火箭喷流波系的数值研究

根据ＭＵＳＣＬ格式的基本思想，对格式进行了部分修改，数值模拟了火箭喷流流场的波系结构。     

具有U_（qp）（U_3）U_（qp）（U_2）U_（qp）（SO_2）对称

构造了具有Ｕｑｐ（Ｕ３）Ｕｑｐ（Ｕ２）Ｕｑｐ（ＳＯ２）对称的双参数ｑｐ－形变二维相互作用玻色子模型（ＩＢＭ），并给出了其能谱和跃迁矩阵元．结果表明，能谱和跃迁矩阵元极其敏感地依赖于第二个形变参数．     

透平级非设计工况气动性能的数值模拟

采用新型 ＬＵ隐式格式和改良型高阶 ＭＵＳＣＬ ＴＶＤ格式求解全三维雷诺平均的 Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程和 ｑ－ｗ低雷诺数双方程湍流模型,对一台ＮＡＳＡ跨音单级透平在不同工况下的内部流场进行了详细的数值模拟,并与可能得到的实验结果进行了对比。总结了小流量工况下动叶内部流动的分离模式。     

低展弦比跨音速轴流风扇转子流场三维数值模拟

应用基于时间推进的有限差分法求解跨音速压气机风扇转子内部三维粘性流场．该方法以新型ＬＵ隐式格式和改良型 ＭＵＳＣＬ ＴＶＤ格式为基础,对三维可压缩雷诺平均 Ｎａｖｉｅ－Ｓｔｏｋｅｓ方程和低雷诺数ｑ－ω双方程湍流模型进行求解．计算得到了ＮＡＳＡ Ｌｅｗｉｓ ６７跨音速、低展弦比轴流风扇转子的性能曲线并重点分析了近最高效率点工况和近失速工况下的内部流场．计算与实验结果的对比表明此方法能够得到三维粘性流场的流动特性且计算精度较高,可用来模拟跨音速风扇转子内部流动．     

标量算符本征值对g壳层LSQ耦合态的完全分类计算

按（Ｕ,Ｄ）Ｌ－ＬＳＱ格式构造ｌ壳层ＬＳＱ耦合态,这里Ｕ（Ｄ）是自旋向上（向下）电子的轨道角动量,Ｌ、Ｓ、Ｑ是总轨道角动量、总自旋和准旋。由４个产生－湮灭算符构造与轨道、自旋准旋算符均为易的标量算符并用基本征值对ＬＳＱ耦合态进上步分类,实现了对ｆ、ｇ壳层耦合态的完全分类,列出了ｇ壳层耦合态完全分类的主要结果。     

多级轴流压气机全工况特性数值模拟

采用一种快速求解三维粘性流场的计算方法求解某多级轴流压气机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，使用多重网格迭代加速收敛技术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．首先对一个五排压气机（进口导叶加两级）进行了全工况特性计算，并对计算结果做了详细分析．然后对前三排（进口导叶加一级）进行了全工况特性计算并与五排联赛的计算结果进行了对比，对多级环境对单级性能的影响机理做了初步探讨。     

基于扩散速度方法粘性流场的离散涡数值模拟

基于扩散速度方法粘性流场的离散涡数值模拟吴文权，李春，卜千里（上海机械学院上海２０００９３）关键词：扩散速度模型，粘性流场，离散涡方法。ＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＯＦＶＩＳＣＯＵＳＦＬＯＷＦＩＥＬＤＳＵＳＩＮＧＤＩＦＦＵＳＩＯＮＶＥＬＯＣ...     

离心叶栅内气固两相流动的数值模拟

离心叶栅内气固两相流动的数值模拟蔡体菁，王文琪，郁斌（东南大学动力工程系南京２１００１８）关键词：离心叶栅，粒子轨迹，龙格－库塔方法。ＮＵＭＥＲＩＣＡＬＭＯＤＥＬＩＮＧＦＯＲＧＡＳ－ＳＯＬＩＤＳＦＬＯＷＳＴＨＲＯＵＧＨＡＣＥＮＴＲＩＦＵＧＡＬＣＡＳＣ...     

振荡机翼跨音速非定常粘性绕流的数值计算

以非定常Ｎ－Ｓ方程为主管方程，采用ＬＵ－ＮＮＤ混合差分格式，Ｃ和Ｃ－Ｈ型贴体运动网格，Ｂ－Ｌ双层代数紊流模型，求解绕振荡翼型和三维机翼的跨音速非定常粘性流场，分别计算了ＮＡＣＡ００１２翼型和Ｍ６机翼作俯仰振荡时跨音速非定常粘性绕流流场。研究了非定常绕流的气动特性，部分计算结果和风洞实验值作了比较。     

利用高阶添加项构造原参数气动方程组的差分格式

本文在详细分析以往隐格式构造思想的基础上，提出了一种无近似因子分解、无矩阵运算、且计算量小的隐格式构造思想，并将该格式构造思想用于ＭａｃＣｏｒｍａｃｋ显格式中去，得到的ＭＣ－ＬＢ格式通过算例分析，其在收敛性激波捕获能力及三维流动的稳定性方面均有较好表现。     

数值求解Navier-Stokes方程的一个新的系数矩阵分裂法

在一个单步格式的基础上构造了一个新的隐式系数矩阵分裂法来数值求解可压Navier-St-okes方程。对方程中的无粘项部分利用守恒型方程中流通量向量为一齐次函数这一特性,根据Jacobian矩阵特征值的符号而将流通向量分裂成两部分。在此基础上据风向而构造逼近于无粘项的差分格式。对方程中的粘性项部分利用算子附加修正的方法来改进计算的收敛过程。所建立的差分格式被用来数值求解Couette流以考查这一方法。     

近尾迹流动的数值模拟

通过数值求解可压缩Navier-Stokes方程的方法来模拟近尾迹的分离流动。Navier-Stokes方程^[1]是利用中所给出的方法进行差分逼近的。这一方法兼备显式格式和隐式格式的优点。这是一隐式格式,因而可放松稳定性对时间步长的限制。这一格式又具有显式格式的简单性,差分方程的解可显式表达出来。求解过程中避免了通常隐式格式所要求的大量数值矩阵求逆和大量的矩阵运算。文中对不同的马赫数M_∞和雷诺数Re进行了计算。数值实验表明,本文所采用的方法是模拟底部分离流动的一个简单而有效的方法,可用来计算高马赫数和高雷诺数的分离流动。     

A tailored solver for bifurcation analysis of ocean-climate models

In this paper, we present a new linear system solver for use in a fully-implicit ocean model. The new solver allows to perform bifurcation analysis of relatively high-resolution primitive-equation ocean-climate models. It is based on a block-ILU approach and takes special advantage of the mathematical structure of the governing equations. In implicit models Jacobian matrices have to be constructed. Analytical construction is hard for complicated but more realistic representations of mixing. This is overcome by evaluating the Jacobian in part numerically. The performance of the new implicit ocean model is demonstrated using (i) a high-resolution model of the wind-forced double-gyre flow problem in a (relatively small) midlatitude spherical basin, and (ii) a medium-resolution model of thermohaline and wind-driven flows in an Atlantic size single-hemispheric basin.     

An Implicit Scheme for Nonideal Magnetohydrodynamics

A new implicit algorithm is developed for solving the time-dependent, nonideal magnetohydrodynamic equations. It can also be used as an efficient relaxation scheme for steady state solutions. The algorithm is a finite-volume scheme that uses an approximate Riemann solver for the hyperbolic fluxes and central differencing applied on nested control volumes for the parabolic fluxes that arise from the non-ideal terms (i.e., resistivity and viscosity). In one dimension the scheme is second-order accurate in space and time. In two or three dimensions, the accuracy is between first and second order. For the class of problems considered, the implicit formulation is stable for any size time step, thus allowing efficient tracking of slower transients. The implicit operator is inverted using a lower–upper symmetric Gauss–Seidel iteration. Results from several test cases are presented that show good agreement with analytical solutions and illustrate the advantages of the scheme.     

Numerical solution of the one-dimensional Burgers’ equation: Implicit and fully implicit exponential finite difference methods

This paper describes two new techniques which give improved exponential finite difference solutions of Burgers’ equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers’ equation. As the Burgers’ equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton’s method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable.     

叶轮机械三元跨声速势流多重网格分解因式格式数值解

基于作者本人发展的用于分析求解叶轮机械三元跨声速势流的AF2格式,并结合Jameson发展的用于求解二元跨声速势流的MAD格式,本文提出了一种用于快速求解叶轮机械三元跨声速势流的新的全隐式多重网格分解因式格式(MAF格式)并用其对西德DFVLR单级轴流式压气机转子三元跨声速流场进行了求解计算。     

有限差分-有限元混合方法的隐式格式研究

利用文[1]提出的有限差分-有限元混合方法,给出一种新的有限元隐式格式,它避免了在传统有限元方法中采用隐式格式时需要求解大型带状稀疏矩阵以及存储量大等问题,同时利用差分法中近似因式分解方法和PuliamTH等人为避免块对角矩阵的求解提出的对角化技术,以期提高计算效率。     

Stability Analysis of a Fully Coupled Implicit Scheme for Inviscid Chemical Non-Equilibrium Flows

Von Neumann stability theory is applied to analyze the stability of a fully coupled implicit (FCI) scheme based on the lower-upper symmetric Gauss-Seidel (LU-SGS) method for inviscid chemical non-equilibrium flows. The FCI scheme shows excellent stability except the case of the flows involving strong recombination reactions, and can weaken or even eliminate the instability resulting from the stiffness problem, which occurs in the subsonic high-temperature region of the hypersonic flow field. In addition, when the full Jacobian of chemical source term is diagonalized, the stability of the FCI scheme relies heavily on the flow conditions. Especially in the case of high temperature and subsonic state, the CFL number satisfying the stability is very small. Moreover, we also consider the effect of the space step, and demonstrate that the stability of the FCI scheme with the diagonalized Jacobian can be improved by reducing the space step. Therefore, we propose an improved method on the grid distribution according to the flow conditions. Numerical tests validate sufficiently the foregoing analyses. Based on the improved grid, the CFL number can be quickly ramped up to large values for convergence acceleration.     

A new five-term simple chaotic attractor

A new chaotic attractor is presented with only five terms in three simple differential equations having fewer terms and simpler than those of existing seven-term or six-term chaotic attractors. Basic dynamical properties of the new attractor are demonstrated in terms of equilibria, Jacobian matrices, non-generalized Lorenz systems, Lyapunov exponents, a dissipative system, a chaotic waveform in time domain, a continuous frequency spectrum, Poincaré maps, bifurcations and forming mechanisms of its compound structures.     

Effect of discretization order on preconditioning and convergence of a high-order unstructured Newton-GMRES solver for the Euler equations

This article studies the effect of discretization order on preconditioning and convergence of a high-order Newton–Krylov unstructured flow solver. The generalized minimal residual (GMRES) algorithm is used for inexactly solving the linear system arising from implicit time discretization of the governing equations. A first-order Jacobian is used as the preconditioning matrix. The complete lower–upper factorization (LU) and an incomplete lower–upper factorization (ILU(4)) techniques are employed for preconditioning of the resultant linear system. The solver performance and the conditioning of the preconditioned linear system have been compared in detail for second, third, and fourth-order accuracy. The conditioning and eigenvalue spectrum of the preconditioned system are examined to investigate the quality of preconditioning.