一种新的可计算可压缩流动的预处理方法

针对使用可压缩流动数值方法求解不可压缩流动存在的刚性问题,基于虚拟压缩法思想,构造了一种以Mach数、速度、密度、温度等变量为元素的预处理矩阵,改变了控制方程组的特征根并使其量级更接近.通过理论推导与分析,证明新方法相比Weiss, Pletcher, Dailey和Choi的方法而言,不仅能降低方程组的刚性,提高了数值求解效率,而且拥有更好的稳定性,此外还能实现低速流动和高速流动之间的光滑过渡.采用有限差分格式进行离散,对流项的Roe格式作为基本加权无振荡(WENO)格式的求解器,黏性项则使用中心型紧致差分格式来计算,与预处理矩阵相结合展开数值实验,结果表明新预处理方法可以实现对无黏和有黏不可压缩流动问题的高精度模拟,且拥有比Weiss和Pletcher等提出的方法更好的收敛性和稳定性.     

低速流动的预处理多重网格求解

本文采用预处理的时间推进方法,求解可压形式的Euler/Navier-Stokes方程,数值模拟低马赫数范围内的无粘、粘性流动.为了进一步加速收敛,并使用了多重网格技术.计算表明预处理能够保持可压缩求解方法在高速时的收敛特征,对于低速流动计算可以加速收敛并提高精度.     

任意马赫数非定常流动数值模拟的统一算法

发展适用于从低速到高速任意马赫数非定常流动数值模拟的统一算法.通过引入一个伪时间导数项和一个新的预处理矩阵,得到双时间非定常预处理可压缩Navier-Stokes方程.方程的对流项采用三阶Roe通量近似差分格式离散,粘性项采用二阶中心差分格式离散.基于数值通量的线性化技术,实现伪时间步的隐式ADI-LU格式迭代,进而获得物理时间步的二阶推进精度.重点以低马赫数流动为例,求解了圆柱绕流和NACA0015翼型等速上仰动态失速问题.计算结果表明该统一算法能够较好地模拟低马赫数乃至任意马赫数非定常流动.     

跨音速轴流压气机级三维粘性流场全工况数值模拟

采用一种快速求解三维粘性流场的计算方法求解跨音速轴流压气机级内部流场及全工况特性。该方法以LU-SGS-GE隐式格式和MUSCL TVD迎风格式为基础,结合壁面函数方法和简单的混合长度湍流模型,对三维可压缩雷诺平均Navie-Stokes方程进行求解。叶列间参数的传递采用混合平面方法并应用了微机网络并行计算技术。计算得到了NASA 37号低展弦比、跨音速轴流压气机级70％设计转速下的全工况性能曲线,并重点分析了其中一些典型工况下的内部流场。计算与实验结果的对比表明此方法能快速得到三维粘性流场的流动特性且计算精度较高,可用来模拟跨音速轴流压气机级内的全工况三维粘性流动。     

低速湍流模拟的预处理技术研究

本文开展低速湍流的预处理技术研究. 该预处理技术采用守恒型变量及主控方程与湍流方程相耦合的隐式求解方法, 并为确保迭代求解稳定性, 发展了合理的参考马赫数定义、双时间步无矩阵方法迭代求解形式以及湍流源项隐式处理方法等, 从而真正实现全速湍流软件平台统一形式. 在喷管、翼型和方柱等低速湍流数值模拟中, 本文方法正确刻画了流场结构特征, 计算与理论、实验等相关结果符合较好, 具有很强的迭代收敛性和结果精度.     

一种隐式预处理方法及其在定常和非定常流动数值模拟中的应用

将Choi-Merkle矩阵预处理方法与LU-SGS隐式方法、双时间法以及多重网格方法结合,发展适用于绕飞行器定常和非定常粘性流动的高效隐式预处理计算方法和程序.介绍一种针对定常和非定常流动的LU-SGS隐式预处理方法的统一表述方法.在不改变流动解的前提下,对Navier-Stokes方程的伪时间导数项实施Choi-Merkle矩阵预处理,从而改善可压缩控制方程在低速情况下的系统刚性,使基于LU-SGS时间推进格式的数值模拟方法同时适用于从极低马赫数到可压缩范围内的数值模拟.对Jameson中心格式的人工粘性进行相应的修改,以提高低速流动的计算精度.翼型、机翼以及翼身组合体绕流的数值模拟研究表明,隐式预处理方法获得了很高的计算效率,可使马赫数0.1左右的低速流动计算时间减少50%以上;通过对现有可压缩计算程序进行小量改动,便可使其均匀覆盖整个低速流动范围,提高CFD程序在飞行器绕流数值模拟中的实用性.     

全速度Roe格式低速性质解析证明

全速度Roe格式是一种新型的可压不可压统一计算格式,这一格式表达了这样一个新观点:有别于预处理方法,可以直接修正标准Roe格式耗散中的非线性特征值,从而使Roe格式耗散性质满足低速流动的要求.为了更好地支持这一新观点,需要有数学上的证明.通过摄动法,本文在理论上证实了这一观点.首先证明了低速Roe格式的性质与连续的方程一致,这一证明较为简单;随后证明了在低马赫数条件下,全速度Roe格式是低速Roe格式的有限放大.从而说明用全速度Roe格式离散的方程的低速性质,也与连续的方程一致.证明过程中,还得到了速度压力失耦现象的解释.     

可压缩流动离散涡方法

推导了可压缩流动旋涡动力学基本方程,并分析了其基本性质。如同不可压流动,在可压缩流动中旋涡同样具有场与物质两重特征。得出了可压缩流中的旋涡诱导速度公式,对Ｂｉｏｔ－Ｓａｖａｒｔ方程进行了可压缩修正。基于Ｌａｇｒａｎｇｉａｎ框架下的粒子方法,求解可压缩流中的胀量项,从而用离散涡模型求解了非定常、不稳定、可压缩流场。数值实验验证了提议的计算方法有效性。并分析了可压缩流动中旋涡运动的特征,与不可压流动的差别。     

隐式间断有限元方法的参数化边界修正

本文采用并行任意阶精度隐式格式的间断有限元方法,求解来流马赫数为0.01的低速可压缩无黏流动,为增强间断有限元对网格的适应性,采用参数化的方法同时对曲线边界上的积分点位置及外法向向量进行修正,计算结果表明在不做预处理的情况下,隐式间断有限元方法也能较好的计算低速流动,本文所做的参数化边界修正方法有助于间断有限元方法使用通用非结构网格进行高精度的计算.     

一种求解可压缩Navier-Stokes方程的隐式迭代时间推进方法

针对有壁面边界的可压缩流动问题,提出与基于非等距网格的高精度紧致型差分格式相结合的简化隐式迭代时间推进法,建立求解可压缩Navier-Stokes方程的直接数值模拟方法,提高了计算效率.应用该方法,直接数值模拟两种有壁面边界的二维可压缩流动问题,即可压缩平板边界层流动和可压缩槽道流动.     

Implicit preconditioned WENO scheme for steady viscous flow computation

A class of lower–upper symmetric Gauss–Seidel implicit weighted essentially nonoscillatory (WENO) schemes is developed for solving the preconditioned Navier–Stokes equations of primitive variables with Spalart–Allmaras one-equation turbulence model. The numerical flux of the present preconditioned WENO schemes consists of a first-order part and high-order part. For first-order part, we adopt the preconditioned Roe scheme and for the high-order part, we employ preconditioned WENO methods. For comparison purpose, a preconditioned TVD scheme is also given and tested. A time-derivative preconditioning algorithm is devised and a discriminant is devised for adjusting the preconditioning parameters at low Mach numbers and turning off the preconditioning at intermediate or high Mach numbers. The computations are performed for the two-dimensional lid driven cavity flow, low subsonic viscous flow over S809 airfoil, three-dimensional low speed viscous flow over 6:1 prolate spheroid, transonic flow over ONERA-M6 wing and hypersonic flow over HB-2 model. The solutions of the present algorithms are in good agreement with the experimental data. The application of the preconditioned WENO schemes to viscous flows at all speeds not only enhances the accuracy and robustness of resolving shock and discontinuities for supersonic flows, but also improves the accuracy of low Mach number flow with complicated smooth solution structures.     

A discontinuous Galerkin method for inviscid low Mach number flows

In this work we extend the high-order discontinuous Galerkin (DG) finite element method to inviscid low Mach number flows. The method here presented is designed to improve the accuracy and efficiency of the solution at low Mach numbers using both explicit and implicit schemes for the temporal discretization of the compressible Euler equations. The algorithm is based on a classical preconditioning technique that in general entails modifying both the instationary term of the governing equations and the dissipative term of the numerical flux function (full preconditioning approach). In the paper we show that full preconditioning is beneficial for explicit time integration while the implicit scheme turns out to be efficient and accurate using just the modified numerical flux function. Thus the implicit scheme could also be used for time accurate computations. The performance of the method is demonstrated by solving an inviscid flow past a NACA0012 airfoil at different low Mach numbers using various degrees of polynomial approximations. Computations with and without preconditioning are performed on different grid topologies to analyze the influence of the spatial discretization on the accuracy of the DG solutions at low Mach numbers.     

Efficient computation of compressible and incompressible flows

The combination of explicit Runge–Kutta time integration with the solution of an implicit system of equations, which in earlier work demonstrated increased efficiency in computing compressible flow on highly stretched meshes, is extended toward conditions where the free stream Mach number approaches zero. Expressing the inviscid flux Jacobians in terms of Mach number, an artificial speed of sound as in low Mach number preconditioning is introduced into the Jacobians, leading to a consistent formulation of the implicit and explicit parts of the discrete equations. Besides extension to low Mach number flows, the augmented Runge–Kutta/Implicit method allowed the admissible Courant–Friedrichs–Lewy number to be increased from O(1 0 0) to O(1 0 0 0). The implicit step introduced into the Runge–Kutta framework acts as a preconditioner which now addresses both, the stiffness in the discrete equations associated with highly stretched meshes, and the stiffness in the analytical equations associated with the disparity in the eigenvalues of the inviscid flux Jacobians. Integrated into a multigrid algorithm, the method is applied to efficiently compute different cases of inviscid flow around airfoils at various Mach numbers, and viscous turbulent airfoil flow with varying Mach and Reynolds number. Compared to well tuned conventional methods, computation times are reduced by half an order of magnitude.     

High-resolution viscous flow simulations at arbitrary Mach number

A characteristic-based unsteady viscous flow solver is developed with preconditioning that is uniformly applicable for Mach numbers ranging from essentially incompressible to supersonic. A preconditioned flux-difference formulation for nondimensional primitive variables is a key element of the present approach. The simple primitive-variable numerical flux is related to Roe’s flux-difference scheme and preserves contact discontinuities using primitive variables, with or without preconditioning. Preconditioning by a single-parameter diagonal matrix conditions the system eigenvalues in terms of nondimensional local velocity and local temperature. An iterative implicit solution algorithm is given for the preconditioned formulation and is used for several simple test and validation cases. These include an inviscid shock-tube case, flat-plate boundary layer flow at low Mach number, viscous flow past a circular cylinder at low Reynolds number and with different thermal boundary conditions, and validation cases for incompressible and transonic flows.     

Gas-kinetic numerical studies of three-dimensional complex flows on spacecraft re-entry

The gas-kinetic numerical algorithm solving the Boltzmann model equation is extended and developed to study the three-dimensional hypersonic flows of spacecraft re-entry into the atmosphere in perfect gas. In this study, the simplified velocity distribution function equation for various flow regimes is presented on the basis of the kinetic Boltzmann–Shakhov model. The discrete velocity ordinate technique and numerical quadrature methods, such as the Gauss quadrature formulas with the weight function 2/π^1/2exp(?V²) and the Gauss–Legendre numerical quadrature rule, are studied to resolve the barrier in simulating complex flows from low Mach numbers to hypersonic problems. Specially, the gas-kinetic finite-difference scheme is constructed for the computation of three-dimensional flow problems, which directly captures the time evolution of the molecular velocity distribution function. The gas-kinetic boundary conditions and numerical procedures are studied and implemented by directly acting on the velocity distribution function. The HPF (high performance fortran) parallel implementation technique for the gas-kinetic numerical method is developed and applied to study the hypersonic flows around three-dimensional complex bodies. The main purpose of the current research is to provide a way to extend the gas-kinetic numerical algorithm to the flow computation of three-dimensional complex hypersonic problems with high Mach numbers. To verify the current method and simulate gas transport phenomena covering various flow regimes, the three-dimensional hypersonic flows around sphere and spacecraft shape with different Knudsen numbers and Mach numbers are studied by HPF parallel computing. Excellent results have been obtained for all examples computed.     

An all-speed relaxation scheme for interface flows with surface tension

We consider interface flows where compressibility and capillary forces (surface tension) are significant. These flows are described by a non-conservative, unconditionally hyperbolic multiphase model. The numerical approximation is based on finite-volume method for unstructured grids. At the discrete level, the surface tension is approximated by a volume force (CSF formulation). The interface physical properties are recovered by designing an appropriate linearized Riemann solver (Relaxation scheme) that prevents spurious oscillations near material interfaces. For low-speed flows, a preconditioning linearization is proposed and the low Mach asymptotic is formally recovered. Numerical computations, for a bubble equilibrium, converge to the required Laplace law and the dynamic of a drop, falling under gravity, is in agreement with experimental observations.     

跨流域高超声速绕流环境Boltzmann模型方程统一算法研究

如何准确可靠地模拟从外层空间高稀薄流到近地面连续流的航天器高超声速绕流环境与复杂流动变化机理是流体物理的前沿基础科学问题. 基于对Boltzmann方程碰撞积分的物理分析与可计算建模, 确立了可描述自由分子流到连续流区各流域不同马赫数复杂流动输运现象统一的Boltzmann模型速度分布函数方程, 发展了适于高、低不同马赫数绕流问题的离散速度坐标法和直接求解分子速度分布函数演化更新的气体动理论数值格式, 建立了模拟复杂飞行器跨流域高超声速飞行热环境绕流问题的气体动理论统一算法. 对稀薄流到连续流不同Knudsen数0.002 ≤Kn_∞ ≤1.618、不同马赫数下可重复使用卫星体再入过程(110–70 km)中高超声速绕流问题进行算法验证分析, 计算结果与典型文献的Monte Carlo直接模拟值及相关理论分析符合得较好. 研究揭示了飞行器跨流域不同高度高超声速复杂流动机理、绕流现象与气动力/热变化规律, 提出了一个通过数值求解介观Boltzmann模型方程, 可靠模拟高稀薄自由分子流到连续流跨流域高超声速气动力/热绕流特性统一算法.     

求解非定常不可压N-S方程的预处理方法

应用预处理技术,对不可压非定常N-S方程使用双时间推进法求解.当沿物理时间层推进时,连续性方程和动量方程沿伪时间方向使用隐式线Gauss-Seidel迭代法求解,对流项采用三阶迎风差分法离散.通过对不同Reynolds数、不同深宽比下非定常驱动腔内流动的模拟,数值研究了预处理法计算非定常不可压粘性流动的收敛特性,分析了沿伪时间层的迭代收敛速度对流场Reynolds数的依赖特征.     

模拟可压缩流体的格子Boltzmann模型

在简单声速可调模型的基础上,通过在演化方程中引入一个吸引势来降低有效声速从而提高Mach数,建立高Mach数下的可压缩格子Boltzmann模型．利用Chapman-Enskog渐进展开法推导相应的宏观流体力学方程．与粘滞流体的Navier-Stokes方程比较表明,该模型有降低声速的功能．模拟结果表明,该模型可将Mach数提高到3以上,且与理论值符合．该模型的建立为用格子气模拟可压缩流体打开广阔前景． 关键词：