基于边界分析的重载轮胎滚动过程接地角和印记非对称性分析与验证

基于解析弹性基础的柔性胎体模型,并考虑胎体圆环的径向变形与切向变形之间的耦合关系,为重载大扁平比轮胎建立了柔性环二维轮胎低频动力学模型。采用接地边界求解方法探究了轮胎的接地滚动过程中的接地角和接地印记的非对称特性,并进行了轮胎接地刚度和接地印记非线性实验验证。结果表明:采用接地边界求解可准确计算接地角和接地印记;基于胎内应变传感器的接地印记估计方法可间接测量轮胎滚动过程中的接地印记。

基于有限差分法研究和模拟空气污染

有限差分法是用来解决平面连续问题的有限元法。主要讨论有限差分法的理论及方法,以及有限差分法在流体动力学中的应用。通过分析势流场方程和流体扩散方程,使用差分法进行离散化并给出一定的边界条件进行数值分析。在空气污染中,烟雾扩散是典型的平面连续问题,这里将采用有限差分法来分析模拟烟雾的扩散。

软开关变换电路精细离散映射建模方法研究

针对软开关变换电路系统的快尺度动力学行为分析,通过引入精细时间尺度概念,提出了精细离散映射模型的构建方法,分析了该离散映射模型在跨边界映射时误差产生的机理。针对边界条件的求解,在跨边界映射中引入了一种修正映射,并重点解决在修正映射中边界点的准确计算以及零时间映射的构建问题。通过在离散模型的映射序列嵌入该修正映射,能很好地解决边界条件求解时的误差产生问题,同时又不会显著增加模型计算工作量。

Numerical Simulation of the Flow around Two-dimensional Partially Cavitating Hydrofoils

In the present study, a new approach is applied to the cavity prediction for two-dimensional （2D） hydrofoils by the potential based boundary element method （BEM）. The boundary element method is treated with the source and doublet distributions on the panel surface and cavity surface by usethe of the Dirichlet type boundary conditions. An iterative solution approach is used to determine the cavity shape on partially cavitating hydrofoils. In the case of a specified cavitation number and cavity length, the iterative solution method proceeds by addition or subtraction of a displacement thickness on the cavity surface of the hydrofoil. The appropriate cavity shape is obtained by the dynamic boundary condition of the cavity surface and the kinematic boundary condition of the whole foil surface including the cavity. For a given cavitation number the cavity length of the 2D hydrofoil is determined according to the minimum error criterion among different cavity lengths, which satisfies the dynamic boundary condition on the cavity surface. The NACA 16006, NACA 16012 and NACA 16015 hydrofoil sections are investigated for two angles of attack. The results are compared with other potential based boundary element codes, the PCPAN and a commercial CFD code （FLUENT）. Consequently, it has been shown that the results obtained from the two dimensional approach are consistent with those obtained from the others.

Boundary Element Method with Non-overlapping Domain Decomposition for Diffusion Equation

A boundary element method based on non-overlapping domain decomposition method to solve the time-dependent diffusion equations is presented. The time-dependent fundamental solution is used in the formulation of boundary integrals and the time integration process always restarts from the initial time condition. The process of replacing the interface values, which needs a summation of boundary integrals related to the boundary values at previous time steps can be treated in parallel iterative procedure. Numerical experiments demonstrate that the implementation of the present algorithm is efficient.

Singular Hybrid Boundary Node Method for Solving Poisson Equation

As a boundary-type meshless method, the singular hybrid boundary node method（SHBNM） is based on the modified variational principle and the moving least square（MLS） approximation, so it has the advantages of both boundary element method（BEM） and meshless method. In this paper, the dual reciprocity method（DRM） is combined with SHBNM to solve Poisson equation in which the solution is divided into particular solution and general solution. The general solution is achieved by means of SHBNM, and the particular solution is approximated by using the radial basis function（RBF）. Only randomly distributed nodes on the bounding surface of the domain are required and it doesn＇t need extra equations to compute internal parameters in the domain. The postprocess is very simple. Numerical examples for the solution of Poisson equation show that high convergence rates and high accuracy with a small node number are achievable.

Heteroclinic Breather-Wave Solutions for Davey-Stewartson Equation

Exact heteroclinic breather-wave solutions for Davey-Stewartson （DSI, DSII） system with periodic boundary condition are constructed using Hirota＇s bilinear form method and generalized ansatz method. The heteroclinic structure of wave is investigated.

Solving Two-Dimensional Moving-Boundary Problems with Meshless and Level Set Method

During the past decade, increasing attention has been given to the development of meshless methods using radial basis functions for the numerical solution of Partial Differential Equations （PDEs）. A level set method is a promising design tool for tracking, modelling and simulating the motion of free boundaries in fluid mechanics, combustion, computer animation and image processing. In the conventional level set methods, the level set equation is solved to evolve the interface using a capturing Eulerian approach. The solving procedure requires an appropriate choice of the upwind schemes, reinitialization, etc. Our goal is to include Multiquadric Radial Basis Functions （MQ RBFs） into the level set method to construct a more efficient approach and stabilize the solution process with the adaptive greedy algorithm. This paper presents an alternative approach to the conventional level set methods for solving moving-boundary problems. The solution was compared to the solution calculated by the exact explicit lime integration scheme. The examples show that MQ RBFs and adaptive greedy algorithm is a very promising calculation scheme.

б-sharpen immersed boundary method(б-SIBM)—New method for solving the horizontal pressure-gradient force(PGF) problem of б-coordinate

Although G-coordinate is one of the most popular methods used in marine and estuarine modeling, it has long suffered from the so-called ＂steep boundary problem＂, namely, the PGF problem. In this paper, a new method called the ＂σ-sharpen immersed boundary method＂ （σ-SIBM） is put forward. In this method, the virtual flat bottom boundary is creatively introduced in regions with the steep boundary and is taken as the boundary of numerical domain. By this, OH/Ox of numerical domain changes to be a controllable value and the steep bottom problem is then transformed to the non-conforming boundary problem, which is, in turn, solved by the SIBM. The accuracy and efficiency of the σ-sharpen immersed boundary method （σ-SIBM） has been showed by both comparative theoretical analysis and classical numerical tests. First, it is shown that the σ-SIBM is more effective than the z-level method, in that σ-SIBM needs special treatment only in the steep section, but the z-level method needs the special treatment in each grid note. Second, it is superior to the p-method in that it is not restricted by the density distribution. This paper revisits the classical seamount numerical test used in numerous studies to prove the sigma errors of the pressure gradient force （PGFE） and their long-term effects on circulation. It can be seen that, as for the maximum erroneous velocity and kinetic energy, the value of σ-SIBM is much less than that of the z-level method and the traditional σ-method.

An alternating direction method of multipliers for elliptic equation constrained optimization problem

We propose an alternating direction method of multipliers(ADMM)for solving the state constrained optimization problems governed by elliptic equations.The unconstrained as well as box-constrained cases of the Dirichlet boundary control,Robin boundary control,and right-hand side control problems are considered here.These continuous optimization problems are transformed into discrete optimization problems by the finite element method discretization,then are solved by ADMM.The ADMM is an efficient first order algorithm with global convergence,which combines the decomposability of dual ascent with the superior convergence properties of the method of multipliers.We shall present exhaustive convergence analysis of ADMM for these different type optimization problems.The numerical experiments are performed to verify the efficiency of the method.

A full multigrid method for nonlinear eigenvalue problems

We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of the nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and nonlinear eigenvalue problems on the coarsest finite element space. The linearized boundary value problems are solved by some multigrid iterations.Besides the multigrid iteration, all other efficient iteration methods for solving boundary value problems can serve as the linear problem solver. We prove that the computational work of this new scheme is truly optimal,the same as solving the linear corresponding boundary value problem. In this case, this type of iteration scheme certainly improves the overfull efficiency of solving nonlinear eigenvalue problems. Some numerical experiments are presented to validate the efficiency of the new method.

Inner wall running state monitoring for the main pipe of nuclear power

The heat conduction equation is solved in this paper under specific boundary conditions.The coefficients of the obtained distribution equation are simplified with the piecewise integral method.Then the associated model for the cylindrical thermal equipment is established.The relationship of the surface temperatures,the material properties and the inner wall state of the cylindrical thermal equipment is described in the associated model.This model is applied to the inner wall running state monitoring of the main pipe.A multi-channel distributed optical fiber temperature measurement system is designed to acquire the external surface temperatures of the main pipe.Then the associated model can be used to analyze the surface temperature data of the main pipe.The location and the physical dimension of the inner wall defect can be got.Therefore,the inner wall defect monitoring of the main pipe can be realized.The feasibility of this method is verified by experiment.This method also provides a theoretical basis for the real-time monitoring of the main pipe’s internal state.

Error Estimates for Finite-Element Navier-Stokes Solvers without Standard Inf-Sup Conditions

The authors establish error estimates for recently developed finite-element methods for incompressible viscous flow in domains with no-slip boundary conditions.The methods arise by discretization of a well-posed extended Navier-Stokes dynamics for which pressure is determined from current velocity and force fields.The methods use C1 elements for velocity and C0 elements for pressure.A stability estimate is proved for a related finite-element projection method close to classical time-splitting methods of Orszag,Israeli,DeVille and Karniadakis.