A Positivity-Preserving Well-Balanced Central Discontinuous Galerkin Method for the Nonlinear Shallow Water Equations

In this paper, we consider the development of central discontinuous Galerkin methods for solving the nonlinear shallow water equations over variable bottom topography in one and two dimensions. A reliable numerical scheme for these equations should preserve still-water stationary solutions and maintain the non-negativity of the water depth. We propose a high-order technique which exactly balances the flux gradients and source terms in the still-water stationary case by adding correction terms to the base scheme, meanwhile ensures the non-negativity of the water depth by using special approximations to the bottom together with a positivity-preserving limiter. Numerical tests are presented to illustrate the accuracy and validity of the proposed schemes.     

Hydrodynamic Instabilities in Well-Balanced Finite Volume Schemes for Frictional Shallow Water Equations. The Kinematic Wave Case

We report the developments of hydrodynamic instabilities in several well-balanced finite volume schemes that are observed during the computation of the temporal evolution of an out-balance flow which is essentially a kinematic wave. The numerical simulations are based on the one-dimensional shallow-water equations for a uniformly sloping bed with hydraulic resistance. Subsequently, we highlight the need of low dissipative high-order well-balanced filter schemes for non-equilibrium flows with variable cut-off wavenumber to compute the out-balance flow under consideration, i.e. the kinematic wave.     

Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on Unstructured Triangular Meshes

The shallow water equations model flows in rivers and coastal areas and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. In “Xing et al. Adv. Water Resourc. 33: 1476–1493, 2010)”, the authors constructed high order discontinuous Galerkin methods for the shallow water equations which can maintain the still water steady state exactly, and at the same time can preserve the non-negativity of the water height without loss of mass conservation. In this paper, we explore the extension of these methods on unstructured triangular meshes. The simple positivity-preserving limiter is reformulated, and we prove that the resulting scheme guarantees the positivity of the water depth. Extensive numerical examples are provided to verify the positivity-preserving property, well-balanced property, high-order accuracy, and good resolution for smooth and discontinuous solutions.     

A Well-Balanced Reconstruction of Wet/Dry Fronts for the Shallow Water Equations

In this paper, we construct a well-balanced, positivity preserving finite volume scheme for the shallow water equations based on a continuous, piecewise linear discretization of the bottom topography. The main new technique is a special reconstruction of the flow variables in wet–dry cells, which is presented in this paper for the one dimensional case. We realize the new reconstruction in the framework of the second-order semi-discrete central-upwind scheme from (Kurganov and Petrova, Commun. Math. Sci., 5(1):133–160, 2007). The positivity of the computed water height is ensured following (Bollermann et al., Commun. Comput. Phys., 10:371–404, 2011): The outgoing fluxes are limited in case of draining cells.     

Hybrid Well-balanced WENO Schemes with Different Indicators for Shallow Water Equations

In (J. Comput. Phys. 229: 8105–8129, 2010), Li and Qiu investigated the hybrid weighted essentially non-oscillatory (WENO) schemes with different indicators for Euler equations of gas dynamics. In this continuation paper, we extend the method to solve the one- and two-dimensional shallow water equations with source term due to the non-flat bottom topography, with a goal of obtaining the same advantages of the schemes for the Euler equations, such as the saving computational cost, essentially non-oscillatory property for general solution with discontinuities, and the sharp shock transition. Extensive simulations in one- and two-dimensions are provided to illustrate the behavior of this procedure.     

High-Order Well-Balanced Finite Difference WENO Schemes for a Class of Hyperbolic Systems with Source Terms

In this paper, we generalize the high order well-balanced finite difference weighted essentially non-oscillatory (WENO) scheme, designed earlier by us in Xing and Shu (2005, J. Comput. phys. 208, 206–227) for the shallow water equations, to solve a wider class of hyperbolic systems with separable source terms including the elastic wave equation, the hyperbolic model for a chemosensitive movement, the nozzle flow and a two phase flow model. Properties of the scheme for the shallow water equations (Xing and Shu 2005, J. Comput. phys. 208, 206–227), such as the exact preservation of the balance laws for certain steady state solutions, the non-oscillatory property for general solutions with discontinuities, and the genuine high order accuracy in smooth regions, are maintained for the scheme when applied to this general class of hyperbolic systems     

几种复合型数值方法的算法模拟与性能比较

浅水波问题的数值模拟一直是计算数学、计算流体力学的研究热点之一,采用低阶方法和高阶方法相复合的数值方法引起了人们的注意,并在水力学的数值模拟中取得了很大的成功.文中对三种复合型的数值方法,即Lax-Wendroff(LW)格式与Lax-Friedrichs(LF)格式的复合算法,Upwind格式与Lax-Wendroff(LW) 格式的复合算法,WENO格式与LW格式的复合算法,进行了分析比较和改进,并就计算流体力学中的一维浅水波方程的两个算例分别做了数值对比试验,在解的光滑性、锐利性,计算速度等几个方面做了比较,模拟结果表明三种方法均能准确捕捉激波又不产生非物理震荡.     

几种复合型数值方法的算法模拟与性能比较

浅水波问题的数值模拟一直是计算数学、计算流体力学的研究热点之一,采用低阶方法和高阶方法相复合的数值方法引起了人们的注意,并在水力学的数值模拟中取得了很大的成功。文中对三种复合型的数值方法,即Lax-Wendroff(LW)格式与Lax-Friedrichs(LF)格式的复合算法,Upwind格式与Lax-Wendroff(LW)格式的复合算法,WENO格式与LW格式的复合算法,进行了分析比较和改进,并就计算流体力学中的一维浅水波方程的两个算例分别做了数值对比试验,在解的光滑性、锐利性,计算速度等几个方面做了比较,模拟结果表明三种方法均能准确捕捉激波又不产生非物理震荡。     

Simulations of Shallow Water Equations with Finite Difference Lax-Wendroff Weighted Essentially Non-oscillatory Schemes

In this paper we study a Lax-Wendroff-type time discretization procedure for the finite difference weighted essentially non-oscillatory (WENO) schemes to solve one-dimensional and two-dimensional shallow water equations with source terms. In order to maintain genuinely high order accuracy and suit to problems with a rapidly varying bottom topography we use WENO reconstruction not only to the flux but also to the source terms of algebraical modified shallow water equations. Extensive simulations are performed, as a result, the WENO schemes with Lax-Wendroff-type time discretization can maintain nonoscillatory properties and more cost effective than that with Runge-Kutta time discretization.     

An Energy-Stable High-Order Central Difference Scheme for the Two-Dimensional Shallow Water Equations

An energy-stable high-order central finite difference scheme is derived for the two-dimensional shallow water equations. The scheme is mathematically formulated using the semi-discrete energy method for initial boundary value problems described in Olsson (1995, Math. Comput. 64, 1035–1065): after symmetrizing the equations via a change to entropy variables, the flux derivatives are entropy-split enabling the formulation of a semi-discrete energy estimate. We show experimentally that the entropy-splitting improves the stability properties of the fully discretized equations. Thus, the dependence on numerical dissipation to keep the scheme stable for long term time integrations is reduced relative to the original unsplit form, thereby decreasing non-physical damping of solutions. The numerical dissipation term used with the entropy-split equations is in a form which preserves the semi-discrete energy estimate. A random one-dimensional dam break calculation is performed showing that the shock speed is computed correctly for this particular case, however it is an open question whether the correct shock speed will be computed in generalMSC: 35Q35; 65M12; 65M06Supported in part by the New Zealand Marsden Fund, grant UOA827     

中央空调恒温系统解决方案

本文主要介绍台达机电产品在中央空调恒温系统上的整体解决方案。该系统通过将冰水阀门的开度控制纳入控制架构中以适时地调节冰水的流量,同时结合温控器上的PID参数设置,对电动机转速及冰水阀的开度进行适当配合,以实现恒温控制的目的。运行实践证明,台达产品运行安全稳定,性价比高,值得业界推广。     

基于单片机的恒定水位控制系统

针对供水、造纸等行业中的恒定水位系统,提出恒定水位控制的控制方案.在分析电机机械特性的基础上,完成了控制系统结构设计,给出了系统中每一部分的传递函数.采用PID调节器作为转速调节器,实现了数字PID调节器的单片机程序,采用归一参数整定法完成了PID参数整定.实验证明,该水位控制系统能够完成恒水位控制,具有成本低,结构简单等优点.     

捏合机恒温供水系统的研究

本文分析了捏合机生产过程的特殊性，并结合温度控制要求，提出一种恒温供水系统解决方案。在该方案中，恒温供水系统用一个控制水箱对捏合锅夹套进行水循环，达到控制被混合物料反应温度的目的。实施结果表明：恒温供水系统可以简化结构，降低故障发生率，并取得良好的温度控制效果，     

基于PLC变频恒压供水系统设计

研究的是由可编程控制器(PLC)、压力传感器、变频器共同构成了闭环变频恒压供水系统。介绍了基于汇川PLC以及变频器在恒压供水系统中的硬件配置及软件设计。该系统具有节能环保、简单实用、可靠性好、便于维护等特点。     

PLC控制变频调速恒压供水系统

介绍采用PLC进行逻辑控制,用变频器进行压力调节,自动控制水泵投入的台数和电机转速,在保持恒压状况下,达到控制流量的目的。     

基于背景差的实时行人检测和记数的图像系统

提出了一种新的用于行人检测的背景模型建模方法。为了提高系统的运行速度,采用了多线程的程序设计方法。该系统能够实时地检测出复杂背景中行人的数目,并且能够把包含行人的图像记录下来,具有视频回放功能。实验结果表明,该系统具有良好的实时性,并能够快速地适应环境的改变。     

Sonardyne浅水声学定位系统概述

水下声学定位系统是目前应用效果最好的海底检波器定位技术,已成为海上勘探的标配设备.Sonardyne浅水声学定位系统(TZ/OBC)由英国Sonardyne公司生产,用来测定地震电缆、水听器或其他在海底的目标物体的位置.本文概括地介绍了相关领域的现状,详细说明了该套系统的工作原理、系统组成、性能指标及实际操作,并系统地分析了该系统的技术优势及应用前景,为相关领域的应用与研究提供重要参考.     

自来水加压泵站自动恒压供水系统

本文以某自来水加压站为例,介绍了一种可编程控制器恒压供水监控系统的原理、结构、特点以及其在实际中的应用。