68 GS13 Abstracts

68 GS13 Abstracts IP1 IP4 Approximation of Transport Processes Using Junior Scientist Award Lecture: Interpreting Geo- Eulerian-Lagrangian Techniques logical Observations Through the Analysis of Non- linear Waves Transport processes are common in geoscience applications, and find their way into models of, e.g., the atmo- Geological and environmental systems are rich in examples sphere, oceans, shallow water, subsurface, seismic inver- of self-organization and pattern formation. These patterns sion, and deep earth. Our objective is to simulate transport contain information about processes as diverse as seawa- processes over very long time periods, as needed in, e.g., ter intrusion into coastal aquifers, the long-term safety of the simulation of geologic carbon sequestration. A good geological CO2 storage, and the formation of the oceanic numerical method would be locally mass conservative, pro- crust. I will discuss how important observations in these duce no or minimal over/under-shoots, produce minimal three areas can be explained by non-linear waves. This numerical diffusion, and require no CFL time-step limit for illustrates the potential of the mathematical analysis of stability. The latter would allow better use of parallel com- non-linear waves to contribute to our understanding of fun- puters, since time-stepping is essentially a serial process. damental geological phenomena and applied environmental Moreover, it would be good for the methods to be of high problems. order accuracy. Our approach is to develop locally conservative Eulerian-Lagrangian (or semi-Lagrangian) methods Marc A. Hesse combined with ideas from Eulerian WENO schemes, since University of Texas they have the potential to attain the desired properties. Department of Geological Sciences [email protected] Todd Arbogast Dept of Math; C1200 University of Texas, Austin IP5 [email protected] An Unstructured Grid Model Suitable for Flooding Studies with Applications to Mega-tsunamis IP2 Mega-thrust earthquakes and tsunamis cause untold de- The Spatiotemporal Dynamics of Waterborne Dis- struction. In this talk a new finite volume unstructured eases grid tsunami model is presented. The model is a finite volume analogue of the P1nc-P1 finite element, in which Dynamics of waterborne diseases in space and time is stud- mass conservation is guaranteed not only in a global sense, ied via multi-layer network models, consisting of coupled but within each cell. The model conserves momentum, and ODEs. They account for the interplay between epidemio- accurately handles flooding and drying problems. Results logical dynamics, hydrological transport and long-distance from the Indian Ocean and Japanese Tsunami compare dissemination of pathogens due to human mobility, de- well with flooding and run-up data. scribed by gravity models. Conditions for the outbreak of an epidemic are given in terms of the dominant eigen- Julie Pietrzak value of an appropriate reproduction matrix, while the ini- Faculty of Civil Engineering and Geosciences tial disease distribution is linked to the dominant eigen- Delft University of Technology vector. The theory is tested against epidemiological data [email protected] of the extensive cholera outbreaks occurred in KwaZulu- Natal (South Africa) during 2000-2001 and in Haiti during Haiyang Cui, Guus Stelling 2010-2012. Delft University of Technology [email protected], [email protected] Marino Gatto Politecnico di Milano [email protected] IP6 Data Assimilation in Global Mantle Flow Mod- els:Theory, Modelling and Uncertainties to Recon- IP3 struct Earth Structure Back in Time Career Award Lecture: Some Successes and Chal- lenges in Coastal Ocean Modeling The ability to extract the history of motion associated with large-scale geologic structures that are now imaged seismi- The coastal ocean is rich with physical and biological pro- cally in the Earth’s interior, such as plumes and subducting cesses, often occurring at vastly different scales. In this slabs, is crucial to constrain the fundamental deformation talk, we will outline some of these processes and their math- processes of mantle convection. Here we show how fluid ematical description. We will then discuss the current state dynamic inverse theory, based on a variational approach, of numerical methods for coastal ocean modeling and re- can be applied in a global circulation model of the mantle cent research into improvements to these models, focusing to project Earth structure back in time. We present the on accuracy and efficiency for high performance comput- basic theory of the forward and inverse problem, review ing. We will also highlight some of the successes of these geologic constraints, provide computational considerations models in simulating complex events, such as hurricane relevant to the global flow problem with about 1 billion storm surges. Finally, we will outline several interesting finite elements, and discuss uncertainties. The latter re- challenges which are ripe for future research. strict the problem in practice, as our knowledge of deep Earth structure and its interpretation in terms of dynam- Clint Dawson ically relevant buoyancy anomalies is necessarily limited. Institute for Computational Engineering and Sciences University of Texas at Austin [email protected] Hans-Peter Bunge Department of Earth and Environmental Sciences, LMU GS13 Abstracts 69 Munich DMMMSA [email protected] University of Padova [email protected] IP7 Carlo Janna, Massimiliano Ferronato Data Assimilation and Inverse Modeling in Earth Dept. ICEA - University of Padova System Sciences [email protected], [email protected] Physical theories in the Earth System sciences are designed to explain and possibly predict natural phenomena. Both, CP1 the explanation and prediction necessarily include a quan- Coupled Geomechanics and Flow for Unstructured titative representation of the natural system state. Quan- Naturally Fractured Reservoir Models titative assessment of the actual, true, state is fundamen- tally achievable only by measurements. The theories and We consider unstructured reservoir models composed of models based on them are consequently designed to ex- a deformable saturated matrix and a network of natural plain and predict the measurements. A synergy of the fractures. A finite-volume method is used for the flow. models and measurements is necessary for achieving such Galerkin finite elements are used to discretize the poro- goal. Methodology of data assimilation and inverse model- elasto-plasticity equations. We account for normal and ing provides objective means for that purpose. An overview shear stresses on the fracture surfaces. The correspond- of the currently used methodology will be presented, in- ing nonlinear coupled equations are solved using either cluding examples of application in atmospheric sciences in the sequential-implicit fixed-stress approach, or the fully- domain of cloud analysis and modeling and tropical cyclone implicit method. The framework is demonstrated using modeling and prediction. several test cases with discrete fracture models. Tomislava Vukicevic Timur T. Garipov NOAA Department of Energy Resources Engineering, AOML Hurricane Research Division, Miami Stanford University [email protected] [email protected] IP8 Hamdi Tchelepi Stanford University Efficient Numerical Numerical Computation of Energy Resources Engineering Department Multi-Phase Flow in Porous Media [email protected] Appropriate models, accurate discretization schemes and efficient solvers for the arising linear systems are the ba- CP1 sis for any numerical simulation. In this talk I will address these aspects by first considering a model for compositional Mechanics of Fluid Injection into Deformable two-phase flow with equilibrium phase exchange that is Porous Materials able to handle phase appearance/disapperance properly. Poroelasticity, where the mechanical deformation of a Then a new fully-coupled discontinuous Galerkin scheme porous solid is coupled to internal fluid flow, has been for two-phase flow with heterogeneous capillary pressure studied intensely in geophysics in the context of pressure will be presented. The third part of the talk is devoted to buildup during fluid injection, such as in carbon seques- the efficient solution of the arising linear systems by means tration or enhanced oil recovery. Here, we develop a novel of algebraic multigrid methods. All numerical schemes experimental system that allows us to visualize and quan- have been implemented in the Distributed and Unified Nu- tify the dynamic, flow-driven deformation of a quasi-two- merics Environment and have been scaled up to 300000 dimensional poroelastic material. We use it to study the cores. This is joint work with Olaf Ippisch and Rebecca coupling between fluid injection and mechanical deforma- Neumann. tion patterns. Peter Bastian Christopher W. MacMinn Interdisciplinary Center for Scientific Computing MIT University of Heidelberg Mechanical Engineering [email protected] [email protected] CP1 Eric Dufresne A Mixed and Galerkin Finite Element Formulation Yale University for Coupled Poroelasticity New Haven, CT, USA [email protected] The numerical treatment of coupled poroelasticity is a de- manding task because of the instabilities affecting the pore John S. Wettlaufer pressure solution. A combination of Mixed and Galerkin Yale University Finite Element methods is employed to obtain stable nu- [email protected] merical

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