A Virtual Boundary Element Method for Three-Dimensional Inverse Heat Conduction Problems in Orthotropic Media

This paper aims to apply a virtual boundary element method(VBEM)to solve the inverse problems of three-dimensional heat conduction in orthotropic media.This method avoids the singular integrations in the conventional boundary element method,and can be treated as a potential approach for solving the inverse problems of the heat conduction owing to the boundary-only discretization and semi-analytical algorithm.When the VBEM is applied to the inverse problems,the numerical instability may occur if a virtual boundary is not properly chosen.The method encounters a highly illconditioned matrix for the larger distance between the physical boundary and the virtual boundary,and otherwise is hard to avoid the singularity of the source point.Thus,it must adopt an appropriate regularization method to deal with the ill-posed systems of inverse problems.In this study,the VBEM and different regularization techniques are combined to model the inverse problem of three-dimensional heat conduction in orthotropic media.The proper regularization techniques not only make the virtual boundary to be allocated freer,but also solve the ill-conditioned equation of the inverse problem.Numerical examples demonstrate that the proposed method is efficient,accurate and numerically stable for solving the inverse problems of three-dimensional heat conduction in orthotropic media.

An improved boundary element-free method (IBEFM) for two-dimensional potential problems

The interpolating moving least-squares （IMLS） method is discussed first in this paper. And the formulae of the IMLS method obtained by Lancaster are revised. Then on the basis of the boundary element-free method （BEFM）, combining the boundary integral equation （BIE） method with the IMLS method, the improved boundary element-free method （IBEFM） for two-dimensional potential problems is presented, and the corresponding formulae of the IBEFM are obtained. In the BEFM, boundary conditions are applied directly, but the shape function in the MLS does not satisfy the property of the Kronecker ~ function. This is a problem of the BEFM, and must be solved theoretically. In the IMLS method, when the shape function satisfies the property of the Kronecker 5 function, then the boundary conditions, in the meshless method based on the IMLS method, can be applied directly. Then the IBEFM, based on the IMLS method, is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied directly and easily, thus it gives a greater computational precision. Some numerical examples are presented to demonstrate the method.

Two-Dimensional Simulation of the Navier-Stokes Equations for Laminar and Turbulent Flow around a Heated Square Cylinder with Forced Convection

Few studies jointly investigate thermal and turbulent effects. In general, these subjects are treated separately. The purpose of this paper is to use the Immersed Boundary Method (IBM) coupled with the Virtual Physical Model (VPM) to investigate incompressible two-dimensional Newtonian flow around a heated square cylinder at constant temperature on its surface with forced convection and turbulence. The VPM model dynamically evaluates the force that the fluid exerts on the immersed surface and the thermal exchange between both in the Reynolds numbers (Re) window 40 ≤ Re ≤ 5×103 . For simulations of turbulence the Smagorinsky and Spalart-Allmaras models are used. The first model uses the Large Eddy Simulation (LES) methodology and is based on the local equilibrium hypothesis for small scales associated with the Boussinesq hypothesis, such that the energy injected into the spectrum of the turbulence balances the energy dissipated by convective effects. The second model uses the concept Unsteady Reynolds Averaged Navier-Stokes Equations (URANS), with only one transport equation for turbulent viscosity, being calibrated in pressure gradient layers. The goal of this work is to analyse the combination of the heat-transfer phenomena with the turbulence for the thermo-fluid-structure interaction in a square cylinder. For this, it was developed a C/C++ code that requires low computational costs in regards to memory and computer facilities. It is observed that, with the increase of the Reynolds number, an increase of the drag coefficient occurs, as well as reinforces the influence of the pressure distribution downstream of the cylinder, which is strongly influenced by the formation and detachment of vortices on the upper and lower sides of the square cylinder.

The Calculation of Stress-Strain State of Anisotropic Composite Finite-Element Area with Different Boundary Conditions on the Surface

The numerical analytic research approach of stress-strain state of anisotropic composite finite element area with different boundary conditions on the surface, is represented below. The problem is solved by using a spatial model of the elasticity theory. Differential equation system in partial derivatives reduces to one-dimensional problem using spline collocation method in two coordinate directions. Boundary problem for the system of ordinary higher-order differential equation is solved by using the stable numerical technique of discrete orthogonalization.

Electric Field Evaluation for Slender Conductors Using Collocation Boundary Element Method

Evaluation of the electric field at the surface of a conductor,which is well described by the Poisson equation,is of great importance on many occasions in power systems.This paper proposes a collocation boundary element method where the unknown surface charge density function is assumed to be either azimuth independent or dependent.Detailed formulas,including the quadrature rules and how to accelerate the computation when the target point lies far away from the integral element,are proposed.Numerical examples are shown to confirm the convergence of the method,and manifest the great advantage for the evaluation of the electric field around slender conductors.

基于真实细观形貌的固体推进剂力学性能虚单元预示方法

真实的细观形貌是进行固体推进剂细观力学性能预示的基础。通过CT扫描图片处理获得了固体推进剂真实的细观几何形貌及各组分参数,并生成了固体推进剂颗粒填充模型;采用多边形网格剖分方案,减少使用常规单元时各组分颗粒尺度差异带来的低质量网格影响;通过对单元和节点的后处理,设计了应对真实细观形貌的周期边界条件处理方案;引入虚单元法(VEM)开展固体推进剂细观力学性能预示,设计含夹杂算例,验证了VEM以及周期边界条件处理方案的可行性和准确性;利用内聚力单元模拟基体与颗粒间的“脱湿”效应,对真实细观模型以及颗粒填充模型开展了等效松弛模量测试。仿真结果表明,真实细观模型中不规则的颗粒几何形状会抑制“脱湿”现象的发生,其表现出的等效松弛模量较颗粒填充模型大。此外,两类模型预示的松弛模量最大相对误差为13.1%,这表明在固体推进剂配方设计中颗粒填充模型可以替代真实的几何模型进行固体推进剂等效力学性能的预示。结合VEM在应对固体推进剂各组分几何尺度差异以及周期性边界条件设计方面的优势,可进一步利用VEM开展三维固体推进剂力学性能的预示。

基于数据驱动的浅海波导声辐射预测方法

结合计算力学和深度学习理论,提出一种基于数据驱动的浅海波导声辐射预测方法。通过集成有限元法—虚质量法—基于虚源法的边界元法的计算框架,获取浅海波导声辐射响应,为深度学习提供大量声压数据;进而,通过训练ConvNeXt卷积神经网络提取采样点声场特征;最终实现浅海水下结构辐射声压级的快速预测,并通过算例表明预测方法的有效性。

Virtual design and performance prediction of a silencing air cleaner used in an I.C.engine intake system

This paper reports results of the authors’ studies on the virtual design method used in the development of low noise intake system of I.C. engine. The resulting high pass-by noise at level above the legislative target at full throttle when engine speed was around 5200 r/min necessitated a BEM-aided redesign task, following the typical process of design and development of an intake system. During the initial design, based on the acoustic theory and the requirements (1. The air flux of the redesigned should equal to or exceed the value of the original flux; 2. The filtering area must not be degraded), and considering the constraint of space in the engine compartment, total volume and rough internal dimensions were determined. During the detailed design, the exact internal dimensions of the air cleaner were determined, and an effective method was applied to improve the acoustic performance at low frequency. The predicted sound power of the intake system indicated that the objective of reducing the overall engine noise by minimizing intake system noise was achieved.

Nondestructive testing method of wood moisture content based on a planar capacitance sensor model

For our research, a new hybrid experimental-computational method is presented. We applied a least squares fitting method （LSFM） to reconstruct the wood moisture content （WMC） from the data measured with a planar capacitance sensor. A boundary element method （BEM） was used to compute the relationship between capacitance and the dielectric constant. A functional relationship between MC and the dielectric constant was identified by LSFM. The agreement of this final computation result with the experimental data indicates that this method can be used to estimate the WMC quickly and effectively with engineering analysis. Compared with popular statistical methods, a large number of experiments are avoided, some costs of testing are reduced and the efficiency of testing is enhanced.

Boundary element-free method for elastodynamics

The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.

An interpolating boundary element-free method (IBEFM) for elasticity problems

The paper begins by discussing the interpolating moving least-squares (IMLS) method. Then the formulae of the IMLS method obtained by Lancaster are revised. On the basis of the boundary element-free method (BEFM), combining the boundary integral equation method with the IMLS method improved in this paper, the interpolating boundary element-free method (IBEFM) for two-dimensional elasticity problems is presented, and the corresponding formulae of the IBEFM for two-dimensional elasticity problems are obtained. In the IMLS method in this paper, the shape function satisfies the property of Kronecker δ function, and then in the IBEFM the boundary conditions can be applied directly and easily. The IBEFM is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution to the nodal variables. Thus it gives a greater computational precision. Numerical examples are presented to demonstrate the method.

数理方程的虚边界元法及其与相关方法的关系

自1984年至今国内外在数理方程的数值解法中先后出现了叠加法、域外奇点法、虚边界元法和边界点（全特解场）法．这些方法之间虽然名称各异，但其理论基础是相同的．例如叠加法、域外奇点法、虚边界元一配点法和边界点法就是这样．阐明了虚边界元与其余方法的差异，并给出数值例题，表明了其优异的效果；另外证明上述四种方法理论基础是完全相同的，以便取得同行们的共识．

虚边界元最小二乘配点法

本方法是在虚边界上进行数值积分，在实边界上有限个点处满足给定问题边界条件的一种数值算法。在虚边界上积分是为了能寻求到使原问题得到正确解的较好的分布虚体力；在实边界上配点，是依据加权残数法中超额配点，即最小二乘配点法的思想。文中给出了本文方法的基本思想，并给出了壳体的算例。

厚壳三维分析的虚边界元最小二乘法

给出虚边界元最小二乘法的基本思想，并计算了厚壳问题．与边界元直接法相比，避免了奇异积分的数值处理，且系数阵是对称的；程序实现较容易，节省近一半机子内存．由数值算例表明，计算精度是令人满意的．该思想同样适于求解各类数学物理和工程技术问题。

复变量移动最小二乘法及其应用

提出了复变量移动最小二乘法,并详细讨论了基于正交基函数的复变量移动最小二乘法.然后,将复变量移动最小二乘法和弹性力学的边界无单元法结合,提出了弹性力学的复变量边界无单元法,推导了相应的公式,并给出了数值算例.基于正交基函数的复变量移动最小二乘法的优点是不形成病态方程组、精度高,所形成的无网格方法计算量小.复变量边界无单元法是边界积分方程的无网格方法的直接列式法,容易引入边界条件,且具有更高的精度.

无单元法及其在岩土工程中的应用

无单元法可以求解复杂边界条件的边值问题，它只需结点信息而不需单元信息，故信息简单，特别适用于岩土工程数值分析。它的理论基础是滑动最小二乘法。本文对无单元法的基本理论作了阐述，并用算例说明了它的广泛应用前景。

无单元法及其工程应用

无单元法可以求解复杂边界条件的边值问题，它只需结点信息而不需单元信息，故信息简单，特别适用于岩土工程数值分析．它的理论基础是滑动最小二乘法．本文对无单元法的基本理论作了研究，并用算例说明了研究成果．

板弯曲问题三维虚边界元分析

本文抛弃以往解板弯曲问题的假设，直接从三维弹性力学微分方程出发，依据三维弹性力学问题的Kelvin解，应用最小二乘法建立了三维虚边界元法解板弯曲问题的一般方法。文中给出了具有各种约束的矩形板的数值算例，以作为本方法的应用。本文方法与边界元直接法相比，优点在于无需处理奇异积分，且系数阵是对称的：再者，本文方法思想简单，且程序实现容易，易于被工程界接受。

弹性力学问题的虚边界元-配点法

本文提出虚边界方法,建立了离散化虚边界元-配点法,给出了离散化求系数的积分解析式。本文方法完全避免了边界奇异积分及其复杂耗时的运算,成功地提高了普通边界元法(以下简称边界元法)中边界附近区域内包括边界上解的精度,保留了边界元法的优点并扬弃了其弱点。边界元间接法是本文方法中的一个特例。数值算例表明,程序可靠,节省机时,计算精度较高。

并行求解含有电位悬浮导体的静电场数值问题

并行计算是电磁场数值模拟的主要工具,但是对于含有悬浮电位导体的静电场问题的并行模拟却很少提及。该文提供了一种针对这类问题的区域分解方法,并利用强加齐次边界条件法对有限元矩阵进行处理,进而利用并行机群系统求解含有多个电位悬浮导体的计算模型。通过对含有3个悬浮电位导体的平行板电容器模型和330 kV架空输电线路的玻璃绝缘子串场计算模型的并行模拟,验证了该方法在二维和三维静电场问题中的有效性。该文提出的方法能够很好的解决因悬浮导体存在而带来的并行处理中的模型分区困难,并且可以很好的并行求解多导体问题,对该类问题的并行计算提供了可能。