Abstract

In a variety of disciplines including atmospheric, oceanic, hydrologic and environmental sciences, large numerical simulations have become an essential tool for understanding the physical processes, synthesizing data, and for prediction. A key problem for modeling these dynamical systems is how to deal with uncertainties and error in the models’ representation of key physical processes. This talk will introduce some of the recent ensemble-based data assimilation approaches such as the use of an ensemble Kalman filter for Simultaneous State and Parameter Estimation (SSPE) in the treatment and quantification of model error and uncertainties. Applications of SSPE to a variety of phenomena ranging from the atmospheric boundary layer transport, air-sea fluxes and a physically based land-surface hydrologic model will be presented.

Biography

Prof. Zhang’s research interests include atmospheric dynamics and predictability, data assimilation, tropical cyclones, gravity waves and regional-scale climate. He earned his B.S. and M.S. in meteorology from Nanjing University, China in 1991 and 1994, respectively, and his Ph.D. in atmospheric science in 2000 from North Carolina State University. He has authored/co-authored over 150 peer reviewed journal publications that have a total of more than 3300 citations. He has received numerous awards for his research and service.

Wear is the process of material removal under abrasion. Multi-material systems are characterized by non-uniform wear-rates that are leading to non-planar profiles under polishing. Some recent iterative models have predicted with success the well established experimental fact, that under an initially uniform pressure load, multi-component wearing surfaces reach asymptotically a steady-state profile that continues to recess at a constant rate. In a first part, a continuous model is derived from the original iterative scheme, and extrapolated to a mathematical, abstract, but versatile framework. It is shown that the steady-state can be computed directly by solving a time-independent elliptic partial differential equation, providing a substantial computational gain against the first iterative scheme. In a second part, this formulation is used to apply modern shape optimization methods to optimize wear performance of bi-material systems. Several objectives for systems undergoing wear are identified and formalized with shape derivatives. As an example, the unit-cell of 2D multi-material composites is optimized using a level-set based method. A minimum feature size must be taken into account to avoid the convergence of minimizing design sequences toward composite materials. To address this issue, a variant of a the level-set topology optimization method is developed . Through the use of a single updating equation, this scheme conveniently enforces volume equality constraints, controls the complexity of design features with a perimeter penalization, and nucleates material inclusions with the use of the topological gradient. Keywords: topology and shape optimization, wear, multi-composite surface, level-set methods.

A stochastic optimization methodology is formulated for computing energy-optimal paths from among time-optimal paths of autonomous vehicles navigating in a dynamic flow field. To set up the energy optimization, the relative vehicle speed and headings are considered to be stochastic, and new stochastic Dynamically Orthogonal (DO) level-set equations that govern their stochastic time-optimal reachability fronts are derived. Their solution provides the distribution of time-optimal reachability fronts and corresponding distribution of time-optimal paths. An optimization is then performed on the vehicle’s energy-time joint distribution to select the energy-optimal paths for each arrival time, among all stochastic time-optimal paths for that arrival time. The accuracy and efficiency of the DO level-set equations for solving the governing stochastic level-set reachability fronts are quantitatively assessed, including comparisons with independent semi-analytical solutions. The stochastic DO level-set equations is then extended to account for uncertainties in the flow field. Time-optimal planning is completed in a wind-driven barotropic quasi-geostrophic stochastic double-gyre ocean circulation (these stochastic flow fields are simulated using our DO Navier Stokes equations). Energy-optimal missions are studied in wind-driven barotropic quasi-geostrophic double-gyre circulations, and in realistic data-assimilative re-analyses of multiscale coastal ocean flows. The latter re-analyses are obtained from multi-resolution 2-way nested primitive-equation simulations of tidal-to-mesoscale dynamics in the Middle Atlantic Bight and Shelbreak Front region. The effects of tidal currents, strong wind events, coastal jets, and shelfbreak fronts on the energy-optimal paths are illustrated and quantified. Results showcase the opportunities for longer-duration missions that intelligently utilize the ocean environment to save energy, rigorously integrating ocean forecasting with optimal control of autonomous vehicles.

Congratulations to Florian Feppon for being awarded the Médaille Louis-Édouard Rivot of the French Académie des Sciences. This is in recognition for the scientific research on “Design and optimization for Wear of Bi-Material Composite Surfaces” that he performed at Lehigh University (Bethlehem, PA) as a visiting research scholar, under the direction of Prof. Grégoire Allaire (Centre de Mathématiques Appliquées, École Polytechnique) and Prof. Vermaak (Mechanical Engineering, Lehigh University).