Workshop Opening Presentation of the DYNAS Project

Transcription

1 Workshop Opening Presentation of the DYNAS Project Alexandre Ern, Eric Gaume, Cyril Kao, Jérôme Jaffré CERMICS École Nationale des Ponts et Chausées Marne-la-Vallée, France DYNAS Workshop 06-08/12/04 p.1

2 Introduction DYNAS : DYNAmics of Shallow watertables Cooperative Research Action supported by Inria 5 teams (8 researchers, 2 post-docs, 4 PhD students) 2 year project ( ) DYNAS Workshop 06-08/12/04 p.2

3 A multi-disciplinary project CERMICS, Enpc (H. Beaugendre, A. Ern) numerical schemes, adaptive meshes CEREVE, Enpc (T. Esclaffer, E. Gaume) surface hydrology DEAN, Cemagref (B. Augeard, J.-P. Carlier, I. Ginzburg, C. Kao) surface and subsurface hydrology DYNAS Workshop 06-08/12/04 p.3

4 A multi-disciplinary project Estime project, Inria (F. Clément, J. Jaffré, E. Marchand, J. Roberts) numerical schemes, parameter identification IMFS Strasbourg (Ph. Ackerer, B. Belfort) computational flows in porous media DYNAS Workshop 06-08/12/04 p.4

5 General framework watertable dynamics variably saturated subsurface flows watertable/ground interaction generation of overland flow hillslopes exposed to heavy rainfall localization of contributing saturated zones DYNAS Workshop 06-08/12/04 p.5

6 General framework watertable infiltration exfiltration overland flow stream DYNAS Workshop 06-08/12/04 p.6

7 General framework in situ experiments often difficult to identify the contribution of each hydrological process virtual hillslopes a valuable complement to in situ experiments recent work includes, among others, Ogden & Watts 00, Cloke et al. 03, Weiler & McDonnell 04 DYNAS Workshop 06-08/12/04 p.7

8 Goals of DYNAS project short-term: simulate some well-identified hydrological processes infiltration, watertable dynamics, watertable/ground interaction, overland flow design suitable numerical methods define benchmark problems for code validation long-term: hillslope hydrology simulation tool suitable for virtual hillslopes identify dominating processes and controlling variables DYNAS Workshop 06-08/12/04 p.8

9 Methodology detailed modeling of elementary processes subsurface flow Richards equation, soil hydrodynamic functions two-phase flow equation overland flow Saint-Venant equation, diffusive wave, kinematic wave coupling between subsurface and surface flows DYNAS Workshop 06-08/12/04 p.9

10 Methodology numerical method design continuous finite element methods (FEM) mixed FEM discontinuous finite elements (DG) box schemes lattice Boltzmann methods (LBM) DYNAS Workshop 06-08/12/04 p.10

11 Test cases Abdul Gilham 84: metric scale Ogden Watts 00: hectometric scale DYNAS test case: hectometric scale so far, restricted to 2D hillslopes DYNAS Workshop 06-08/12/04 p.11

12 DYNAS test case A H L 1 L = L + L 1 2 B L 2 A (0;15) B (10;14.8) C (39.85;11) D (54.85;10.8) E (54.85;7.8) F (39.85;8) G (10;11.8) H (0;12) G Ls water table C D F E DYNAS Workshop 06-08/12/04 p.12

13 Simulation tools FEM/Richards code with overland flow (Cermics/Cereve) LB/Richards code (Cemagref) two-phase flow code (Inria) commercial code Hydrus-2D: FEM/Richards and advection/dispersion code DYNAS Workshop 06-08/12/04 p.13

14 Overview of results numerical experiments on Dynas test case and variants influence of soil hydrodynamic parameters influence of IC and BC coupling of subsurface and overland flow soil heterogeneity spatial and temporal variations of rainfall DYNAS Workshop 06-08/12/04 p.14

15 Overview of results LB approach to Richards equation a two-phase flow model equivalent hydraulic conductivity for mixed FEM DYNAS Workshop 06-08/12/04 p.15

16 Dynas test case influence of soil hydrodynamic parameters example: van Genuchten Mualem model (1 + ( αψ) n ) 1+ 1 n ψ < 0 θ(ψ) = 1 ψ 0 θ: reduced volumetric water content, ψ: matrix potential DYNAS Workshop 06-08/12/04 p.16

17 Dynas test case constant rainfall intensity i/k s = 2% reference soil: Yolo Light Clay (YLC) α = 3.6 m 1, n = 1.9 impact on time to reach equilibrium soil YLC n = 1.31 n = 3.9 α = 0.3 α = 8.0 T e [h] DYNAS Workshop 06-08/12/04 p.17

18 Dynas test case influence of overland flow model 1: obstacle-type problem neglect height of overland flow for subsurface flow BC neglect re-infiltration model 2: diffusive wave equation for overland flow coupled to Richards equation for subsurface flow DYNAS Workshop 06-08/12/04 p.18

19 Dynas test case time evolution of saturated ground fraction and of relative exfiltration flux Ls/L (%) Qexf/Qrain (-) overland flow obstacle model Time t (h) overland flow obstacle model Time t (h) DYNAS Workshop 06-08/12/04 p.19

20 Lattice Boltzmann method Extension of LB techniques to generic advection and anisotropic dispersion equations LB equilibrium formulations for Richards equation: exactly conservative, moisture content and mixed forms Application to anisotropic layered media DYNAS Workshop 06-08/12/04 p.20

21 Lattice Boltzmann method Infiltration into a semi-infinite dry column with moisture content LB formulation: θ(0, z) = Class of analytical solution is constructed for Versatile Non-linear Model of Broadbridge & White 88, Watson et al. 95 K r ( θ) = C 1 C θ (β 1 θ + β 2 θ2 ) K r h θ( θ) = D 0C 2 (C θ) 2 β 1 + β 2 = 1 C > 1 DYNAS Workshop 06-08/12/04 p.21

22 Lattice Boltzmann method Example: C = 1.02 and C = 1.5, q in /K s = 1.2, β 1 = 0, β 2 = 1 0 Dimensionless depth theory, C=1.02 LB, C=1.02 theory, C=1.5 LB, C= Effective water content DYNAS Workshop 06-08/12/04 p.22

23 A two-phase flow model In Richards equations, air pressure assumed to be invariant full two-phase flow equations necessary to take into account the influence of air In the field of reservoir simulation (oil-water flows), a global pressure formulation is used to reduce the coupling between saturation and pressure equations (existence theorem) We compare these formulations with the standard, full two-phase flow formulation DYNAS Workshop 06-08/12/04 p.23

24 A two-phase flow model s 0 s 20 s 40 s 100 s 200 classical formulation s 0 s 20 s 40 s 100 s 200 global pressure formulation DYNAS Workshop 06-08/12/04 p.24

25 Conclusions difficulties associated with parameter identification and variability initial conditions robustness of numerical methods over wide range of hydrological situations (infiltration, exfiltration, overland flow) upscaling to hillslope DYNAS Workshop 06-08/12/04 p.25

26 Conclusions current achievements of DYNAS project dedicated simulation tools progress in the definition of benchmark problems progress in understanding the internal dynamics of contributing saturated zones cross-fertilization between numericians and hydrologists DYNAS Workshop 06-08/12/04 p.26