微重力环境下板式贮箱内推进剂流动的数值模拟

为了研究微重力环境下板式表面张力贮箱内推进剂的流动规律，本文对板式贮箱导流板的驱动机理进行了分析，得到了微重力环境下板式贮箱内部定常和非定常流动的基本方程。应用四阶龙格-库塔法对定常流动方程进行求解，得到定常流动时导流板上液带的分布规律，应用MacCormack数值离散方法，对非定常流动方程进行求解，得到了不同时刻导流板上液带的分布规律及液带恢复稳定所需的时间。计算结果为板式贮箱的设计提供了数值依据，奠定了板式贮箱的设计基础。     

含摩擦滑移铰及驱动约束多刚体系统数值算法

研究了具有驱动约束及非光滑滑移铰多体系统动力学方程的建模与数值计算方法．将驱动约束视为非定常约束，非光滑滑移铰视为双边定常约束，滑移铰的摩擦模型采用库仑摩擦模型；应用第一类Lagrange方程建立系统的动力学方程，应用距离函数建立滑移铰的约束方程；将线性互补方法和Baumgarte约束稳定化方法引入，以解决滑移铰法向约束力的计算以及约束方程违约问题．最后应用曲柄摇杆机构作为算例，说明该方法的有效性．     

三维非定常不可压涡量—速度Navier—Stokes方程组的有限差分法

提出了一种数值求解三维非定常涡量—速度形式的不可压Navier-Stokes方程组的有限差分方法,该方法在空间方向上具有二阶精度,并且系数矩阵具有对角占优性,因此适合高雷诺数问题的数值求解．同时,给出了适合的二阶涡量边界条件．通过对有精确解的狄利克雷边值问题和典型的驱动方腔流问题的数值实验,验证了本文格式的精确性、稳定性和有效性．     

一种二维数值网格的构造方法

１．引言二维数值网格构造是一种二维区域上的自动网格生成技术．是为了适应数值求解任意形状二维区域上的偏微分方程而发展起来的．它产生以后,对于一些不规则区域上对边值敏感问题以及非定常二维流动问题等的数值计算起了重要的作用．从本世纪六十年代开始,有许多欧美和前苏联等学者在网格构造方面做了许多开拓的和内容较为丰富的工作．人们也越来越认识到网格构造无论是在差分法还是有限元的数值计算中都具有重要的地位．在求解非定常问题时,可以不管物理区域如何变化,始终保证计算在同一规则的参数区域中．特别在流体力学计算中,由…     

二维无结构三角形网格的高分辨率大粒子有限体积方法

1．引言在非定常流体力学数值方法中，有一类重要的Euler型方法．它们的共同思想是把流体力学基本方程按力学意义分裂成压力梯度加速效应部分和输运效应部分（对弹塑性流动还要加上强度效应部分），再分别差分化·于是一个时间计算步由两步（或三步）组成，如PIC方法【‘］，FLIC方法！‘，‘，‘］（大粒子方法），OIL问方法。HELP【’］方法和流体网格法f’］等．这些方法在非定常流体力学计算中发挥了重要的作用，方法的构造思想在计算流体力学数值方法的发展中有很大的影响．这些方法，除PIC方法外，都是一阶上风格式，分辨率低…     

LB-SGS方法和MRT-LBM方法对高雷诺数顶盖驱动流的数值模拟对比

针对格子Boltzmann方法(Lattice Boltzmann Method,LBM)广泛采用的LBGK模型虽然简单易行,但对高雷诺数流动模拟稳定性不佳的问题,分别采用结合亚格子模型的LBM(LBM with Sub Grid Scale(SGS),LB-SGS)方法和多松驰时间LBM(Multiple Relaxation Time(MRT)LBM,MRT-LBM)方法对高雷诺数顶盖驱动流进行数值模拟.取Re=7 500对比2种方法得到的涡位置与标准解之间的误差,结果表明LB-SGS方法更接近标准解;保持雷诺数和顶盖速度不变并减少格点数观察收敛情况,结果表明MRT-LBM方法更稳定.     

二维流体动力学方程的FCT方法

sl．引育在计算非定常流体动力学问题时，使用多步法解Eul6r坐标系中流体动力学方程组是一类重要方法，它特别适用于解多维空间中流体具有大畸变的流动问题．多步法一般把一个时间步的计算分成两步（或三步）完成：第一步，忽略对流效应，解Lopangian方程；第二步，考虑对流效应，按质量、动量和能量守恒原则将第一步的计算结果在原来的Euler网格上进行质量、动量和能量的重新分配，即所谓的回映步．为了提高间断解的分辨率，山对Laaransian方程给出一个交错网格的FCT方法，并给出一个相应的二阶数值对流算法．在推广到二维问题时，有时…     

一阶非定常双曲问题的间断-差分流线扩散法及其误差估计

本文提出了求解一阶非定常双曲问题的一种新型有限元方法．间断-差分流线扩散法(DFDSD方法),建立了Euler型DFDSD格式,并对格式解的稳定性和收敛性进行了理论分析,最后给出了数值算例说明算法的有效性．     

二维复杂向量场可视化方法研究及应用

向量场数据广泛存在于科学和工程计算中,面当前缺少和有效的复杂向量场可视化方法,使得在一些研究领域中计算出来的数据无法得到很好的理解和使用。通过分析点噪声方法和非定常网格数据场的特点,提出适用于二维非定常网格数据折可视化方法;非定常点噪声方法。该方法主要解决变化网格及数据时间精度不足带来的问题,通过对惯性约束聚变的数值模拟数据进行可视化,取得了令人满意的结果,结果表明该方法是一种对复杂向量场有效的可视化方法。     

多重网格技术对SIMPLER算法的加速性能研究

将多重网格技术引入SIMPLER算法以加快其收敛速度,从而节约计算时间。通过计算不同雷诺数下的二维方腔顶盖驱动流,研究了多重网格方法中的V循环、W循环对SIMPLER算法的加速效果,并讨论了网格层数对加速性能的影响。研究结果表明,在不同雷诺数下,多重网格方法均可以起到良好的加速效果;在相同雷诺数和精度要求下,W循环方式的外迭代次数少于V循环方式的外迭代次数,而且网格层数对多重网格加速性能的影响并不显著。     

Incompressible flow calculations with a consistent physical interpolation finite volume approach

The computation of incompressible three-dimensional viscous flow is discussed. A new physically consistent method is presented for the reconstruction for velocity fluxes which arise from the mass and momentum balance discrete equations. This closure method for fluxes allows the use of a cell-centered grid in which velocity and pressure unknowns share the same location, while circumventing the occurrence of spurious pressure modes. The method is validated on several benchmark problems which include steady laminar flow predictions on a two-dimensional cartesian (lid driven 2D cavity) or curvilinear grid (circular cylinder problem at Re = 40), unsteady three-dimensional laminar flow predictions on a cartesian grid (parallelopipedic lid driven cavity) and unsteady two-dimensional turbulent flow predictions on a curvilinear grid (vortex shedding past a square cylinder at Re = 22,000).     

Evaluation of multigrid acceleration for preconditioned time-accurate Navier-Stokes algorithms

The development of a two-dimensional time-accurate dual time step Navier-Stokes flow solver with time-derivative preconditioning and multigrid acceleration is described. The governing equations are integrated in time with both an explicit Runge-Kutta scheme and an implicit lower-upper symmetric-Gauss-Seidel scheme in a finite volume framework, yielding second-order accuracy in space and time. Issues concerning the implementation of multigrid for preconditioned, dual time step algorithms are discussed. Steady and unsteady computations were made of lid driven cavity flow, thermally driven cavity flow and pulsatile channel flow for a variety of conditions to validate the schemes and evaluate the effectiveness of multigrid for time-accurate simulations. Significant speedups were observed for steady and unsteady simulations. The speedups for unsteady simulations were problem dependent, a function of how rapidly the flow varied in time and the size of the allowable time step.     

Numerical simulation of flow-induced cavity noise in self-sustained oscillations

The generation and near-field radiation of aerodynamic sound from a low-speed unsteady flow over a two-dimensional automobile door cavity is simulated by using a source-extraction-based coupling method. In the coupling procedure, the unsteady cavity flow field is first computed solving the Reynolds- averaged Navier–Stokes (RANS) equations. The radiated sound is then calculated by using a set of acoustic perturbation equations with acoustic source terms which are extracted from the time-dependent solutions of the unsteady flow. The aerodynamic and its resulting acoustic field are computed for the Reynolds number of 53,266 based on the base length of the cavity. The free stream flow velocity is taken to be 50.9 m/s. As first stage of the numerical investigation of flow-induced cavity noise, laminar flow is assumed. The CFD solver is based on a cell-centered finite volume method. A dispersion-relation-preserving (DRP), optimized, fourth-order finite difference scheme with fully staggered-grid implementation is used in the acoustic solver.     

Manifold method coupled velocity and pressure for Navier-Stokes equations and direct numerical solution of unsteady incompressible viscous flow

Numerical manifold method (NMM) application to direct numerical solution for unsteady incompressible viscous flow Navier-Stokes (N-S) equations was discussed in this paper, and numerical manifold schemes for N-S equations were derived based on Galerkin weighted residuals method as well. Mixed covers with linear polynomial function for velocity and constant function for pressure was employed in finite element cover system. The patch test demonstrated that mixed covers manifold elements meet the stability conditions and can be applied to solve N-S equations coupled velocity and pressure variables directly. The numerical schemes with mixed covers have also been proved to be unconditionally stable. As applications, mixed cover 4-node rectangular manifold element has been used to simulate the unsteady incompressible viscous flow in typical driven cavity and flow around a square cylinder in a horizontal channel. High accurate results obtained from much less calculational variables and very large time steps are in very good agreement with the compact finite difference solutions from very fine element meshes and very less time steps in references. Numerical tests illustrate that NMM is an effective and high order accurate numerical method for unsteady incompressible viscous flow N-S equations.     

Implementation of density-based solver for all speeds in the framework of OpenFOAM

In the framework of open source CFD code OpenFOAM, a density-based solver for all speeds flow field is developed. In this solver the preconditioned all speeds AUSM+(P) scheme is adopted and the dual time scheme is implemented to complete the unsteady process. Parallel computation could be implemented to accelerate the solving process. Different interface reconstruction algorithms are implemented, and their accuracy with respect to convection is compared. Three benchmark tests of lid-driven cavity flow, flow crossing over a bump, and flow over a forward-facing step are presented to show the accuracy of the AUSM+(P) solver for low-speed incompressible flow, transonic flow, and supersonic/hypersonic flow. Firstly, for the lid driven cavity flow, the computational results obtained by different interface reconstruction algorithms are compared. It is indicated that the one dimensional reconstruction scheme adopted in this solver possesses high accuracy and the solver developed in this paper can effectively catch the features of low incompressible flow. Then via the test cases regarding the flow crossing over bump and over forward step, the ability to capture characteristics of the transonic and supersonic/hypersonic flows are confirmed. The forward-facing step proves to be the most challenging for the preconditioned solvers with and without the dual time scheme. Nonetheless, the solvers described in this paper reproduce the main features of this flow, including the evolution of the initial transient.     

Molecular spin in nano-confined fluidic flows

In this paper, we study the effect of molecular spin on the fluid dynamics of molecular nano-confined fluids using the extended Navier–Stokes equations. We show that the effect of spin is non-negligible for non-steady flows and we then discuss two examples, namely, a zero mean oscillatory flow and an oscillatory lid driven cavity flow. In the discussion of the former, we propose a dimensionless quantity that qualitatively predicts the effect of the spin. From this it is shown that only for sufficiently small system sizes and extremely high frequencies will molecular spin be relevant, depending on the molecular fluid’s rotational inertia and the rotational viscosity. In the lid driven cavity flow we observe that the thermodynamic energy dissipation due to molecular spin undergoes period doubling when increasing the Reynolds number and, under some circumstances, it may be negative.     

Numerical experiments with the lid driven cavity flow problem

The centerline velocity profiles obtained from the solution of the two- and three-dimensional representations of the lid driven cavity flow problem are compared for different Reynolds numbers. Two configurations were used in this study: a unit cavity and a cavity with an aspect ratio of 2. The Reynolds numbers ranged from 100 to 5000 for all of the configurations studied. A new method of extending the Jacobi collocation technique called spectral difference is developed in this paper together with a unique computational grid. In addition, an iterative method for solving the pressure problem is also developed. This new numerical method allowed the calculation of three-dimensional Navier-Stokes equations to be performed in computers with very modest computational capabilities such as workstations.     

An explicit Chebyshev pseudospectral multigrid method for incompressible Navier-Stokes equations

The two-dimensional steady incompressible Navier-Stokes equations in the form of primitive variables have been solved by Chebyshev pseudospectral method. The pressure and velocities are coupled by artificial compressibility method and the NS equations are solved by pseudotime method with an explicit four-step Runge-Kutta integrator. In order to reduce the computational time cost, we propose the spectral multigrid algorithm in full approximation storage (FAS) scheme and implement it through V-cycle multigrid and full multigrid (FMG) strategies. Four iterative methods are designed including the single grid method; the full single grid method; the V-cycle multigrid method and the FMG method. The accuracy and efficiency of the numerical methods are validated by three test problems: the modified one-dimensional Burgers equation; the Taylor vortices and the two-dimensional lid driven cavity flow. The computational results fit well with the exact or benchmark solutions. The spectral accuracy can be maintained by the single grid method as well as the multigrid ones, while the time cost is greatly reduced by the latter. For the lid driven cavity flow problem, the FMG is proved to be the most efficient one among the four iterative methods. A speedup of nearly two orders of magnitude can be achieved by the three-level multigrid method and at least one order of magnitude by the two-level multigrid method.     

A Conservative Isothermal Wall Boundary Condition for the Compressible Navier–Stokes Equations

We present a conservative isothermal wall boundary condition treatment for the compressible Navier-Stokes equations. The treatment is based on a manipulation of the Osher solver to predict the pressure and density at the wall, while specifying a zero boundary flux and a fixed temperature. With other solvers, a non-zero mass flux occurs through a wall boundary, which is significant at low resolutions in closed geometries. A simulation of a lid driven cavity flow with a multidomain spectral method illustrates the effect of the new boundary condition treatment.