Seminars

Fast Spectral Time-Domain PDE Solvers for Complex Structures: The Fourier-Continuation Method

Oscar P. Bruno

Professor
Department of Applied and Computational Mathematics
CalTech
Pasadena, CA

We present fast spectral solvers for time-domain Partial Differential Equations. Based on a novel Fourier-Continuation (FC) method for the resolution of the Gibbs phenomenon, these methodologies give rise to time-domain solvers for PDEs for general engineering problems and structures. The methods enjoy a number of desirable properties, including spectral time evolution essentially free of pollution or dispersion errors for general PDEs in the time domain, with conditional/unconditional stability for explicit/alternating-direction methods and high order of temporal accuracy. A variety of applications to linear and nonlinear PDE problems will be presented, including the diffusion and wave equations, the Navier-Stokes equations and the elastic wave equation, demonstrating the significant improvements the new algorithms can provide over the accuracy and speed resulting from other approaches.

Oscar Bruno received his Ph.D. degree from the Courant Institute of Mathematical Sciences, New York University. Following graduation, he held a two-year position as Visiting Assistant Professor with the University of Minnesota, and he then joined the faculty of the Georgia Institute of Technology (Georgia Tech), where he served as Assistant and Associate Professor. After a four-year period with Georgia Tech, in 1995 he joined the faculty of the California Institute of Technology (Caltech), where he has served as Professor in the Department of Applied and Computational Mathematics since 1998, and as Executive Officer of that department during 1998-2000. Dr. Bruno’s research interests lie in areas of optics, elasticity and electromagnetism, remote sensing and radar, overall electromagnetic and elastic behavior of materials (solids, fluids, composites materials, multiple-scale geometries), and phase transitions. Dr. Bruno has directed 37 graduate students and postdocs during his career, and his research efforts have resulted in the publication of more than 100 refereed articles, and have been acknowledged by his plenary presentations at many international conferences, his service on editorial boards of important scientific journals, including the SIAM Journal of Applied Mathematics, the SIAM Journal on Scientific Computing, and the Proceedings of the Royal Society of London, and his election to honorary societies, most notably the Council for the Society for Industrial and Applied Mathematics. Dr. Bruno is a recipient of the Sigma-Xi faculty award, the Friedrichs Award for an outstanding dissertation in mathematics, a Young Investigator Award from the National Science Foundation. and a Sloan Foundation Fellowship. Dr. Bruno is a SIAM Fellow in the class of 2013, and a National Security NSSEFF Vannevar Bush fellow, in the class of 2016.

Wednesday, August 28, 2019
3:30 PM
Stauffer Science Lecture Hall, Room 102 (SLH 102)

Refreshments will be served at 3:15 pm.

host: Pahlevan

Insights into the Nonlinear Evolution of Flame Fronts through Experiments and Models

Basile Radisson

Postdoctoral Scholar
Department of Aerospace & Mechanical Engineering
USC

Due to the exothermicity of combustion reaction, premixed flames are intrinsically unstable. Consequently, cellular patterns are formed on the flame front resulting in rich and complex dynamics. Combustion involves several hundreds of elementary chemical reactions occurring at a submillimetric interface, rendering a detailed description computationally intractable. Simplified models offer much insight into these complex dynamics. Through asymptotic analysis, the shape of the flame front can be described by a set of poles and their dynamic evolution in the complex plane. Here, we demonstrate for the first time the validity of such model in comparison to experimental flame evolution. A premixed flame propagates in a reactive mixture held between two vertically oriented ceramic glass plates separated by a 5mm gap. By extracting a flame front from this experiment, we demonstrate the feasibility of describing the shape of the front by a set of poles’ solutions. The flame front dynamics are well described for approximately ten times the characteristic time of the instability. Beyond this time, the comparison is limited by the sensitivity to initial condition. However, by studying statistical properties of the flame front (here statistics of cell sizes), we demonstrate that the pole description is still valid at long time. Moreover, these statistics satisfy a gamma distribution, characteristic of phenomena for which the elementary interaction rule is of additive nature and which results here from the pole to pole attraction. This analytical prediction of the cell-size distribution could be of great interest for the understanding of turbulent flame dynamics.

We will conclude this presentation by commenting on the role of gravity and the influence of burner walls.

Basile Radisson is a post-doctoral scholar in the Aerospace and Mechanical Engineering department at the University of Southern California since June 2019. Prior to joining USC, Basile received his PhD from IRPHE, Aix-Marseille Université, France, working on flame front dynamics under the supervision of C. Almarcha and B. Denet. Basile’s research interests lie in instability phenomena driven by geometric non-linearities. He is currently working on snap instabilities in fast elastic filaments under the supervision of E. Kanso.

Wednesday, September 4, 2019
3:30 PM
Stauffer Science Lecture Hall, Room 102 (SLH 102)

Refreshments will be served at 3:15 pm.

host: Kanso

Settling of Cohesive Sediment: Particle-resolved Simulations

Eckart Meiburg

Professor
Department of Mechanical Engineering
UC Santa Barbara
Santa Barbara, CA

We develop a physical and computational model for performing fully coupled, grain-resolving Direct Numerical Simulations of cohesive sediment, based on the Immersed Boundary Method. The model distributes the cohesive forces over a thin shell surrounding each particle, thereby allowing for the spatial and temporal resolution of the cohesive forces during particle-particle interactions.

We test and validate the cohesive force model for binary particle interactions in the Drafting-Kissing-Tumbling (DKT) configuration. Cohesive sediment grains can remain attached to each other during the tumbling phase following the initial collision, thereby giving rise to the formation of flocs. The DKT simulations demonstrate that cohesive particle pairs settle in a preferred orientation, with particles of very different sizes preferentially aligning themselves in the vertical direction, so that the smaller particle is drafted in the wake of the larger one. This preferred orientation of cohesive particle pairs is found to remain influential for much larger simulations of 1,261 polydisperse particles released from rest. These simulations reproduce several earlier experimental observations by other authors, such as the accelerated settling of sand and silt particles due to particle bonding, the stratification of cohesive sediment deposits, and the consolidation process of the deposit. This final phase also shows the build-up of cohesive and direct contact intergranular stresses. The simulations demonstrate that cohesive forces accelerate the overall settling process primarily because smaller grains attach to larger ones and settle in their wakes. An investigation of the energy budget shows that the work of the collision forces substantially modifies the relevant energy conversion processes.

Eckart Meiburg received his Ph.D. from the University of Karlsruhe. After a postdoc at Stanford, he became an assistant professor in applied mathematics at Brown. He then moved to USC as associate then full professor. He later moved to UC Santa Barbara.

Meiburg’s research interests are fluid dynamics and transport phenomena, primarily computational fluid dynamics. He uses highly resolved direct numerical simulations to investigate physical mechanisms governing the spatio-temporal evolution of a wide variety of geophysical, porous media, and multiphase flow fields. Some of his current interests are gravity and turbidity currents, Hele-Shaw displacements, double-diffusive phenomena in particle laden flows, and internal bores.

Meiburg has received a Presidential Young Investigator Award, a Humboldt Senior Research Award, and a Senior Gledden Fellowship (Institute of Advanced Studies, University of Western Australia). He is fellow of the American Physical Society and the ASME, was the 2012 Lorenz G. Straub Award Keynote Speaker (Univ. Minn.), gave the Ronald F. Probstein Lecture at MIT in 2018, and was Shimizu Visiting Professor at Stanford University.

Wednesday, September 11, 2017
3:30 PM
Stauffer Science Lecture Hall, Room 102 (SLH 102)

Refreshments will be served at 3:15 pm.

host: Bermejo-Moreno

Design & Implementation of a 3D-PTV System

Dana Dabiri

Associate Professor
William E. Boeing Department of Aeronautics & Astronautics
University of Washington
Seattle, WA

The dream of experimental fluid dynamicists is to be able to measure complex, three-dimensional turbulent flow fields globally with very high spatial and temporal resolution. While we are still far from fully realizing this dream, significant progress has been made towards this goal during the last three decades. Early quantitative measurement methods using Pitot tubes, Venturi tubes and later measurement methods, such as Hot Wire Anemometry (HWA) and Laser-Doppler Anemometry (LDA), by their nature, were measurement methods that provided instantaneous velocity signals at single-points through time. Early emphasis in turbulence research and its theoretical advancement therefore necessitated a statistical description of turbulent flow fields, which relied heavily upon measurements provided by these single-point measurement techniques. Since the early seventies, the discovery of the existence of three-dimensional coherent structures within turbulent flows using qualitative flow visualization methods (i.e. shadowgraphs, Schlieren systems, dye injection, etc.) has been of significant interest for turbulence researchers. While flow visualization techniques have been around since the days of Prandtl, it is only due to the advent of modern imaging, laser, and data acquisition technology has allowed for qualitative flow visualization to become quantitative. These advents have allowed for the development and advancement of are relatively new measurement technique, Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV) in two dimensions, and more recently in 3 dimensions. Because of its ability to provide global two/three-dimensional kinematic information as well as its ability to map the evolution of coherent structures through time, PIV/PTV has become a powerful tool in studying, understanding, and modeling fluid flow behavior. In this talk, I will describe the particulars of the 3D Particle Tracking Velocimetry method we have developed and touch on some applications in microflows and LES studies.

Dana Dabiri is Associate Professor at the William E. Boeing Department of Aeronautics & Astronautics at the University of Washington, in Seattle. He received his B.S. in Mechanical Engineering at the University of California, San Diego in 1985; he received his M.S. in Mechanical Engineering at the University of California, Berkeley in 1987; and he received his PhD in Aerospace Engineering at the University of California, San Diego in 1992. He was a Post-doc at Caltech from 1992-1993, and continued at Caltech as a research scientist until the end of 2001. In 2002, he joined the faculty at the William E. Boeing Department of Aeronautics & Astronautics as an Assistant Professor, and was promoted as an Associate Professor in 2009. He serves as an associate editor for the Journal of Visualization since 2009. His work pursues developing novel ways for quantitatively visualizing the movements of fluids. Most recently, Professor Dabiri’s research activities have developed novel implementations of 2D and 3D digital particle tracking velocimetry (2DPTV & 3DPTV) system that allows for high-resolution measurements of fluid flows.

Wednesday, September 25, 2019
3:30 PM
Stauffer Science Lecture Hall, Room 102 (SLH 102)

Refreshments will be served at 3:15 pm.

host: Pahlevan

Navigating in a Turbulent Environment

Mimi Koehl

Professor
Department of Integrative Biology
University of California, Berkeley
Berkeley, CA

When organisms locomote and interact in nature, they must navigate through complex habitats that vary on many spatial scales, and they are buffeted by turbulent wind or water currents and waves that also vary on a range of spatial and temporal scales. We have been using the microscopic larvae of bottom-dwelling marine animals to study how the interaction between the swimming or crawling by an organism and the turbulent water flow around them determines how they move through the environment. Many bottom-dwelling marine animals produce microscopic larvae that are dispersed to new sites by ambient water currents, and then must land and stay put on surfaces in suitable habitats. Field and laboratory measurements enabled us to quantify the fine-scale, rapidly-changing patterns of water velocity vectors and of chemical cue concentrations near coral reefs and along fouling communities (organisms growing on docks and ships). We also measured the swimming behavior of larvae of reef-dwelling and fouling community animals, and their responses to chemical and mechanical cues. We used these data to design agent-based models of larval behavior. By putting model larvae into our real-world flow and chemical data, which varied on spatial and temporal scales experienced by microscopic larvae, we could explore how different responses by larvae affected their transport and their recruitment into reefs or fouling communities. The most effective strategy for recruitment depends on habitat.

Mimi Koehl, a Professor of the Graduate School in the Department of Integrative Biology at the University of California, Berkeley, earned her Ph.D. in Zoology at Duke University. She studies the physics of how organisms interact with their environments, focusing on how microscopic creatures swim and capture food in turbulent water flow, how organisms glide in turbulent wind, how wave-battered marine organisms avoid being washed away, and how olfactory antennae catch odors from water or air moving around them.

Professor Koehl is a member of the National Academy of Sciences and the American Academy of Arts and Sciences, and is a Fellow of the American Physical Society. Her awards include a MacArthur “genius grant”, a Presidential Young Investigator Award, a Guggenheim Fellowship, the John Martin Award (Association for the Sciences of Limnology and Oceanography, for “for research that created a paradigm shift in an area of aquatic sciences”), the Borelli Award (American Society of Biomechanics, for “outstanding career accomplishment”), the Rachel Carson Award (American Geophysical Union, for “cutting-edge ocean science”), and the Muybridge Award (International Society of Biomechanics “highest honor”).

Wednesday, October 2, 2019
3:30 PM
Stauffer Science Lecture Hall, Room 102 (SLH 102)

Refreshments will be served at 3:15 pm.

host: Kanso

Active Particles in Complex Fluids

Gwynn Elfring

Associate Professor
Department of Mechanical Engineering
and
Institute of Applied Mathematics
University of British Columbia
Vancouver, BC

Active particles are self-driven objects, biological or otherwise, which convert stored or ambient energy into systematic motion. The motion of small active particles in Newtonian fluids has received considerable attention, with interest ranging from phoretic propulsion to biological locomotion, whereas studies on active bodies immersed in complex fluids are comparatively scarce. In this talk I will discuss a theoretical formalism for understanding the motion of active particles in complex fluids and then discuss the effects of viscosity gradients, viscoelasticity and shear-thinning rheology in the context of biological locomotion and the propulsion of colloidal Janus particles.

Gwynn Elfring is an Associate Professor in the Department of Mechanical Engineering and the Institute of Applied Mathematics at the University of British Columbia, and currently a Visiting Associate in the Division of Chemistry and Chemical Engineering at the California Institute of Technology. His group at UBC conducts research on biological locomotion and fluid-body interactions in complex fluids and interfaces. Previously, he completed a Ph.D. at the University of California San Diego under the supervision of Eric Lauga and a postdoctoral fellowship with L. Gary Leal and Todd M. Squires at the University of California Santa Barbara.

Wednesday, October 9, 2019
3:30 PM
Stauffer Science Lecture Hall, Room 102 (SLH 102)

Refreshments will be served at 3:15 pm.

host: Kanso

host: Pantano

host: Pahlevan

host: Pahlevan

host: Kanso

host: Luhar

host: Oberai

Bermejo Moreno