ALE中的重映算法

介绍了二维非结构网格上的守恒重映算法，重点是基于SFB／DC思想的通量重映算法。用统一的公式表示不同的单元量重映算法，包括原始的贡献网格法、Barth—Jespersen方法、最小二乘法，不同算法间的区别体现为梯度求法的差异。对于交错网格上速度的重映，介绍了SALE和HIS算法。此外，为保证重映算法的有界性，引入了修补方法。     

求解可压缩流的高精度非结构网格WENO有限体积法

提出-种基于最小二乘重构和WENO限制器的非结构网格高精度有限体积方法.用中心网格的某些邻居网格建立重构多项式,给出-定的原则搜索和存储足够多的邻居网格以建立重构多项式,采用最小二乘法求解重构多项式的系数.用-种通用的方法控制重构邻居个数,以减少存储和计算,采用WENO限制器和旋转Riemann求解器以达到统-的高精度并且抑制守恒律方程求解中的非物理振荡.为检验上述算法,以基于节点的梯度重构,Bath and Jesperson限制器的二阶算法为基准,给出三阶和四阶格式与二阶格式以及高阶格式若干经典算例计算结果的对比和分析.     

一维含化学反应流体力学方程组的ALE间断有限元方法

研究一维含化学反应流体力学方程组的数值模拟方法.结合理想气体状态方程并利用HLLC解法器在各个单元边界处的数值通量，给出ALE间断有限元方法.高阶计算时，使用TVD斜率限制器对数值解可能产生的非物理振荡进行抑制.结果表明：该算法能够保持物理量的守恒性和高精度，并能够清晰地捕捉爆轰波的结构特征.     

用偏压限制器控制KT—5C托卡马克等离子体边缘电场的实验研究

在托卡马克ＫＴ－５Ｃ上，我们首次采用可灵活组合的多块限制器进行了施加偏压以控制等离子体边缘电场的实验。结果表明，在本装置上限制器加正偏压优于加负偏压、正偏压改变等离子体边缘电场效果更明显。偏压限制器收集面积、纵场和偏置电压的大小对偏压效果的影响都是敏感的。改变限制器收集面积和偏压导致的边缘电场的变化最终将趋于饱和。     

用偏压限制器控制KT－5C托卡马克等离子体边缘电场的实验研究

在托卡马克ＫＴ－５Ｃ上，我们首次采用可灵活组合的多块限制器进行了施加偏压以控制等离子体边缘电场的实验，结果表明，在本装置上限制器加正偏压优于加负偏压，正偏压改变等离子体边缘电场效果更明显。偏压限制器收集面积、纵场和偏置电压的大小对偏压效果的影响都是敏感的。改变限制器收集面积和偏压导致的边缘电场的变化最终将趋于饱和，另外发现，偏压限制器与等离子体柱的相对位置对等离子体边缘电场的影响也是重要的。     

拉氏数值模拟中的人工粘性方法

较好的人工粘性需要满足较小的计算开销、不能去除真实具有的涡运动等条件.提出一种应用于拉氏数值模拟中基于Lew人工粘性,同时增加了限制器的人工粘性方法.可以有效减少数值模拟结果对网格的依赖;采用特征值限制器控制施加的人工粘性大小,通过限制器能够区分激波压缩和等熵压缩;方便应用在二维、三维,结构网格或者非结构网格上.     

二维Lagrangian坐标系下可压气动方程组的间断Petrov-Galerkin方法

构造矩形网格下求解Lagrangian坐标系下气动方程组的单元中心型格式. 空间离散采用控制体积间断Petrov-Galerkin方法,时间离散采用二阶TVD Runge-Kutta方法. 利用限制器来抑制非物理震荡并保证RKCV算法的稳定性. 构造的算法可以保证物理量的局部守恒. 与Runge-Kutta间断Galerkin（RKDG）方法相比较,RKCV方法的计算公式少一项积分项使得计算较简单. 给出一些数值算例验证了算法的可靠性及效率.     

二维Lagrangian坐标系下可压气动方程组的间断Petrov-Galerkin方法（英文）

构造矩形网格下求解Lagrangian坐标系下气动方程组的单元中心型格式.空间离散采用控制体积间断Petrov-Galerkin方法,时间离散采用二阶TVD Runge-Kutta方法.利用限制器来抑制非物理震荡并保证RKCV算法的稳定性.构造的算法可以保证物理量的局部守恒.与Runge-Kutta间断Galerkin(RKDG)方法相比较,RKCV方法的计算公式少一项积分项使得计算较简单.给出一些数值算例验证了算法的可靠性及效率.     

机动目标逆合成孔径激光雷达方位成像快速算法

针对逆合成孔径激光雷达对机动目标成像时存在方位多普勒时变的问题,提出了一种基于方位时频域keystone变换的机动目标逆合成孔径激光雷达方位成像快速算法.利用多分量线性调频子回波信号的调频斜率与起始频率的比值为常量这一特点,在方位时频域采用keystone变换将多分量线性调频信号同时转换为多分量单频信号,利用快速傅里叶变换实现方位聚焦.采用基于分数阶傅里叶变换和最小熵的线性调频参量估计方法,实现了对调频斜率与起始频率比值的精确、快速估计.结果表明,与现有的基于Radon-Wigner变换的距离-瞬时多普勒成像算法相比,所提出的算法成像效率大大提高,且能够保留更多的目标细节信息,适合于逆合成孔径激光雷达的实时成像.     

低耗散非结构网格多维限制器

基于极值原理分析非结构网格多维限制器的构造准则，通过引入约束位置和约束模板的定义，将非结构网格多维限制器构造方法统一化，并以此为基础提出一种新型非结构网格多维限制器.通过典型算例计算与已有限制器进行比较.结果表明：对于包含激波、接触间断等复杂波系干扰流动，新型多维限制器在保证数值稳定的条件下具有更低的数值耗散，对于复杂波系结构具有更高的流动分辨率.     

Anti-diffusion method for interface steepening in two-phase incompressible flow

In this paper, we present a method for obtaining sharp interfaces in two-phase incompressible flows by an anti-diffusion correction, that is applicable in a straight-forward fashion for the improvement of two-phase flow solution schemes typically employed in practical applications. The underlying discretization is based on the volume-of-fluid (VOF) interface-capturing method on unstructured meshes. The key idea is to steepen the interface, independently of the underlying volume-fraction transport equation, by solving a diffusion equation with reverse time, i.e. an anti-diffusion equation, after each advection time step of the volume fraction. As the solution of the anti-diffusion equation requires regularization, a limiter based on the directional derivative is developed for calculating the gradient of the volume fraction. This limiter ensures the boundedness of the volume fraction. In order to control the amount of anti-diffusion introduced by the correction algorithm we propose a suitable stopping criterion for interface steepening. The formulation of the limiter and the algorithm for solving the anti-diffusion equation are applicable to 3-dimensional unstructured meshes. Validation computations are performed for passive advection of an interface, for 2-dimensional and 3-dimensional rising-bubbles, and for a rising drop in a periodically constricted channel. The results demonstrate that sharp interfaces can be recovered reliably. They show that the accuracy is similar to or even better than that of level-set methods using comparable discretizations for the flow and the level-set evolution. Also, we observe a good agreement with experimental results for the rising drop where proper interface evolution requires accurate mass conservation.     

Spline based least squares integration for two-dimensional shape or wavefront reconstruction

In this work, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. The noise influence is studied by adding white Gaussian noise to the slope data. Experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.     

Accuracy preserving limiter for the high-order accurate solution of the Euler equations

Higher-order finite-volume methods have been shown to be more efficient than second-order methods. However, no consensus has been reached on how to eliminate the oscillations caused by solution discontinuities. Essentially non-oscillatory (ENO) schemes provide a solution but are computationally expensive to implement and may not converge well for steady-state problems. This work studies the extension of limiters used for second-order methods to the higher-order case. Requirements for accuracy and efficient convergence are discussed. A new limiting procedure is proposed. Ringleb’s flow problem is used to demonstrate that nearly nominal orders of accuracy for schemes up to fourth-order can be achieved in smooth regions using the new limiter. Results for the fourth-order accurate solution of transonic flow demonstrates good convergence properties and significant qualitative improvement of the solution relative the second-order method. The new limiter can also be successfully applied to reduce the dissipation of second-order schemes with minimal sacrifices in convergence properties relative to existing approaches.     

Hierarchical reconstruction for discontinuous Galerkin methods on unstructured grids with a WENO-type linear reconstruction and partial neighboring cells

The hierarchical reconstruction (HR) [Y.-J. Liu, C.-W. Shu, E. Tadmor, M.-P. Zhang, Central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction, SIAM J. Numer. Anal. 45 (2007) 2442-2467] is applied to the piecewise quadratic discontinuous Galerkin method on two-dimensional unstructured triangular grids. A variety of limiter functions have been explored in the construction of piecewise linear polynomials in every hierarchical reconstruction stage. We show that on triangular grids, the use of center biased limiter functions is essential in order to recover the desired order of accuracy. Several new techniques have been developed in the paper: (a) we develop a WENO-type linear reconstruction in each hierarchical level, which solves the accuracy degeneracy problem of previous limiter functions and is essentially independent of the local mesh structure; (b) we find that HR using partial neighboring cells significantly reduces over/under-shoots, and further improves the resolution of the numerical solutions. The method is compact and therefore easy to implement. Numerical computations for scalar and systems of nonlinear hyperbolic equations are performed. We demonstrate that the procedure can generate essentially non-oscillatory solutions while keeping the resolution and desired order of accuracy for smooth solutions.     

基于ARMA模型的受损限幅器模型建立方法

针对限幅器遭受功能或物理损伤而发生的非线性效应, 给出了一种基于信号分析的受损限幅器非线性效应研究新视角, 并从该视角出发, 提出了模型建立方法。该方法首先测得受损限幅器幅频响应序列, 将其转化为零均值实平稳序列; 然后计算该序列的自相关函数和偏相关函数, 估计自回归滑动平均(ARMA)模型的阶数; 最后采用最小二乘法估计出模型的表达式, 并采用最终预测误差(FPE)准则对该表达式进行校验。试验结果和理论分析验证了该方法的良好效果。     

一种基于高阶节点间断Galerkin方法的新型限制器设计

使用高阶间断Galerkin(discontinuous Galerkin, DG)方法求解双曲守恒律方程组时, 非物理效应常常导致计算过程的中断, 这在很大程度上制约着该方法在计算流体力学中的应用.文章结合局部单元上原始流动变量的Taylor展开, 设计了一种新型的限制器, 通过对各阶空间导数的重构, 有效地消除了非物理振荡的不利影响.对二维Euler方程的计算结果表明, 该限制器不仅能够捕捉高质量的激波, 而且能够保证残值的有效收敛.      

The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids

Novel limiters based on the weighted average procedure are developed for finite volume methods solving multi-dimensional hyperbolic conservation laws on unstructured grids. The development of these limiters is inspired by the biased averaging procedure of Choi and Liu [10]. The remarkable features of the present limiters are the new biased functions and the weighted average procedure, which enable the present limiter to capture strong shock waves and achieve excellent convergence for steady state computations. The mechanism of the developed limiters for eliminating spurious oscillations in the vicinity of discontinuities is revealed by studying the asymptotic behavior of the limiters. Numerical experiments for a variety of test cases are presented to demonstrate the superior performance of the proposed limiters.     

基于非结构网格间断有限元方法在可压缩流体中的应用

本文开发了一套基于非结构网格的间断有限元方法(DG)程序,并对与单元形状无关的斜率限制器进行了研究。此程序支持多种网格类型,能够方便应用于具有混合单元的非结构网格,具有处理复杂几何结构的能力,为研究叶轮机械内部复杂流动现象提供了有效的研究工具。本文利用该程序对若干典型无黏和黏性问题进行数值模拟,结果表明,该程序具有较高的可信度,能够处理具有混合单元的非结构网格,并给出良好的数值模拟结果。     

Iteration scheme for solution of inverse problem of probing for a radially inhomogeneous cylinder

An algorithm is constructed for solution of the inverse problem of probing for a radially stratified cylinder that employs the Newton-Kantorovich iteration procedure and Tikhonov's regularization method. A considerable portion of the calculations within the proposed solution can be performed analytically, which makes computer implementation highly effective. Illustrative results of numerical experiments are presented.Kharkov State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 10, pp. 901–911, October, 1993.