Mathematical Methods for Surface and Subsurface Hydrosystems (Series in Contemporary Applied Mathematics ? Vol. 7) (Series in Contemporary Applied Mathematics)

240 Pages·2007·0.62 MB·English

by  Deguan Wang

Mathematical Methods for Surface
and Subsurface Hydrosystems
Series in Contemporary Applied Mathematics CAM
Honorary Editor: Chao-Hao Gu (Fudun University)
Editors: P. G. Ciarlet (City University ofHong Kong),
Tatsien Li (Fudun University)
1. Mathematical Finance -T heory and Practice
(Eds. Yong Jiongmin, Rama Cont)
2. New Advances in Computational Fluid Dynamics
-T heory, Methods and Applications
(Eds. F. Dubois, Wu Huamo)
3. Actuarial Science -T heory and Practice
(Eds. Hanji Shang, Main Tosseti)
4. Mathematical Problems in Environmental Science and
Engineering
(Eds. Alexandre Ern, Liu Weiping)
5. Ginzburg-Landau Vortices
(Eds. HdimBrezis, Tatsien Li)
6. Frontiers and Prospects of Contemporary Applied
Mathmetics
(Eds. Tatsien Li, Pingwen Zhang)
7. Mathematical Methods for Surface and Subsurface
Hy d rosyste ms
(Eds. Deguan Wang, Christian Duquennoi, Alexandre Ern)
Series in Contemporary Applied Mathematics CAM 7
hematica hods for Surface
M ~ t M i t
and Subsurface Hydrosystems
editors
Deguan Wang
Hohai University in Nanjing, China
Christian Duquennoi
Alexandre Ern
CERMlCS ENPC, France
Higher Education Press
\:
World Scientific
NEW JERSEY * LONDON * SINGAPORE * BElJlNG * SHANGHAI * HONG KONG * TAIPEI CHENNAI
Deguan Wang Christian Duquennoi Alexandre Ern
College of Environmental Le centre d’A ntony Ecole nationale des ponts et
Science and Engineering Parc de Tourvoie chaussCes
Hohai University BP 44 6 et 8 avenue Blake Pascal
1 Xikang Road 92163 Antony Cedex, 77455 Marne-la-VallCe,
Nanjing, 210098, France France
China
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Copyright @ 2006 by
Higher Education Press
4 Dewai Dajie, Beijing 100011 , P. R. China, and
World Scientific Publishing Co Pte Ltd
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All rights reserved. No part of this book may be reproduced or transmitted in any form
or by any means, electronic or mechanical, including photocopying, recording or by
any information storage and retrieval system, without permission in writing from the
Publisher.
ISBN 7-04-020256-5
Printed in P. R. China
Preface
The ISFMA Symposium on Mathematical Models for Surface and
Subsurface Hydrosystems was held on September 13-17, 2004 at Hohai
University, Nanjing, China. With the increasing awareness of the heavy
burden placed on environmental resources and the need of industry and
public institutions to cope with more stringent regulations, the scope
of the Symposium was to focus on some specific, but very important,
environmental problems, namely surface and subsurface hydrosystems.
The purpose was to present state-of-the-art techniques to model such
systems, to promote the exchange of scientific ideas between French and
Chinese experts, and to foster new collaborations between France and
China in this field. Approximately 70 participants, including five French
representatives attended the Symposium.
The activities of the Symposium included five 3-hour keynote lec-
tures elaborating from the basics to recent advances in hydrosystem
modeling and several contributed presentations dealing with more spe-
cific problems. This volume collects the material presented in the key-
note lectures and some selected contributed lectures. The topics covered
include mixed finite element method, finite volume formulation, sharp
front modeling, biological process modeling, red tide simulation, and
contaminant transfer in coastal waters. As such, this volume should be
useful to graduate students, post-graduate fellows and researchers both
in applied mathematics and in environmental engineering.
As organizers of this Symposium, we would like to express our grati-
tude to various institutions for their supports: National Nature Science
Foundation of China, Mathematical Center of Ministry of Education of
China, Hohai University, French Embassy in Beijing, Consulate General
of France in Shanghai, ISFMA (Institut Sino-Franqais de Mathkmatiques
Appliquhes) and SOGREAH. We also thank all the lecturers and partici-
pants for their contributions. Our deepest appreciation goes to Professor
Li Tatsien for his support in launching this Symposium. Special thanks
also to Matthieu Jouan for his instrumental help in the organization.
Deguan Wang, Christian Duquennoi, and Alexandre Ern
October 2005
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Contents
Preface
Series Talks
P. Ackerer, A. Younes: A Finite Volume Formulation of the
Mixed Finite Element Method for Triangular Elements ......... 1
Alexandre Ern: Finite Element Modeling of Hydrosystems with
Fully Saturated, Variably Saturated, and Overland Flows ...... 19
Patrick Goblet: Sharp Front Modeling ............................ 60
Catherine Gourlay , Marie-H k lk ne, Tusseau- Vuillemin:
Numerical Modeling of Biological Processes: Specificities,
Difficulties and Challenges .................................... 75
Deguan Wang: Ecological Simulation of Red Tides in Shallow
Sea Area ...................................................... 99
Ling Li: Subsurface Pathways of Contaminants to Coastal
Waters: Effects of Oceanic Oscillations ....................... 126
Invited Talks
Tingfang Wang, Sixun Huang, Huadong DU,G ui Zhang: Studies on
Retrieval of the Initial Values and Diffusion Coefficient of
Water Pollutant Advection and Diffusion Process ............ 174
Jing Chen, Zhifang Zhou: Application of Tabu Search Method
to the Parameters of Groundwater Simulation Models ........ 191
Xiaomin Xu, Deguan Wang: Several Problems in River
Networks Hydraulic Mathematics Model ..................... 201
viii Contents
Jue Yang, Deguan Wang, Ying Zhang: Study on the Character of
Equilibrium Point and Its Impact on the Changing Rate of
Phytoplankton Concentration Using a Simple Nutrient-
Phytoplankton Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Jae Zhou, Deguan Wang, Haiping Jiang, Xijun Lai: A Numerical
Simulation of Thermal Discharge into Tidal Estuary with FVM 223
1
A Finite Volume Formulation of the Mixed
Finite Element Method for Triangular
Elements
P. Ackerer, A. Younes
IMFS UMR 7507 CNRS - ULP Strasbourg
2, *rueB oussingault 67000 STRASBO URG FRANCE
1 Introduction
Numerous mathematical models are based on conservation principles and
constitutive laws, which are formulated by,
dU
s-+v.q= f
dt
where s is a storage coefficient, K is the flux related parameter and q
is the flux of the associated state variable u. Equation (1.1) states for
the conservation principle and (1.2) states for the constitutive law like
Fourier’s law (u is the temperature), Fick’s law (u is the concentration
of a solute), Ohm’s law (u is the electric potential) or Darcy’s law (u is
the hydraulic head). The associated initial and boundary conditions are
of Dirichlet or Neumann type,
u(x,0 ) = uo(x) X € R
u(z,t )= 91b,t ) (z E dR1,t > 0) (1.3)
(-KVu) . nan = g2(z,t) (z E dR2,t > 0)
where 0 is a bounded, polygonal open set of R2,8 0’ and dR2 are parti-
tions of the boundary dR of R corresponding to Dirichlet and Neumann
boundary conditions and nan the unit outward normal to the boundary
dR.
This system is often solved by finite volumes (FV) or finite elements
(FE) methods of lower order (see LeVeque [l]a nd Ern & Guermond [2]
among others). FV ensures an exact mass balance over each element
and continuous fluxes across common element boundaries. FE ensures
an exact mass balance on a dual mesh but leads to discontinuous fluxes
at common elements edges. However, finite element is considered as