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Numerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs).
In numerical analysis, a multigrid method is an algorithm for solving differential equations using a hierarchy of discretizations. They are an example of a class of techniques called multiresolution methods, very useful in problems exhibiting multiple scales of behavior. For example, many basic relaxation methods exhibit different rates of convergence for short- and long-wavelength components, suggesting these different scales be treated differently, as in a Fourier analysis approach to multigrid. MG methods can be used as solvers as well as preconditioners.
Fluid mechanics is the branch of physics concerned with the mechanics of fluids and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and biomedical engineering, geophysics, oceanography, meteorology, astrophysics, and biology.
Applied mechanics is the branch of science concerned with the motion of any substance that can be experienced or perceived by humans without the help of instruments. In short, when mechanics concepts surpass being theoretical and are applied and executed, general mechanics becomes applied mechanics. It is this stark difference that makes applied mechanics an essential understanding for practical everyday life. It has numerous applications in a wide variety of fields and disciplines, including but not limited to structural engineering, astronomy, oceanography, meteorology, hydraulics, mechanical engineering, aerospace engineering, nanotechnology, structural design, earthquake engineering, fluid dynamics, planetary sciences, and other life sciences. Connecting research between numerous disciplines, applied mechanics plays an important role in both science and engineering.
J. Tinsley Oden is the Associate Vice President for Research, the Cockrell Family Regents' Chair in Engineering #2, the Peter O'Donnell, Jr. Centennial Chair in Computing Systems, a Professor of Aerospace Engineering and Engineering Mechanics, a Professor of Mathematics, and a Professor of Computer Science at The University of Texas at Austin. Oden has been listed as an ISI Highly Cited Author in Engineering by the ISI Web of Knowledge, Thomson Scientific Company.
Thomas Joseph Robert Hughes is a Professor of Aerospace Engineering and Engineering Mechanics and currently holds the Computational and Applied Mathematics Chair (III) at the Oden Institute at The University of Texas at Austin. Hughes has been listed as an ISI Highly Cited Author in Engineering by the ISI Web of Knowledge, Thomson Scientific Company.
Sir Richard Vynne Southwell, FRS was a British mathematician who specialised in applied mechanics as an engineering science academic.
Gretar Tryggvason is Department Head of Mechanical Engineering and Charles A. Miller Jr. Distinguished Professor at Johns Hopkins University. He is known for developing the front tracking method to simulate multiphase flows and free surface flows. Tryggvason was the editor-in-chief of Journal of Computational Physics from 2002–2015.
In fluid dynamics, hydrodynamic stability is the field which analyses the stability and the onset of instability of fluid flows. The study of hydrodynamic stability aims to find out if a given flow is stable or unstable, and if so, how these instabilities will cause the development of turbulence. The foundations of hydrodynamic stability, both theoretical and experimental, were laid most notably by Helmholtz, Kelvin, Rayleigh and Reynolds during the nineteenth century. These foundations have given many useful tools to study hydrodynamic stability. These include Reynolds number, the Euler equations, and the Navier–Stokes equations. When studying flow stability it is useful to understand more simplistic systems, e.g. incompressible and inviscid fluids which can then be developed further onto more complex flows. Since the 1980s, more computational methods are being used to model and analyse the more complex flows.
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Charbel Farhat is the Vivian Church Hoff Professor of Aircraft Structures in the School of Engineering and the inaugural James and Anna Marie Spilker Chair of the Department of Aeronautics and Astronautics, at Stanford University. He is also Professor of Mechanical Engineering, Professor in the Institute for Computational and Mathematical Engineering, and Director of the Stanford-King Abdulaziz City for Science and Technology Center of Excellence for Aeronautics and Astronautics. He currently serves on the Space Technology Industry-Government-University Roundtable.
Gábor Stépán, Hungarian professor of applied mechanics, member of the Hungarian Academy of Sciences, fellow of the International Academy for Production Engineering (CIRP), fellow of the Society for Industrial and Applied Mathematics (SIAM), former dean of the Faculty of Mechanical Engineering in the Budapest University of Technology and Economics. Won the Széchenyi Prize in 2011, the Thomas K. Caughey Dynamics Award in 2015, and the Delay Systems Lifetime Achievements Award in 2021. His research fields include nonlinear vibrations, delay-differential equations, and stability theory. He was elected as a fellow of the Society for Industrial and Applied Mathematics in 2017, "for contributions to the theory and analysis of delayed dynamical systems and their applications".
Marco Amabili is a professor who holds the Canada Research Chair in Vibrations and Fluid-Structure Interaction, Department of Mechanical Engineering at McGill University, Montreal, Québec, Canada.
Lois Graham was a professor of thermodynamics and cryogenics. She was the first woman to earn a mechanical engineering PhD in the United States.
Amit Agrawal is an Indian engineer and an institute chair professor at the department of mechanical engineering of the Indian Institute of Technology, Bombay. He leads a group of scientists who are involved in the development of next-generation diagnostic microdevices.
Rajat Mittal is a computational fluid dynamicist and a professor of mechanical engineering in the Whiting School of Engineering at Johns Hopkins University. He holds a secondary appointment in the Johns Hopkins University School of Medicine. He is known for his work on immersed boundary methods (IBMs) and applications of these methods to the study of fluid flow problems.
Francine Battaglia is an American aerospace engineer specializing in computational fluid dynamics, including the study of fluidized beds and of fire, fire whirls, and flame spread. Her other research interests include ventilation and energy usage in architectural design, and alternative and renewable energy systems. She is professor and chair in the Department of Mechanical and Aerospace Engineering of the University at Buffalo, where she directs the Computational Research for Energy Systems and Transport Laboratory.
Laura Lynn Pauley is an American mechanical engineer specializing in computational fluid dynamics, including the simulation of cavitation, flow separation, and large eddy simulation, with applications including the design of airfoils, boat propellors, and centrifugal pumps. She is a professor of mechanical engineering in the Penn State College of Engineering, the former Arthur L. Glenn Professor of Engineering Education at Penn State, and the interim executive director of the Penn State faculty senate.
Arezoo M. Ardekani is an Iranian-American physicist who is a professor at Purdue University. Her research considers the flow of complex fluids. She was elected a Fellow of the American Society of Mechanical Engineers in 2020 and a Fellow of the American Physical Society in 2022.
References
- ↑ Ghia, U; Ghia, K.N; Shin, C.T (December 1982), "High-Re solutions for incompressible flow using the Navier–Stokes equations and a multigrid method", Journal of Computational Physics, 48 (3): 387–411, doi:10.1016/0021-9991(82)90058-4
- 1 2 "Ghia, Urmila PhD", UC Directory, University of Cincinnati, retrieved 2022-12-24
- 1 2 3 4 5 6 Chalifoux, Amanda (October 2009), "Engineering her destiny: India native's career sets example for aspiring female scientists", UC Magazine, University of Cincinnati, retrieved 2022-12-24
- 1 2 3 4 "Alumni recognition awards: Professor Urmila Ghia", Vectors, Illinois Institute of Technology, p. 20, 2007, retrieved 2022-12-24– via Yumpu
- ↑ Worldcat catalog entry for Incremental L2-norm stability of systems governed by nonlinear partial differential equations , retrieved 2022-12-24
- ↑ McAfee, Katy (September 23, 2020), "UC program dedicated to closing the gender gap", The News Record, retrieved 2022-12-24
- ↑ All Fellows (PDF), ASME, 2022, retrieved 2022-12-24
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