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A NEW IMPLICIT SCHEME FOR SOLVING 3-D SHALLOW WATER FLOWS

Journal of Hydrodynamics 2009年第6期21卷 790-798页

作者： ZHANG Zhuo SONG Zhi-yao LV Guo-nian State Key Laboratory of Hydrology Water Resources and Hydraulic Engineering Ocean College Hohai University Nanjing 210098 China Key Laboratory of Virtual Geographic Environment Ministry of Education Nanjing Normal University Nanjing 210097 China

Based on the improved adi method, this article proposes an improved implicit finite difference scheme for solving 3-D shallow water flows. The main objective is to design a numerical relation between the horizontal velocity on each layer and the depth-averaged velocity for employing the improved adi method. With the free surface elevation and the depth-averaged velocity obtained by using essentially 2-D depth-averaged mode, the velocity profiles can be obtained easily and simultaneously. The wind-induced flows, the open channel flows due to the pressure gradient and the tidal flows in coastal waters are simulated, and the results are consistent well with the analytical solution and the field data, which shows that the present implicit scheme is stable and effective, and the established model is practical. Moreover, when only one vertical layer is specified, the present 3-D numerical model is reducea to the 2-D depth-averaged model.

关键词： shallow water equation adi method wind-induced flow gravity-drived flow tidal flow

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Fully HOC Scheme for Mixed Convection Flow in a Lid-Driven Cavity Filled with a Nanofluid

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Advances in Applied Mathematics and Mechanics 2013年第1期5卷 55-77页

作者： Dingfang Li Xiaofeng Wang Hui Feng School of Mathematics and Statistics Wuhan UniversityWuhan 430072HubeiChina Department of Mathematics Henan Institute of Science and TechnologyXinxiang 453003HenanChina

A fully higher-order compact(HOC)finite difference scheme on the 9-point two-dimensional(2D)stencil is formulated for solving the steady-state laminar mixed convection flow in a lid-driven inclined square enclosure filled with water-Al2O3 *** cases are considered depending on the direction of temperature gradient imposed(Case I,top and bottom;Case II,left and right).The developed equations are given in terms of the stream function-vorticity formulation and are nondimensionalized and then solved numerically by a fourth-order accurate compact finite difference *** other compact solution procedure in literature for this physical configuration,the present method is fully compact and fully higher-order *** fluid flow,heat transfer and heat transport characteristics were illustrated by streamlines,isotherms and averaged Nusselt *** with previously published work are performed and found to be in excellent agreement.A parametric study is conducted and a set of graphical results is presented and discussed to elucidate that significant heat transfer enhancement can be obtained due to the presence of nanoparticles and that this is accentuated by inclination of the enclosure at moderate and large Richardson numbers.

关键词： HOC difference scheme pseudo-time derivative mixed convection adi method

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Symmetric Energy-Conserved Splitting FDTD Scheme for the Maxwell’s Equations

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Communications in Computational Physics 2009年第9期6卷 804-825页

作者： Wenbin Chen Xingjie Li Dong Liang School of Mathematical Sciences Fudan UniversityShanghai200433China School of Mathematics University of MinnesotaMinneapolisMN 55455USA Department of Mathematics and Statistics York UniversityTorontoON M3J 1P3Canada

In this paper,a new symmetric energy-conserved splitting FDTD scheme(symmetric EC-S-FDTD)for Maxwell’s equations is *** new algorithm inherits the same properties of our previous EC-S-FDTDI and EC-S-FDTDII algorithms:energy-conservation,unconditional stability and computational *** keeps the same computational complexity as the EC-S-FDTDI scheme and is of second-order accuracy in both time and space as the EC-S-FDTDII *** convergence and error estimate of the symmetric EC-S-FDTD scheme are proved rigorously by the energy method and are confirmed by numerical experiments.

关键词： Maxwell’s equation adi method FDTD energy-conserved second-order accuracy symmetric scheme

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Numerical Model of Storm Surge and Inundation in Bohai Bay

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Transactions of Tianjin University 2011年第1期17卷 57-61页

作者：李大鸣付庆军解以扬白玲 Key Laboratory of Harbor and Ocean Engineering of Ministry of Education of China School of Civil Engineering Tianjin University Department of Civil and Environmental Engineering University of Houston Institute of Tianjin Meteorological Bureau

A two-dimensional numerical model of extratropical storm surge and inundation in Bohai Bay was built based on the unsteady flow Navier-Stokes equations. The model included two sections, one was for the simulation of storm surge tidal level and the other for the simulation of storm surge inundation in the coastal area. While simulating the storm surge tidal level, the alternating direction implicit (adi) method was applied to dispersing and solving 2D storm surge equations. In the simulation of storm surge inundation, the 2D unsteady flow equations were dispersed and solved using the structureless grids of finite volume method (FVM). A coupling calculation mode of the process of inundation and storm surge tidal level variation was proposed, therefore the storm surge inundation process and area could be calculated while simulating and forecasting the process of storm surge tidal setup. Furthermore, an extratropical storm surge and inundation in Bohai Bay were simulated using this numerical model. Simulation results are in good agreement with the measured data, which shows that this numerical model provides a new method of simulating and forecasting storm surge and inundation in Bohai Bay.

关键词： extratropical storm surge inundation adi method structureless grid

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