多边形交错网格的守恒重映算法

提出基于细分和数值积分思想的一种离散的守恒重映方法——质点重映方法.密度分布可采用一阶精度的分片常数分布,或二阶精度的分片线性分布.分片线性密度分布函数采用面平均方法构造.重映过程中,借助四边形辅助网格,实现了交错网格节点量的重映.质点重映方法既适用于结构网格,也适用于非结构网格,且不要求新旧网格之间一一对应.数值结果表明,一阶精度重映算法健壮性好,但会产生较大的扩散效应;二阶精度重映算法可较好地保持密度分布的特性,但存在单调性问题.为改善二阶精度重映方法单调性,将结构网格质量守恒调整算法推广到非结构网格上,以限制新网格的质量密度.给出了一些重映的例子,并进行了误差分析.     

一种高精度保界的守恒重映方法

Lagrange方法中，当流场发生大变形时，跟踪流体运动的Lagrange网格发生扭曲，使计算无法进行下去，此时必须重分网格，把网格修复成较好的形状。另外，网格自适应技术中的重构、合并与加密，以及同一问题不同程序相继计算的连接，并行计算中相邻块边界区域的数据传递等，这些情况都需要利用旧网格上的物理量来确定新网格上的物理量，是一个物理量重映过程。质点重映方法是基于物理上守恒规律的一种离散的物理量守恒映射方法，既可实现分片常数分布的一阶精度重映计算，又可实现分片线性分布的二阶精度重映计算。这种方法可严格保证守恒量的守恒性，且可以实现任意多边形网格以及节点上物理量的守恒重映。但是，基于分片线性分布的二阶精度重映方法，如果新网格的守恒量没有进行保界调整，那么相应的强度量有可能在其局部的限制范围之外，破坏了原网格物理量的单调性。因而，对二阶精度的质点重映方法进行了进一步研究。在分片线性分布的基础上，将基于结构网格的保界算法扩展到非结构网格上，给出了二阶保界的质点守恒重映方法。     

基于MOF界面重构的多物质ALE方法

提出一种基于MOF(Moment-of-Fluid)界面重构的多物质ALE(Arbitrary Lagrangian-Eulerian)方法.流体力学方程组采用相容有限元方法进行空间离散.提出一种新的二维子网格力学模型,用来计算混合网格中的物理量经过一个拉氏步后发生的变化,混合网格内的界面重构采用MOF方法.提出一种精确积分守恒重映方法.给出数值算例,如空气和水的Riemann问题,Dukowicz问题,水中强激波与空气泡相互作用问题等.结果表明,方法具有较高的精度,能够处理物质界面和网格的大变形问题.     

一种基于MOF界面重构的二维中心型MMALE方法

发展了一种基于MOF（Moment of Fluid）界面重构的二维中心型MMALE（Multi-Material Arbitrary Lagrangian-Eulerian）方法.其中,流体力学方程组采用中心型拉氏方法进行离散求解.混合网格的热力学封闭采用Tipton压力松弛模型.混合网格内的界面重构采用MOF方法,并对MOF方法作了简化和改进.重映步采用一种基于多边形剪裁算法的精确积分守恒重映方法.计算了若干数值例子,包括二维漩涡发展问题、Sedov问题、激波与氦气泡相互作用问题、水中强激波与空气泡相互作用问题、二维RT不稳定性问题等.数值算例表明,该方法具有二阶精度,能够计算界面两侧密度比和压力比很大的问题,并且其健壮性优于交错型MMALE方法,适合计算多介质复杂流体动力学问题.     

基于高阶守恒重映对窗口嵌入技术的改进

采用高阶守恒重映方法提高窗口嵌入技术中非点对点搭接网格界面的流场信息传递精度和分辨率,研究不同精度和模板选择方式下的重构对重映精度的影响.界面守恒变量的数据重构使用常数分布、线性分布和二次多项式分布.结果表明,基于WENO的线性重构在精度和计算量方面获得了较好的平衡.将改进的方法应用于机翼贴片修补问题的数值模拟,成功模拟出修补后翼面压力分布出现的明显跳跃.     

基于任意拉格朗日—欧拉型移动网格的反应流广义黎曼问题方法

提出一种在自由重映移动网格下的广义黎曼问题方法模拟反应流.该方法基于显式的自由重映移动网格广义黎曼问题的解.为保证在时间和空间上的高精度，应用广义黎曼问题方法构造数值通量.为保证反应区的高分辨率，采用变分法生成自适应移动网格.该方法不仅能够保证网格质量，而且能有效地避免任意拉格朗日—欧拉方法中由于显式重映过程而带来的数值误差.包括CJ爆轰及不稳定爆轰的数值实验说明该格式的精确性和鲁棒性，证明这种移动网格下的二阶广义黎曼问题方法可以较好地捕捉反应流的间断与光滑结构.     

求解对流占优Burgers方程的随流格式

在用差分方法求解对流占优的Burgers方程时,许多常用的差分格式的计算精度会下降。为了提高对流占优问题的计算精度,本文提出非线性对流项的差分格式的设计要求,从而得到对流项的新的差分格式-随流格式。本文通过算例来表明随流格式的优点。     

一类基于RBF插值的守恒重映算法

为保证重映过程的高守恒精度和单调性,并且在间断处具有极高的分辨率,基于径向基函数(RBF)插值方法构造了一类适用于任意网格的RBF守恒重映算法,通过计算守恒误差测试重映算法的守恒精度。将该方法用于光滑函数和含有间断的函数,并与其它守恒重映方法比较,表明该方法数值结果较好。     

平面应变问题广义有限元法

结合广义有限元和理性有限元,针对平面应变问题提出一种广义四边形单元.该单元考虑泊松效应,以节点位移自由度约束弹性力学平面应变方程的半解析解,构造单元位移模式的附加项,较准确地反映真实位移场,提高了单元的计算精度.首先推导广义单元及其等参单元的形函数,之后设计分片试验和数值算例来验证单元的精度,数值算例表明,在规则和非规则网格下新单元计算精度均优于传统有限元和广义有限元.新单元精度高且易于程序实现,可应用于实际工程的结构分析.     

三维笛卡儿坐标系中Lagrange流体力学的显式相容有限元方法(英文)

将Caramana等人提出的相容算法思想和有限元方法相结合,提出三维笛卡儿坐标系中Lagrange流体力学的显式相容有限元方法.采用三线性六面体单元和交错网格进行空间离散,利用质量集中进行显式求解,无需求解线性代数方程组.时间离散可采用两步显式Runge-Kutta格式.用边人工粘性消除激波振荡,用子网格扰动压力抑制网格的非物理变形.给出若干标准算例.数值算例表明,该方法具有较高的计算精度和计算效率,同时具有很好的对称性和总能量守恒性,总能量计算误差为计算机浮点计算截断误差.     

Two-step hybrid conservative remapping for multimaterial arbitrary Lagrangian–Eulerian methods

We present a new hybrid conservative remapping algorithm for multimaterial Arbitrary Lagrangian–Eulerian (ALE) methods. The hybrid remapping is performed in two steps. In the first step, only nodes of the grid that lie inside subdomains occupied by single materials are moved. At this stage, computationally cheap swept-region remapping is used. In the second step, nodes that are vertices of mixed cells (cells containing several materials) and vertices of some cells in a buffer zone around mixed cells are moved. At this stage, intersection-based remapping is used. The hybrid algorithm results in computational expense that lies between swept-region and intersection-based remapping We demonstrate the performance of our new method for both structured and unstructured polygonal grids in two dimensions, as well as for cell-centered and staggered discretizations.     

双曲守恒律系统的分段边界层函数方法(PBLM)

本文提出了一个新的高阶Godunov格式。此格式放弃了[9]、[10]中关于参数在格子中满足多项式分布近似及在格子边界上存在间断的假设,直接引入了一个分段边界层型函数分布假设。由于引入的分布函数是单调可微的,因此PBLM格式无需进行如同MUSCL、PPM等格式中的单调性校核。该格式由于不进行单调性修正,在PPM格式中需进行修正而精度降阶的点上仍保持原有精度。对一维激波管的计算表明PBLM格式对激波的展开比PPM格式还要小,计算时间相当。同PPM格式一样,PBLM格式在激波后存在有2%~4%的皮后伪振荡,应加上适当的人工粘性。     

Chirped fiber Bragg gratings with arbitrary group delay responses using stepped-stretching fiber method

We present the design and development of piece-wise stepped-chirp fiber Bragg gratings (FBGs) with arbitrary group delay responses using a uniform phase mask in a pre-stretched fiber. The method involves writing a series of sub-gratings on a pre-stretched fiber whose length is varied during the UV exposure process. Two motorized stages are employed to control the length of the pre-stretched fiber in order to adjust the grating pitch at each writing step to achieve piece-wise stepped chirping of the FBG. To demonstrate the effectiveness of the method to produce chirped FBGs with arbitrary group delay responses, a linear-chirp FBG and a quadratic-chirp FBG were fabricated, and their measured performances agree well with analytical predictions. PACS 42.81.-i; 42.79.Dj; 42.79.Ci     

Second-order sign-preserving conservative interpolation (remapping) on general grids

An accurate conservative interpolation (remapping) algorithm is an essential component of most arbitrary Lagrangian–Eulerian (ALE) methods. In this paper we describe a local remapping algorithm for a positive scalar function. This algorithm is second-order accurate, conservative, and sign preserving. The algorithm is based on estimating the mass exchanged between cells at their common interface, and so is equally applicable to structured and unstructured grids. We construct the algorithm in a series of steps, clearly delineating the assumptions and errors made at each step. We validate our theory with a suite of numerical examples, analyzing the results from the viewpoint of accuracy and order of convergence.     

ENO守恒插值(重映)方法及其在流体计算中的应用

在ENO(Essentially Non-oscillatory)守恒插值方法的基础上,分析和研究现今流体力学计算中涉及的几类网格技术:重叠网格技术、自适应加密技术和运动网格技术.基于ENO插值多项式构造的重映方法具有良好的守恒性,可以有效保证数据传递中物理量的总体守恒.提出该类守恒插值方法在以上几种网格技术中的一些应用前景,并给出一些数值算例.     

A high order cell-centered semi-Lagrangian scheme for multi-dimensional kinetic simulations of neutral gas flows

The term ‘Convected Scheme’ (CS) refers to a family of algorithms, most usually applied to the solution of Boltzmann’s equation, which uses a method of characteristics in an integral form to project an initial cell forward to a group of final cells. As such the CS is a ‘forward-trajectory’ semi-Lagrangian scheme. For multi-dimensional simulations of neutral gas flows, the cell-centered version of this semi-Lagrangian (CCSL) scheme has advantages over other options due to its implementation simplicity, low memory requirements, and easier treatment of boundary conditions. The main drawback of the CCSL-CS to date has been its high numerical diffusion in physical space, because of the 2nd order remapping that takes place at the end of each time step. By means of a modified equation analysis, it is shown that a high order estimate of the remapping error can be obtained a priori, and a small correction to the final position of the cells can be applied upon remapping, in order to achieve full compensation of this error. The resulting scheme is 4th order accurate in space while retaining the desirable properties of the CS: it is conservative and positivity-preserving, and the overall algorithm complexity is not appreciably increased. Two monotone (i.e. non-oscillating) versions of the fourth order CCSL-CS are also presented: one uses a common flux-limiter approach; the other uses a non-polynomial reconstruction to evaluate the derivatives of the density function. The method is illustrated in simple one- and two-dimensional examples, and a fully 3D solution of the Boltzmann equation describing expansion of a gas into vacuum through a cylindrical tube.     

A new symmetrized solution for phase retrieval using the transport of intensity equation

We propose a novel symmetrization method for solving the transport of intensity equation (TIE) using fast Fourier transforms for situations where the input images may or may not exhibit spatial periodicity. The method is derived from the analysis of intensity conservation law and the internal symmetry of the TIE, and is illustrated for both a computational and an experimental data set.