Euler-Lagrange耦合计算的GEL方法

研究了一种Euler-Lagrange耦合数值方法ghost-fluid Euler-Lagrange(GEL)方法,编写了GEL二维计算程序。其中Euler流场计算采用以SCB格式编制的二阶计算程序,Lagrange域计算采用DEFEL二维动力有限元程序。通过一维黎曼问题的计算结果与高精度PPM方法进行的比较,以及二维移动边界cylinder lift-off problem的计算结果与文献的对比,验证了GEL方法和本文程序的正确性。     

二维流体力学有限差分和有限元程序的耦合计算

根据压力和法向速度连续准则,将Euler方法为基础的MFPPM（Piecewise-Parabolic Method）程序和Lagrange方法为基础的DEFEL（2-D Finite ElementsCode,二维流体弹塑性动力有限元）程序进行耦合,发展了基于levelset的GEL（Ghost—fluid Euler-Lagrange）方法。该方法在处理大变形流场与小变形结构以及复杂流动与多物体相互作用等问题具有优越性。通过二维算例的计算结果与文献比较,检验了GEL方法和耦合程序的正确性,并对水下爆炸形成的流场对多物体作用过程进行了数值模拟。     

二维流体力学计算中的人为热流方法

采用Ｗ．Ｆ．Ｎｏｈ提出的人为粘性和人为热流方法，构造了计算人为热流的二维差分格式。应用Ｌａｇｒａｎｇｅ型流体力学计算程序，计算了一种二维轴对称高速碰撞模型。计算结果表明，人为热流方法可以很好地消除人为粘性在碰撞界面处的误差。     

可压缩多介质粘性流体和湍流的大涡模拟

在可压缩多介质粘性流体动力学高精度计算方法MVPPM(multi-viscous-fluid piecewise parabolicmethod)基础上,引入Smagorinsky和Vreman亚格子湍流模型,采用大涡数值模拟方法求解可压缩粘性流体NS(Navier-Stokes)方程,给出适用于可压缩多介质流体界面不稳定性发展演化至湍流阶段的计算方法和二维计算程序MVFT(multi-viscosity-fluid and turbulence)。在2种亚格子湍流模型下计算了LANL(Los Ala-mos National Laboratory)激波管单气柱RM不稳定性实验,分析了气柱的形状、流场速度以及涡的特征,通过与LANL实验和计算结果的比较可知,Vreman模型略优于Smagorinsky模型,MVFT方法和计算程序可用于对界面不稳定性发展演化至湍流阶段的数值模拟。     

MGFM在强激波与物质界面作用中的应用

原始的虚拟流方法(GFM)在计算强激波和物质界面作用时无法得到正确的计算结果,而改进虚拟流方法(MGFM)处理这类问题的能力大大提高.本文用Level set捕获物质界面,用MGFM方法定义虚拟流节点参数,Euler方程采用HLLC格式离散求解,完成了强激波和物质界面作用的一维和二维数值实验.结果表明改进虚拟流方法在强激波与物质界面作用中的应用是成功的.     

界面不稳定性引起混合过程的二维数值计算

在可压缩多介质流体动力学高精度欧拉计算方法多介质流体分段抛物方法(multi-fluid piecewise parabolic method, MFPPM)基础上,运用算子分裂技术,增加二阶空间中心差方法和两步Rung-Kutta时间推进方法计算动力学黏性以及热流部分对流场的影响,发展适用于NS(Navier-Stokes)方程的可压缩多介质黏性流体计算方法多介质黏性流体分段抛物方法(multi-viscousity-fluid piecewise parabolic method, MVPPM). 文中采用MVPPM对英国AWE(atomic weapons establishment)激波管实验进行二维计算,给出了与实验图像基本一致的计算结果;应用MFPPM和MVPPM分别对二维柱对称内爆动力学界面不稳定性及其后期混合过程进行数值模拟,给出内外界面演化、速度历史以及后期中心气穴不同半径内因RT(Rayleigh-Taylor)界面不稳定性引起的混合量分布情况,从计算结果比较可见黏性对物质界面处混合量的分布影响明显.      

欧拉流体力学数值方法中的界面计算

本文所提算法适用于二维和三维多介质流体力学两步欧拉数值方法中输运计算的混合网格(包括自由面网格)界面处理。在一个混合网格中，界面被近似地看作直线(二维)或平面(三维)。整个方法分为三步：(1)第一步，用混合网格周围的八个网格的介质面积份额(二维)或二十六个网格的介质体积份额(三维)确定界面的法线方向；第二步，用混合网格的本身的介质面积份额(二维)或体积份额(三维)确定界面的方程(位置)；第三步，用此直线方程求出通过网格边界的流以及下一时刻网格的面积份额(二维)或体积份额(三维)。最后给出了用此方法所做的一些数值计算及与SLIC算法的比较。     

空气自由场中强爆炸冲击波传播二维数值模拟

编写了适用于模拟具有高密度比、高压力比的强激波问题的二维柱对称多介质流体计算程序。利用有限体积方法求解流体的Euler方程组,采用level set方法捕捉爆炸产物与空气的运动界面,并通过求解物质界面两侧Riemann问题的精确解来计算爆炸产物与空气之间的数值通量。研制了三角形网格自适应技术来实现网格的自动加密和粗化,在保证捕捉激波峰值的前提下有效地提高了计算效率。利用计算程序对1 kt TNT当量的空气自由场强爆炸问题进行数值模拟,计算得到的峰值超压、冲击波到达时间等物理参数与点爆炸理论结果基本一致。     

单模态Richtmyer-Meshkov不稳定性数值模拟

采用VOF(Volume of Fluid)方法和PPM(Piecewise Parabolic Method)方法,发展了可用于可压缩多介质粘性流体动力学问题的数值模拟方法MVPPM(Multi-Viscous-Fluid Piecewise Parabolic Method)。利用MVPPM对多个具有不同初始扰动振幅的二维和三维单模态RM(Richtmyer-Meshkov)不稳定性模型进行了数值计算,并与理论模型的计算结果进行了比较。结果表明,无论二维还是三维情况,当初始扰动振幅相对于波长较小的时候,计算的扰动振幅和增长率与理论模型的计算结果一致。当初始扰动波长不变而振幅逐渐增大时,界面振幅和增长率也逐渐增大。对于具有相同初始扰动的情况,三维计算结果在线性段与二维计算结果相同,但是在非线性段比二维结果大,说明非线性和三维效应在RM不稳定性发展过程中起着重要作用。     

真实虚拟流方法在多介质可压缩流动模拟中的应用

为了克服原始虚拟流方法(ghost fluid method,GFM)在处理激波与大密度比流体-流体（气-水）界面相互作用时遇到的困难,采用真实虚拟流法(real ghost fluid method,RGFM)处理流体界面附近的虚拟点,结合HLLC(Harten-Lax-Van Leer with contact discontinuities)格式求解Euler方程,采用五阶WENO(weighted essentially nonoscillatory)格式求解level set输运方程。通过一维和二维算例的物质界面捕捉研究,证明RGFM在处理小密度比界面问题时优于GFM,同时RGFM还可用于求解激波与大密度比物质界面相互作用问题。计算表明,将RGFM引入到本文算法中,可精确捕捉到激波与界面（气-气、气-水界面）相互作用的变化细节,包括大密度比界面的剧烈变形和破碎,并具有较高的计算分辨率。     

Modeling Three-Dimensional Groundwater Flows by the Body-Fitted Coordinate (BFC) Method: II. Free and Moving Boundary Problems

This paper presents a methodology and solution procedure of the time-dependent body-fitted coordinate (BFC) method for the analysis of transient, three-dimensional groundwater flow problems characterized by free and moving boundaries. The technique consists of numerical grid generation, time-dependent body-fitted coordinate transformation, and application of the finite difference method (FDM) to the transformed partial differential equations. Based on the time-dependent BFC method, a three-dimensional finite-difference computer code, BFC3DGW, was developed and used to solve two unconfined flow problems. The code was verified by comparing numerical results with analytical solutions for a steady-state seepage problem. In order to demonstrate capability of the method in dealing with flow problems with irregular and moving boundary surfaces, an unconfined well-flow problem was solved by the developed code. Difficulties associated with the free and moving irregular boundary have been successfully overcome by employing this method.     

基于知识图谱和GPT模型的可靠性代码自动生成方法

工程结构服役中广泛使用可靠性分析进行结构安全评估,但可靠性分析方法种类多、分析程序代码自动化程度低且复用难,需要研究可靠性代码自动生成方法。生成式预训练转换器GPT(Generative Pre-trained Transformer)模型已经在大量替代编程手工作业,进行代码自动生成。但是,其在工程领域中的应用受限于可学习数据量小和问题匹配度不高。本文提出了一种结合多种类可靠性知识图谱、基于GPT的代码自动完成模型进行Matlab可靠性代码预测的方法,使用精心设计的源代码预处理降噪策略,以及知识图谱传播模拟密集型任务解释意图;采用条件代码生成训练,有效提升了小数据样本量的学习性能,实现高准确率、问题匹配的可靠性代码自动生成。最后通过三个可靠性知识图谱案例验证了所提方法的有效性。     

Modeling Three-Dimensional Groundwater Flows by the Body-Fitted Coordinate (BFC) Method: I. Stationary Boundary Problems

Based on the body-fitted coordinate (BFC) method, a three-dimensional finite difference computer code, BFC3DGW, was developed to simulate groundwater flow problems. Methodology and solution procedures of the BFC method for simulating groundwater flows, particularly when the flow domain is stationary as in the case of confined aquifers, are described. The code was verified by comparing numerical results with analytical solutions for well-flow problems in an isosceles right-triangular aquifer. An example simulation is made to demonstrate capability of the code for solving flow problems in anisotropic aquifers where directions of anisotropy change continuously. The method differs from the conventional finite difference method (FDM) in the ability to use a flexible, nonorthogonal, and body-fitted grid. The main advantages of the method are the convenience of grid generation, the simplified implementation of boundary conditions, and the capability to construct a generalized computer code which can be consistently applied to problem domains of any shape.     

直接基于单元平衡的梁非线性分析方法

以单元力平衡条件为基础建立的梁单元在近年来受到广泛关注,与传统的以单元位移相容条件为基础建立的梁单元相比,基于平衡的梁单元可获得较高的精度。针对基于平衡的梁单元,给出了一种几何非线性分析方法,使用该方法进行几何非线性分析时不需进行单元内部位移场的构造,避免了使用现有位移场构造方法时可能引起的振荡问题,同时降低了有限元程...     

Exact Riemann Solution and Weighted Average Flux Method for Power-law Channel Section

The aim of this work is to extend the Weighted Averaged Flux (WAF) method by E.F. Toro from rectangular to generic regular cross sections, in order to represent the geometric effects of the cross-section on wave propagation along channels. Assuming a power-law variation of the channel width, the 1D conservative shallow water equations, their characteristic form and the shock propagation equations are presented. The exact Riemann solver is derived and is applied to the dam-break problem in valleys with different shape in order to test its efficiency and to check the accuracy order of solutions obtained by approximating the real cross-section with an equivalent rectangle. The WAF method is extended to a power-law channel section and is used to solve the 1D proposed equations taking into account all the source terms that are incorporated into the local Riemann problem. A code based on this method has been developed and results of numerical applications to a Venturi channel and to the attenuation of waves are presented, in order to verify, for well known situations, how accurately the source terms are represented. The code is applied to reproduce one of Brock's experiments (1969; 1970) on roll waves generation in a rectangular channel and results are compared with those obtained with a Godunov-type code developed at CEMAGREF, which is based on a Roe scheme with a later average evaluation of source terms.     

三维自适应FE-SPH耦合算法在多层间隔金属靶侵彻问题中的应用

鉴于有限元算法不能有效地模拟侵彻过程所产生的金属碎片, 本文中基于三维自适应FE-SPH耦合算法的基本理论, 自主开发了模拟多层间隔金属靶侵彻问题的三维FE-SPH耦合计算程序。该程序采用四面体单元对多层间隔金属靶侵彻模型进行初始离散, 计算过程中, 当四面体单元等效塑性应变超过某一设定值时, 单元自动转化为SPH粒子, 并引入有限单元-粒子接触算法和耦合算法, 实现大变形和破碎区域采用SPH方法计算, 克服有限元法单元畸变存在的问题。多层间隔靶侵彻算例分析表明, 三维FE-SPH耦合计算程序采用等效塑性应变作为转化判据计算结果较稳定, 并且能够有效地再现侵彻过程中所产生的碎片, 能够模拟侵彻碎片对后层靶的毁伤效应。     

An efficient method to solve the strongly coupled nonlinear differential equations of impact dampers

In this paper, ongoing studies to solve nonlinear differential equations are extended by combining the Newmark-beta integration method and the piecewise linearization approach. The discussed method is illustrated with a practical example. In doing so, the coupled nonlinear differential equations of an impact oscillator, which incorporates the Hertzian contact, are derived. To investigate this problem, an object-oriented computer code, based on the presented method, is written in MATLAB. Furthermore, the discussed problem is solved numerically using the Runge–Kutta commercial code. To verify the calculated results, the contact durations, which are obtained using the discussed methods, are compared with the previous analytical results. In this study, accuracy of solution and the process time (cost) are selected as two main parameters of the solution method. The so-called adequacy factor is presented to combine the two main parameters of solution. Finally, it is shown that in the case of Hertzian contact, the presented method can be more adequate than the Runge–Kutta method.     

Laboratory astrophysics and non-ideal equations of state: the next challenges for astrophysical MHD simulations

Laboratory astrophysics holds great promise not only as a highly effective validation tool for astrophysical magneto-hydrodynamics (MHD) codes but it also presents a unique challenge for these codes. The high-density plasmas found in these experiments are not well modeled by the ideal equations of state (EOS) found in most astrophysical simulation codes. To solve this problem, we replaced the ideal EOS scheme in an existing MHD code, AstroBEAR, with a non-ideal EOS method and validated our implementation with van der Waals shock tube tests. The improved code is also able to model flows that contain more than one material, as required in laboratory experiments. Simulations of jet experiments performed at the OMEGA Laser reproduce the morphology of the jet much better than when the code used a single material and an ideal EOS.     

The independent set perturbation adjoint method: A new method of differentiating mesh‐based fluids models

A new scheme for differentiating complex mesh‐based numerical models (e.g. finite element models), the Independent Set Perturbation Adjoint method (ISP‐Adjoint), is presented. Differentiation of the matrices and source terms making up the discrete forward model is realized by a graph coloring approach (forming independent sets of variables) combined with a perturbation method to obtain gradients in numerical discretizations. This information is then convolved with the ‘mathematical adjoint’, which uses the transpose matrix of the discrete forward model. The adjoint code is simple to implement even with complex governing equations, discretization methods and non‐linear parameterizations. Importantly, the adjoint code is independent of the implementation of the forward code. This greatly reduces the effort required to implement the adjoint model and maintain it as the forward model continues to be developed; as compared with more traditional approaches such as applying automatic differentiation tools. The approach can be readily extended to reduced‐order models. The method is applied to a one‐dimensional Burgers' equation problem, with a highly non‐linear high‐resolution discretization method, and to a two‐dimensional, non‐linear, reduced‐order model of an idealized ocean gyre. Copyright © 2010 John Wiley & Sons, Ltd.