一个改进的二阶Boussinesq方程模型在线性波浪反射问题中的适用性研究

基于改进型的二阶Boussinesq方程,在交错网络下建立数值模型.利用模型模拟波浪在常水深情况下的传播,波浪反射系数均低于2％.利用该模型模拟波浪在平斜坡前的反射,并将数值结果与解析解进行对比.结果表明,对于相对水深较大情况,坡度较陡时模拟结果明显偏大;对 于相对水深较小情况,坡度超过1:1时,数值结果仍与解析解有....     

三维轴对称驻点流系统的一些研究(英文)

为了研究Navier-Stokes方程相关的三维轴对称驻点流系统的解,给出了一个积分方程系统,扩展了它的用途.并通过研究该积分方程系统的性质,在更广的范围内,利用这个系统的解,得出了与Navier-Stokes方程相关的三维轴对称驻点流系统的相似解.同时还改进了一个相似解的不存在性结果.     

溃坝水流数值计算的非结构有限体积模型

针对溃坝洪水数值计算面临不规则边界和复杂地形等问题,建立了三角形网格下求解二维浅水方程的高精度Godunov型有限体积模型.空间上,引入变量重构和限制器技术,采用HLLC近似Riemann算子计算数值通量;时间上,采用Hancock预测-校正法.将底高程定义于单元顶点,结合单元水位～体积关系,提高了干湿界面处理能力.采...     

非粘性沙坝溃决数学模型及求解

考虑一维陡坡浅水方程与Exner方程耦合构建漫顶溃坝数学模型,利用Roe格式黎曼近似解法求解,并用预测-校正法处理源项保证水流、泥沙侵蚀输运和底床演变过程的计算稳定.模型实例计算结果表明,该方法能较好地计算非粘性模型沙坝漫顶溃决问题,可为溃坝数值计算提供新的思路.     

施密特望远镜CCD BVRI测光系统的初步研究

本文利用Thomson CCD,在北京天文台兴隆站施密特望远镜上进行BVRI四色测光,得到了该测光系统的颜色转换方程,并对所得结果进行了分析探讨。同时论证了BAO-CCD系统在施密特望远镜上用于测光的可行性。     

具有守恒特性的二维溃坝洪水演进数值模型

基于结构网格,采用有限体积法建立了二维水动力学模型,模拟溃坝洪水在复杂实际地形条件下的流动过程。该模型采用中心迎风格式求解界面通量,并结合对界面变量的线性重构,使其具有空间上的二阶精度。分别采用中心差分方法和半隐式方法对底床坡度项和摩擦阻力项进行离散,保证了模型的和谐性和稳定性。对于复杂地形条件下溃坝洪水的模拟,负水深的产生是影响模型稳定的关键因素。当库朗特数小于0.25时,模型能够保证任何时刻的计算水深都是非负的,而无需对负水深单元进行特殊处理。因此,相比于现有的大部分溃坝洪水模型,该模型具有更强的鲁棒性和稳定性。     

应用二阶完全非线性Boussinesq方程模拟破碎波浪

建立了基于高阶Boussinesq水波方程的一维波浪破碎数值模型。基于一组具有二阶完全非线性特征的Boussinesq水波方程,建立了交错网格下的高精度差分格式,推导了适用于该组方程的永形波解析解,其和松弛造波技术相结合实现了数值波浪水槽中(强)非线性波浪的无反射入射。通过模拟封闭容器内水体晃动问题对数值格式进行了验证,通过模拟孤立波在斜坡海岸上的浅化过程说明了将方程从弱非线性发展到完全非线性的必要性。采用涡粘方法处理波浪破碎,利用物理模型实验数据,分析了模型中各波浪破碎参数对数值结果的影响并对参数进行了率定。应用该模型对规则波在斜坡海岸上的传播、变浅以及破碎过程进行了数值模拟研究,数值结果同实验数据吻合良好,验证了模型的有效性。     

The evolution of sub-mesoscale,coherent vortices on the β-plane

Abstract

An investigation is made of the evolution of small-scale, axisymmetric vortices in a stratified fluid with spatially variable Coriolis parameter. The criteria for smadness are a horizontal scale less than or equal to the first internal radius of deformation and a vertical scale less than or equal to that of the ambient stratification. These circumstances match those of Sub-mesoscale, Coherent Vortices frequently observed in the oceans. The dynamical model is the balance equations, which include various effects of finite Rossby number. The principal topics are the regime of nearly uniform propagation, the development of an equilibrium ratio of vertical and horizontal scales (i.e., Burger number selection), and the occurrence of various types of instability for vortices with extremes in amplitude or shape.     

Balancing the source terms in a SPH model for solving the shallow water equations

A shallow flow generally features complex hydrodynamics induced by complicated domain topography and geometry. A numerical scheme with well-balanced flux and source term gradients is therefore essential before a shallow flow model can be applied to simulate real-world problems. The issue of source term balancing has been exhaustively investigated in grid-based numerical approaches, e.g. discontinuous Galerkin finite element methods and finite volume Godunov-type methods. In recent years, a relatively new computational method, smooth particle hydrodynamics (SPH), has started to gain popularity in solving the shallow water equations (SWEs). However, the well-balanced problem has not been fully investigated and resolved in the context of SPH. This work aims to discuss the well-balanced problem caused by a standard SPH discretization to the SWEs with slope source terms and derive a corrected SPH algorithm that is able to preserve the solution of lake at rest. In order to enhance the shock capturing capability of the resulting SPH model, the Monotone Upwind-centered Scheme for Conservation Laws (MUSCL) is also explored and applied to enable Riemann solver based artificial viscosity. The new SPH model is validated against several idealized benchmark tests and a real-world dam-break case and promising results are obtained.