Multiscale Modeling of Flow and Transport. and the simulation toolbox DuMu X

Transkript

1 Multiscale Modeling of Flow and Transport and the simulation toolbox DuMu X Jochen Fritz, Jennifer Niessner, Bernd Flemisch and Rainer Helmig Marie Curie Workshop

2 Outline Multiscale / multiphysics modeling Motivation Concept Outlook DuMu X What is Dune? What is DuMu X? 1p1c / 2p2c multiphysics example

3 LNAPL contamination in the unsaturated zone soil vapor extraction drinking water well 100 m groundwater flow LNAPL in residual saturation unsaturated zone saturated zone several km (Niessner)

4 LNAPL spatial dependence of processes (Niessner) a w n w a n n a w w n w a w a n a w w n 3p3c 1p1c 2p3c 2p 1p2c

5 Motivation General Idea Modeling of complex physical processes in larger domains: (Niessner)

6 Definition of Scales (Niessner)

7 Outline Multiscale/multiphysics modeling Motivation Concept Outlook DuMu X What is Dune? What is DuMu X? 1p1c / 2p2c multiphysics example

8 Concept Modeling of complex processes on fine scale only where needed -> Multiphysics Modeling of simple processes on macro scale with account to local scale heterogeneities -> Multiscale Concept for 2p2c / 3p3c developed by J. Niessner [Niessner & Helmig 2007] No gravity, capillarity, compressibility Isothermal conditions Mass transfer only in Subdomain, one phase immobile Fractional Flow Formulation

9 2p2c concept T U a w a a w a w w a 2p2c 1p1c 2p

10 2P / 2P2C Flow Equations Pressure equation Saturation equation (upscaled) S w t + (f w v +D)=0 Concentration equations C κ t + ( α f α C κ α v)= 0 with and

11 Solution Strategy T,fine 1.Flow Field T,coarse 4. Saturation U 2. Concentration 3. Saturation

12 3p3c concept residual NAPL T U a w a n w n 3p3c n a w n aw a w aw 2p3c n

13 Outline Multiscale/multiphysics modeling Motivation Concept Outlook DuMu X What is Dune? What is DuMu X? 1p1c / 2p2c multiphysics example

14 Enhanced Remediation soil vapor extraction thermal energy 200 C drinking water well 100 m groundwater flow 10 C LNAPL in residual saturation unsaturated zone saturated zone several km

15 Processes and Models Processes Immobile spill of contaminant in saturated zone, isothermal Immobile spill of contaminant in unsaturated zone, isothermal As above, non-isothermal Model in T 1P1C upscaled 2P1C upscaled (as above), T Model in U 2P2C 3P3C (as above), T Locally advection dominated, nonisothermal Locally fast -> no thermal equilibrium (as above), T conductive (as above), T (as above) T conv + cond (as above), T for each phase

16 Multiscale Multiphysics Approach Goals Jennifer Niessner Bernd Flemisch Jochen Fritz Gravity and Capillary Effects Implementation in DUNE Discretizations, Mathematical Multiscale Approaches Compressibility, non-isothermal Processes Multiscale Toolbox Physical Processes Discretizations Math. Modeling Phases/Components Capillary Forces Non-isothermal Effects Spatial Scales (adapt.) Implicit/Explicit Time Element shapes Finite Volume Finite Element Multiscale FV/FE

17 Outline Multiscale/multiphysics modeling Motivation Concept Outlook DuMu X What is Dune? What is DuMu X? 1p1c / 2p2c multiphysics example

18 DuMu X Dune for Multi-{phase, component, scale, physics, } Flow in Porous Media Current development by: Bernd Flemisch Jochen Fritz Onur Dogan Melanie Darcis Klaus Mosthaf

19 What is Dune? Modular toolbox for solving PDEs with grid-based methods. Allows different implementations of the same concept (grids, solvers,...) using a common interface with low overhead. Developed by groups in Stuttgart (AG Bastian), Freiburg (AG Kröner), Berlin (AG Kornhuber), Münster (AG Ohlberger). Free software licensed under GPL: Modules: dune-common, dune-grid, dune-istl, dune-disc, dune-fem Main principles: - Separation of data structures and algorithms by abstract interfaces. - Efficient implementation using generic programming techniques. - Reuse of existing packages with a large body of functionality.

20 Available Dune modules Core, stable dune-common: basic classes used by all modules (debugging, exceptions, ). dune-grid: nonconforming, hierarchically nested, multi-element-type, parallel grids in arbitrary space dimensions. dune-istl: Iterative Solver Template Library (Krylov methods, ILU, algebraic and geometric multigrid, ). External, unstable dune-disc: discretizations, shapefunctions, operators (AG Bastian). dune-fem: discretization algorithms, function spaces, operators (AG Kröner).

21 What is DuMu x? Additional module dune-mux. Inherits functionality from all available Dune modules. Provides a framework for easy and efficient implementation of models from porous media flow problems: - problem formulation. - spatial and temporal discretization schemes. - nonlinear solvers. - concepts for model coupling. Includes ready to use numerical models and example applications.

22 Sample DuMu X Functionality Diffusion model - Generation of K by SIMSET (Bardossy) - Spatial discretizations: FEM, FVM, Mimetic FDM (λk p)= q Transport model - Arbitrary diffusion term (capillarity, upscaling) - Spatial discretisation: FVM - Temporal discretization explicit Runge-Kutta φ S t (f(s)v+ D(S, S))= 0

23 Sample DuMu X Functionality Transport model - Arbitrary diffusion term (capillarity, upscaling) - Spatial discretisation: FVM - Temporal discretization explicit Runge-Kutta φ C κ t α C κ α f(s)v ) =0 Fractional Flow - Combines diffusion and transport model - Time discretisation: IMPES

24 Outline Multiscale/multiphysics modeling Motivation Concept Outlook DuMu X What is Dune? What is DuMu X? 1p1c / 2p2c multiphysics example

25 Example Simulation Initial Condition Permeability Field

26 Example Simulation

27 Example Simulation

28 Example Simulation