Contents -- Preface -- Series Talks -- P. Ackerer, A. Younes: A Finite Volume Formulation of the Mixed Finite Element Method for Triangular Elements -- 1 Introduction -- 2 Resolution of the elliptic case with a scalar flux related parameter -- 2.1 The mixed finite element formulation -- 2.2 The finite volume formulation -- 2.3 The re-formulation of the mixed finite element -- 3 General 2D formulation for the elliptic case -- 3.1 The mixed finite element formulation -- 3.2 The corresponding re-formulation -- 4 The parabolic case -- 4.1 The standard mixte formulation -- 4.2 The re-formulation of the MFE -- 5 Comments and conclusion -- References -- Alexandre Ern: Finite Element Modeling of Hydrosystems with Fully Saturated, Variably Saturated, and Overland Flows -- 1 Introduction -- 2 Finite elements for fully saturated steady flows -- 2.1 Darcy's equations -- 2.2 The pressure primal formulation -- 2.2.1 Conforming approximation -- 2.2.2 Non-conforming approximation -- 2.3 Mixed formulation in [L2(R)Id x Ht(R) -- 2.3.1 Conforming approximation -- 2.3.2 Non-conforming approximation -- 2.4 Mixed formulation in Hdiv x L2(R) -- 2.4.1 The Raviart-Thomas finite element -- 2.4.2 Hybrid finite elements -- 2.5 Mixed formulation in Hdiv x Ht(R) -- 2.5.1 The discrete setting -- 2.5.2 Some properties of the finite volume box scheme -- 2.6 Summary -- 3 Finite elements for variably saturated flows -- 3.1 Richards' equation -- 3.2 Soil hydrodynamic functions -- 3.3 Space and time discretization -- 3.3.1 Conforming approximation in primal form -- 3.3.2 Non-conforming approximation in mixed form -- 3.4 Water-tableground interact ion and the obstacle problem -- 3.4.1 Steady obstacle problem -- 3.4.2 Unsteady obstacle problem -- 4 Overland flow -- 4.1 Model formulation -- 4.2 Coupling with Richards' equation -- 4.3 Numerical method -- 5 Applications.

5.1 One-dimensional infiltration -- 5.1.1 Stationary test case -- 5.1.2 Unstationary test case -- 5.2 Two-dimensional hillslopes -- 5.2.1 Influence of the soil hydrodynamic parameters -- 5.2.2 Influence of the overland flow -- References -- Patrick Goblet: Sharp Front Modeling -- 1 Introduction -- 2 Sharp front problem statement -- 3 Classification of approaches -- 4 Particle techniques -- 5 Improving eulerian approaches -- 5.1 Improving a 1D Finite Difference Scheme -- 5.1.1 First order stabilizing scheme -- 5.1.2 Higher order stabilizing schemes -- 5.2 Improving a 1D Finite Element Scheme -- 5.3 Higher order schemes: spectral elements -- 6 kagrangian approaches -- 7 Eulerian-lagrangian approaches -- 8 Conclusion -- References -- Catherine Gourla y, Marie-Helene, Tusseau- Vuillemin: Numerical Modeling of Biological Processes: Specificities, Difficulties and Challenges -- 1 General statements -- 1.1 How do biological processes differ from others (physical, chemical... )? -- 1.2 The Michaelis- Menten formalism (1911) -- 1.2.1 Enzymatic kinetic -- 1.2.2 Generalisation to biological processes with limiting factors -- 1.3 Principles of a model construction: calibration-validation-extrapolation -- 1.4 Numerical difficulties: non linear phenomena -- 2 Aquatic biogeochemical modeling -- 2.1 Definitions and objects of the modeling -- 2.1.1 Biogeochemical model purposes -- 2.2 Modeling of phytoplankton growth -- 2.3 Usual modeling of organic matter biodegradation -- 2.3.1 Organic matter quantification and biodegradation -- 2.3.2 Streeter and Phelps model (1925) -- 2.3.3 River water quality models -- 2.3.4 Activated Sludge Models (ASM) -- 2.4 Complex biogeochemical modeling of aquatic ecosystems -- 3 Modeling of wastewater biodegradation -- 3.1 ASM1: a widely used wastewater treatment plant model -- 3.1.1 Some basics on wastewater treatment plants.

3.1.2 Presentation of the model and numerical solving -- 3.1.3 Practical application -- 3.2 The estimation of the composition of wastewater samples through inverse modeling -- 3.2.1 Principles of respirometry -- 3.2.2 Identifiability and optimisation problem -- 4. Strategies for a better modeling of bio-logical processes in aquatic systems -- Cited References -- Some Recommended References -- 1. Michaelis-Menten formalism -- 2. Biogeochemical models -- 3. Wastewater treatment plant models -- Deguan Wang: Ecological Simulation of Red Tides in Shallow Sea Area -- 1 Introduction -- 2 The character of equilibrium point and its impact on the changing rate of phyto- plankt on concentration -- 3 Red tide ecological dynamic model -- 3.1 Physical/Biological Coupling -- 3.2 Governing equations -- 3.2.1 Hydrodynamic simulation -- 3.2.2 Three-component ecological simulation -- 3.3 General description of numerical methods -- 3.3.1 Finite element model[20][22][23] -- 3.3.2 Finite volume model (FVM) -- 4 Practical work -- 4.1 The governing equations -- 4.2 The numerical solution method -- 4.3 Results -- 4.3.1 Results from hydrodynamic simulation -- 4.3.2 Results from Nutrient dynamics simulation -- 4.3.3 Results for nutrients-algae-dynamics -- 4.3.4 The equilibrium point of algae trend at, measuring point 9 -- 4.3.5 Analysis of results -- References -- Ling Li: Subsurface Pathways of Contaminants to Coastal Waters: Effects of Oceanic Oscillations -- Abstract -- 1 Introduction -- 2 Tide-induced groundwater oscillations in coastal aquifers -- 2.1 Non-linear effects -- 2.2 Slope effects -- 2.3 Capillary effects -- 2.4 Leakage effects -- 2.5 Low frequency and other oscillations -- 2.6 Vertical flow effects (intermediate depth) -- 2.7 Density effects -- 2.8 Seepage face effects -- 2.9 Two-dimensional tidal propagation.

3 Implications for contaminant transport and transformation in tidally influenced coastal aquifers -- 3.1 Tide-induced flushing and dilution effects on chemical transport processes -- 3.2 Tide-induced mixing of fresh groundwater and seawater -- 3.3 Tidal effects on chemical reactions -- 4 Conclusion -- Acknowledgement -- References -- Invited Talks -- Tingfang Wang, Sixun Huang, Huadong DU, Gui Zhang: Studies on Retrieval of the Initial Values and Diffusion Coefficient of Water Pollutant Advection and Diffusion Process -- Abstract -- 1 Introduction -- 2 The 3-D model of water pollutant advec- tion and diffusion process -- 3 Retrieval in the case of complete observations -- 4 Retrieval in the case of incomplete observations -- 5 Numerical tests -- 6 Conclusions -- Acknowledgement -- References -- Jing Chen, Zhifang Zhou: Application of Tabu Search Method to the Parameters of Groundwater Simulation Models -- Abstract -- 1 Introduction -- 2 General description of tabu search -- 2.1 Initial solution -- 2.2 Neighborhood and movement -- 2.3 Tabu list -- 2.4 Aspiration criteria -- 2.5 Principle to stop searching -- 3 Where can we use tabu search method? -- 4 Application of tabu to the inverse analy- sis of hydrogeological parameters -- 4.1 Evaluation model -- 4.2 Discrete variables and neighbors -- 4.3 Tabu search procedure -- 4.4 result -- 5 Summary -- References -- Xiaomin Xu, Deguan Wang: Several Problems in River Networks Hydraulic Mathematics Model -- Abstract -- 1 Introduction -- 2 Saint-Venant equations and relaxation iterative method -- 2.1 Saint-Venant equations and discretization -- 2.2 Newton iterative -- 2.3 River networks relaxation iterative method -- 3 The convergence of Netwon iterative method -- 4 The new solution method of linear systems -- 4.1 Compress-storage.

4.2 Combined Gaussian elimination with partial piv- oting method with compress-storage -- 5 Case study and conclusions -- References -- 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 -- Abstract -- 1 Introduction -- 2 Phytoplankton population model with constant nutrient concentration -- 2.1 Mat hematical model -- 2.2 Results and discussion -- 3 Phytoplankton population model with non-constant nutrient concentration -- 3.1 Mathematical model -- 3.2 Results and discussion -- 4 Conclusions -- References -- Jie Zhou, Deguan Wang, Haiping Jiang, Xijun Lai: A Numerical Simulation of Thermal Discharge into Tidal Estuary with FVM -- Abstract -- 1 Two dimensional shallow water model to simulate thermal discharge -- 1.1 Main idea -- 1.2 Governing equations -- 1.2.1 Hydrodynamics equations -- 1.2.2 Thermal waste transport governing equation -- 1.3 Numerical methods -- 1.4 Boundary conditions -- 1.4.1 Scope for calculation -- 1.4.2 Boundary conditions -- 2 Validat ion of hydrodynamics model -- 3 Case study -- 4 Conclusions -- References.