Seminar Series #
The Scientific Computing seminar series takes place on Fridays at 13:00. Join on zoom
Upcoming Talks #
- 12.03.2021, 13:00, Tim Dodwell, Alan Turing Institute, University of Exeter, Title: Adaptive Multilevel Delayed Acceptance
Past Talks #
05.02.2021, 13:00, Andy Davis, Courant Institute, Title: Super-parameterized numerical methods for the Boltzmann equation modeling Arctic sea ice dynamics
Abstract: We devise a super-parameterized sea ice model that captures dynamics at multiple spatial and temporal scales. Arctic sea ice contains many ice floes—chunks of ice—whose macro-scale behavior is driven by oceanic/atmospheric currents and floe-floe interaction. There is no characteristic floe size and, therefore, accurately modeling sea ice dynamics requires a multi-scale approach. Our two-tiered model couples basin-scale conservation equations with small-scale particle methods. Unlike many other sea ice models, we do not average quantities of interest (e.g., mass/momentum) over a representative volume element. Instead, we explicitly model small-scale dynamics using the Boltzmann equation, which evolves a probability distribution over position and velocity. In practice, existing numerical methods approximating the Boltzmann equation are computationally intractable when modeling Arctic basin scale dynamics. Our approach decomposes the density function into a mass density that models how ice is distributed in the spatial domain and a velocity density that models the small-scale variation in velocity at a given location. The mass density and macro-scale expected velocity evolve according to a hyperbolic conservation equation. However, the flux term depends on expectations with respect to the velocity density at each spatial point. We, therefore, use particle methods to simulate the conditional density at key locations. We make each particle method independent using a local change of variables that defines micro-scale coordinates. We model small-scale ice dynamics (e.g., collision) in this transformed domain.