Monday, September 11, 8:30 – 9:30

Title:
Multiscale dynamics of reactive fronts in heterogeneous media with fluctuating forcings

Abstract:
Despite significant progress, accurate quantitative predictions of subsurface transport of highly reactive fluids remains a formidable challenge. Current numerical models suffer from significant predictive uncertainty, which undermines our ability to estimate future impact of, and the risks associated with, anthropogenic stressors on the environment. That is because subsurface flow and transport take place in complex highly hierarchical heterogeneous environments, and exhibit nonlinear dynamics and often lack spatiotemporal scale separation. The choice of an appropriate level of hydrogeologic model complexity continues to be a challenge. A physics-based model development follows a bottom-up approach which, through rigorous upscaling techniques, allows one to construct effective medium representations of fine-scale processes with different degrees of coupling and complexity. Yet, current model deployment is generally based on established engineering practices and often relies on ‘simpler’ classical single-point closure continuum descriptions with limited predictive capabilities. Successful modeling of tightly coupled nonlinear systems calls for a new generation of multiphysics capabilities. We discuss the challenges of predictive modeling for multiscale processes in porous media, which exhibit partial or total lack of scale separation. The first part of my talk deals with spatial homogenization by means of multiple-scale expansion both to determine the applicability conditions of macroscopic models and to bound corresponding approximation/upscaling errors. The second part is concerned with multiplicity of temporal scales, as imposed by periodic forcings or boundary conditions. The focus is on reactive transport in porous media driven by temporally fluctuating boundary conditions, whose frequency is much larger than the characteristic time scale at which transport is studied or observed at the macroscopic scale. A typical temporal resolution used in modern simulations significantly exceeds characteristic scales at which the system is driven. This is especially so when systems are simulated over ultra-long time-scales. We introduce a concept of spatiotemporal upscaling in the context of homogenization by multiple-scale expansions, and demonstrate the impact of time-dependent forcings and boundary conditions on macroscopic reactive transport. We discuss the importance of delay mechanisms in the space-time upscaled transport equations and their implications on modeling systems over ultralong temporal scales. The final part of my talk provides an example of physics-based hybridization algorithms, which couples reactive transport at the pore- and continuum-scales by means of Immersed Boundary Methods.

Tuesday, September 12, 8:30 – 9:30

Title:
Multiscale dynamics of reactive fronts in heterogeneous media with fluctuating forcings

Abstract:
Despite significant progress, accurate quantitative predictions of subsurface transport of highly reactive fluids remains a formidable challenge. Current numerical models suffer from significant predictive uncertainty, which undermines our ability to estimate future impact of, and the risks associated with, anthropogenic stressors on the environment. That is because subsurface flow and transport take place in complex highly hierarchical heterogeneous environments, and exhibit nonlinear dynamics and often lack spatiotemporal scale separation. The choice of an appropriate level of hydrogeologic model complexity continues to be a challenge. A physics-based model development follows a bottom-up approach which, through rigorous upscaling techniques, allows one to construct effective medium representations of fine-scale processes with different degrees of coupling and complexity. Yet, current model deployment is generally based on established engineering practices and often relies on ‘simpler’ classical single-point closure continuum descriptions with limited predictive capabilities. Successful modeling of tightly coupled nonlinear systems calls for a new generation of multiphysics capabilities. We discuss the challenges of predictive modeling for multiscale processes in porous media, which exhibit partial or total lack of scale separation. The first part of my talk deals with spatial homogenization by means of multiple-scale expansion both to determine the applicability conditions of macroscopic models and to bound corresponding approximation/upscaling errors. The second part is concerned with multiplicity of temporal scales, as imposed by periodic forcings or boundary conditions. The focus is on reactive transport in porous media driven by temporally fluctuating boundary conditions, whose frequency is much larger than the characteristic time scale at which transport is studied or observed at the macroscopic scale. A typical temporal resolution used in modern simulations significantly exceeds characteristic scales at which the system is driven. This is especially so when systems are simulated over ultra-long time-scales. We introduce a concept of spatiotemporal upscaling in the context of homogenization by multiple-scale expansions, and demonstrate the impact of time-dependent forcings and boundary conditions on macroscopic reactive transport. We discuss the importance of delay mechanisms in the space-time upscaled transport equations and their implications on modeling systems over ultralong temporal scales. The final part of my talk provides an example of physics-based hybridization algorithms, which couples reactive transport at the pore- and continuum-scales by means of Immersed Boundary Methods.

Thursday, September 14, 8:30 – 9:30

Title:
Bridging Scales in Weather and Climate Models with Adaptive Mesh Refinement Techniques 

Co-Authors:
Jared Ferguson, University of Michigan
Hans Johansen, Peter McCorquodale and Phillip Colella, Lawrence Berkeley National Laboratory

Abstract:
Extreme atmospheric events such as tropical cyclones are inherently complex multi-scale phenomena. Such extremes are a challenge to simulate in conventional atmosphere models which typically use rather coarse uniform-grid resolutions. Adaptive Mesh Refinement (AMR) techniques seek to mitigate these challenges. They dynamically place high-resolution grid patches over user-defined features of interest, thus providing sufficient local resolution over e.g. a developing cyclone while limiting the total computational burden. Studying such techniques in idealized simulations enables the assessment of the AMR approach in a controlled environment and can assist in identifying the effective refinement choices for more complex, realistic simulations. 

The talk reviews a newly-developed, non-hydrostatic, finite-volume dynamical core for future-generation weather and climate models. It implements refinement in both space and time on a cubed-sphere grid and is based on the AMR library Chombo, developed by the Lawrence Berkeley National Laboratory. Idealized 2D shallow-water and 3D test cases are discussed including interacting vortices, flows over topography, and a tropical cyclone simulation with simplified moisture processes. These simulations test the effectiveness of both static and dynamic grid refinements as well as the sensitivity of the model results to various adaptation criteria and forcing mechanisms. The AMR results will furthermore be compared to more traditional variable-resolution techniques, such as the use of a statically-nested mesh in NCAR’s Community Atmosphere Model CAM with its Spectral Element (SE) dynamical core. This sheds light on the pros and cons of both approaches.

Wednesday, September 13, 8:30 – 9:30

Title:
Methane hydrate modeling, analysis, and simulation: coupled systems and scales

Abstract:
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.

Wednesday, September 13, 13:00 – 14:00

Title:
High resolution atmospheric turbulence simulations for applied problems

Abstract:
Originally applied to study convective atmospheric boundary layers (CBL), large-eddy simulation (LES) is meanwhile used in many fields of science. This is mainly the consequence of a massive increase in available computer resources. State-of-the-art massively parallel computers have opened the field for a wide variety of new applications. On these machines, simulations with extremely large numerical grids of up to 40003 grid points and even more are currently carried out in acceptable time. In Meteorology, beside for the fundamental research of neutral and stable stratified flows, where the typical eddy size is much smaller than for pure convectively driven flows, LES starts to be used also for more applied topics like air pollution modeling, flow around buildings, or wind energy. Moreover, the interaction of turbulence of different scales can be studied for the first time. Lagrangian particle models coupled to LES allow for further interesting applications, e.g. to calculate footprints of turbulence sensors in heterogeneous terrain, or to simulate the effect of turbulence on the growth of cloud droplets. Respective simulations require both, a large model domain size to capture the large scales and a sufficiently fine grid spacing to resolve the interacting smaller scales, creating a very high demand on computational resources.

The talk will start with a short general introduction to LES and will then give an overview of current studies with very high spatial resolution performed at IMUK, like simulations of coherent structures in the convective boundary layer, simulations of the urban environment, and the effect of turbulence on cloud droplet growth or aircraft during takeoff and landing, as well as LES applications for wind energy systems. 

Monday, September 11, 13:00 – 14:00

Title:
New frontiers in Earth-System Modelling

Abstract:
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.

Thursday, September 14, 13:00 – 14:00

Title:
Coupled problems in porous media with a focus on Biot

Abstract:
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.