutions for a Maxwell fluid are also obtained.     

On some unsteady flows of a non-Newtonian fluid

Some properties of unsteady unidirectional flows of a fluid of second grade are considered for flows impulsively started from rest by the motion of a boundary or two boundaries or by sudden application of a pressure gradient. Flows considered are: unsteady flow over a plane wall, unsteady Couette flow, flow between two parallel plates suddenly set in motion with the same speed, flow due to one rigid boundary moved suddenly and one being free, unsteady Poiseuille flow and unsteady generalized Couette flow. The results obtained are compared with those of the exact solutions of the Navier–Stokes equations. It is found that the stress at time zero on the stationary boundary for the flows generated by impulsive motion of a boundary or two boundaries is finite for a fluid of second grade and infinite for a Newtonian fluid. Furthermore, it is shown that for unsteady Poiseuille flow the stress at time zero on the boundary is zero for a Newtonian fluid, but it is not zero for a fluid of second grade.     

Numerical Investigation of Cavitation Interacting with Pressure Wave

A computational fluid dynamics solver based on homogeneous cavitation model is employed to compute the two-phase cavitating flow. The model treats the two-phase regime as the homogeneous mixture of liquid and vapour which are locally assumed to be under both kinetic and thermodynamic equilibrium. As our focus is on pressure wave formation, propagation and its impact on cavitation bubble, the compressibility effects of liquid water have to be accounted for and hence the flow is considered to be compressible. The cavitating flow disturbed by the introduced pressure wave is simulated to investigate the unsteady features of cavitation due to the external perturbations. It is observed that the cavity becomes unstable, locally experiencing deformation or collapse, which depends on the shock wave intensity and freestream flow speed.     

Continuous compression waves in the two-dimensional Riemann problem

The interaction between a plane shock wave in a plate and a wedge is considered within the framework of the nondissipative compressible fluid dynamic equations. The wedge is filled with a material that may differ from that of the plate. Based on the numerical solution of the original equations, self-similar solutions are obtained for several versions of the problem with an iron plate and a wedge filled with aluminum and for the interaction of a shock wave in air with a rigid wedge. The behavior of the solids at high pressures is approximately described by a two-term equation of state. In all the problems, a two-dimensional continuous compression wave develops as a wave reflected from the wedge or as a wave adjacent to the reflected shock. In contrast to a gradient catastrophe typical of one-dimensional continuous compression waves, the spatial gradient of a two-dimensional compression wave decreases over time due to the self-similarity of the solution. It is conjectured that a phenomenon opposite to the gradient catastrophe can occur in an actual flow with dissipative processes like viscosity and heat conduction. Specifically, an initial shock wave is transformed over time into a continuous compression wave of the same amplitude.     

Numerical analysis of the dynamics of distributed vortex configurations

A numerical algorithm is proposed for analyzing the dynamics of distributed plane vortex configurations in an inviscid incompressible fluid. At every time step, the algorithm involves the computation of unsteady vortex flows, an analysis of the configuration structure with the help of heuristic criteria, the visualization of the distribution of marked particles and vorticity, the construction of streamlines of fluid particles, and the computation of the field of local Lyapunov exponents. The inviscid incompressible fluid dynamic equations are solved by applying a meshless vortex method. The algorithm is used to investigate the interaction of two and three identical distributed vortices with various initial positions in the flow region with and without the Coriolis force.