SIAM Conference on Mathematical and Computational Issues in the Geosciences
September 11—14, 2017 • Erlangen, Germany
Discontinuous Skeletal Methods for Computational Geosciences
Methane hydrate modeling, analysis, and simulation: coupled systems and scales
Methane hydrate is an ice-like substance abundantly present in deep ocean sediments and in the Arctic. Geoscientists recognize the tremendous importance of gas hydrate as a crucial element of the global carbon cycle, a contributor to climate change studied in various deep ocean observatories, as well as a possible energy source evaluated in recent pilot engineering projects in the US and Japan. Hydrate evolution however is curiously not very well studied by computational mathematics community.
In the talk we present the challenges of hydrate modeling, which start with the need to respond to the interests of geophysicists to enable lasting collaborations that deliver meaningful results. Next we present a cascade of complex to simplified models. For the latter, some analysis of the underlying well-posedness in a very weak setting can be achieved. For the former, interesting scenarios involving multiple scales, and coupled phenomena of flow, transport, phase transitions, and geomechanics, can be formulated.
I will report on most recent results obtained jointly with the geophysicists Marta Torres (Oregon State), Wei-Li Hong (Arctic University of Norway), mathematicians Ralph Showalter (Oregon State) and F. Patricia Medina (WPI), computational scientist Anna Trykozko (University of Warsaw), as well as many current and former students to be named in the talk.
High resolution atmospheric turbulence simulations for applied problems
Scalable nonlinear and linear solvers for multiphase flow in heterogeneous porous media
New frontiers in Earth-System Modelling
The gradual progress in global numerical weather prediction includes a systematic approach to assess and quantify the associated forecast uncertainty by means of high-resolution ensembles of assimilation and forecasts. This involves simulations with billions of gridpoints, the continuous assimilation of billions of observations, rigorous verification, validation and uncertainty quantification, and it involves increasing model complexity through completing the descriptions of the global water and carbon cycles. The research requires a deeper understanding of multi-scale interactions within the atmosphere and oceans, and through interactions at the interfaces of atmosphere, land surface, ocean, lakes, and sea-ice. All this is necessary to increase the fidelity of daily forecasts and of European Copernicus Services, e.g. through the provision of state-of-the-art atmospheric monitoring services, warning systems for flood and fires, and providing reanalyses. A particular challenge arises from ensuring energy efficiency for these extreme-scale applications. This talk will comprehensively describe the steps taken towards preparing complex numerical weather predictions systems for potentially disruptive technology changes. This includes adaptation to heterogeneous architectures, accelerators and special compute units, adaptation to hierarchical memory layouts, increasing flexibility to use different numerical techniques with fundamentally different communication and computational patterns, frontier research on algorithm development for extreme-scale parallelism in time and in space, and minimising both time- and energy-to-solution. For example, a significant step towards further savings both in terms of throughput and speed-up is provided by the impact on simulations if numerical precision is selectively reduced in high resolution simulations.
Coupled problems in porous media with a focus on Biot
The key challenge in the successful utilisation of subsurface resources is the coupling of different physical processes involved. The model equations for the coupled behaviour of thermal, hydro, mechanical and chemical effects lead to a system of nonlinear, coupled, possibly degenerate PDEs.
We consider a system of coupled PDEs that incorporates the evolution in the pore-scale geometry. Starting from a reactive flow transport model describing the precipitation-dissolution processes, we visit the recent works that take into account the variation in the pore-scale geometry. Next, we consider the coupled flow and geomechanics model (Biot model) that takes into account the deformations due to the mechanical effects. Specifically, we show the iterative schemes for solving the Biot equation and the different extensions including non-linearities and further physics.