NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION(III)──LARGE DEFLECTION AND POSTBUCKLING OF SHALLOW SHELLS

Exactsolutionsoflargedeflectionandpostbucklingofrectangularplatesaredifficultproblems.Usually,appropriateseriesofsolutionsbasedonspecificboundaryareassumedtosolvetheproblems['].LiuandChengl'lsolvedthenonlinearbendingproblemofsimplysuPPortedrectangularsand…     

A mixed finite element method for a shallow shell problem with a stress function

In this paper we consider the problem of a deflected mode of a shallow shell. The stress function and the normal component of the displacement of the median surface of the shell are unknown functions. We propose a mixed variational statement of the problem, where the second derivatives of the stress function and the normal component of the displacement of the median surface are additional unknowns. This enables us to construct the finite element approximation of the initial problem. We prove the existence of a unique solution of the approximating problem and estimate the rate of convergence of the discrete solution.     

Hugoniót--Maslov Conditions for Vortex Singular Solutions of the Shallow Water Equations

For the phase of vortex singular solutions of the shallow water equations we justify the Hamilton--Jacobi equation corresponding to the hydrodynamical mode of perturbation propagation. We also obtain the next correction to the Cauchy--Riemann conditions describing how the singular part of the solution affects the smooth background.     

Diagonally implicit Runge–Kutta methods for 3D shallow water applications

We construct A‐stable and L‐stable diagonally implicit Runge–Kutta methods of which the diagonal vector in the Butcher matrix has a minimal maximum norm. If the implicit Runge–Kutta relations are iteratively solved by means of the approximately factorized Newton process, then such iterated Runge–Kutta methods are suitable methods for integrating shallow water problems in the sense that the stability boundary is relatively large and that the usually quite fine vertical resolution of the discretized spatial domain is not involved in the stability condition. This revised version was published online in June 2006 with corrections to the Cover Date.     

传输式大功率电火花震源在浅水中及井中的压力波形及频谱分析

本文通过对传输式电火花震源在浅水中及井中所产生压力波形的分析,确定了压力波峰值与放电电极距离的关系,获得了压力波与放电能量、静水压、测量距离 之间的基本关系。并对试验结果进行了分析。     

地下水水质评价中相关性分析方法的应用

在对四川省红层丘陵区浅层地下水水质评价的基础上,应用SPSS和Excel以及Surfer 3种方法分析了样品中的元素含量和进行了相关性分析。结果表明,SPSS和Surfer 8.0联用,能较好地阐明污染物的相关性和元素分布的特征,更直观地作出宜宾市屏山县浅层地下水水质现状评价。     

利用水平阵模态域波束形成判别声源深度*

针对近水面声源和水下声源的深度判别问题,根据近水面声源难以激发低阶模态的物理现象,研究利用声源波数谱结构和波数位置的不同来分辨近水面声源和水下声源。通过采用MVDR的谱估计方法进行模态域波束形成,补偿水平阵各阵元之间各号简正波的相位差,获得主瓣窄、旁瓣低的声源信号波数谱。波数谱的波数位置与频率呈近似线性关系,水中声速剖面、海底参数、海深都会影响波数谱的具体结构和位置。此外,声源信号的到达角估计误差同样也会影响波数谱主瓣的位置估计。数值仿真结果表明,在浅海负跃层声速剖面条件下,可利用水平阵模态域波束形成判别声源深度,区分近水面声源和水下声源。     

A high‐order PIC method for advection‐dominated flow with application to shallow water waves

A hybrid Eulerian‐Lagrangian particle‐in‐cell–type numerical method is developed for the solution of advection‐dominated flow problems. Particular attention is given over to the high‐order transfer of flow properties from the particles to the grid. For smooth flows, the method presented is of formal high‐order accuracy in space. The method is applied to solve the nonlinear shallow water equations resulting in a new, and novel, shock capturing shallow water solver. The approach is able to simulate complex shallow water flows, which can contain an arbitrary number of discontinuities. Both trivial and nontrivial bottom topography is considered, and it is shown that the new scheme is inherently well balanced, exactly satisfying the ‐property. The scheme is verified against several one‐dimensional benchmark shallow water problems. These include cases that involve transcritical flow regimes, shock waves, and nontrivial bathymetry. In all the test cases presented, very good results are obtained.     

Efficiency of randomised dynamic mode decomposition for reduced order modelling

ABSTRACT

The purpose of this paper is the identification of a reduced order model (ROM) from numerical code output by non-intrusive techniques (i.e. not requiring projecting of the governing equations onto the reduced basis modes). In this paper, we perform a comparison between two methods of model order reduction based on dynamic mode decomposition (DMD). The first method is a deterministic (classic) DMD technique endowed with a dynamic filtering criterion of selection of modes used in the ROM model. The second method is an adaptive randomised DMD algorithm (ARDMD) based on a randomised singular value decomposition. This produced an accelerating algorithm, which is endowed with a few additional advantages. In addition, the reduced order model is guaranteed to satisfy the boundary conditions of the full model, which is crucial for surrogate modelling. For numerical illustration, we use the shallow water equations model.