In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics and hydrodynamics. Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.
In continuum mechanics, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point, as would be seen by an observer located at that point and traveling along with the flow. It is an important quantity in the dynamical theory of fluids and provides a convenient framework for understanding a variety of complex flow phenomena, such as the formation and motion of vortex rings.
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of a particular problem can be used for comparison. A final validation is often performed using full-scale testing, such as flight tests.
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, as well as geophysics, oceanography, meteorology, astrophysics, and biology.
Computational aeroacoustics is a branch of aeroacoustics that aims to analyze the generation of noise by turbulent flows through numerical methods.
James Albert Sethian is a professor of mathematics at the University of California, Berkeley and the head of the Mathematics Group at the United States Department of Energy's Lawrence Berkeley National Laboratory.
Fluid–structure interaction (FSI) is the interaction of some movable or deformable structure with an internal or surrounding fluid flow. Fluid–structure interactions can be stable or oscillatory. In oscillatory interactions, the strain induced in the solid structure causes it to move such that the source of strain is reduced, and the structure returns to its former state only for the process to repeat.
In computational fluid dynamics, the immersed boundary method originally referred to an approach developed by Charles Peskin in 1972 to simulate fluid-structure (fiber) interactions. Treating the coupling of the structure deformations and the fluid flow poses a number of challenging problems for numerical simulations. In the immersed boundary method the fluid is represented in an Eulerian coordinate system and the structure is represented in Lagrangian coordinates. For Newtonian fluids governed by the Navier–Stokes equations, the fluid equations are
In fluid dynamics, The projection method is an effective means of numerically solving time-dependent incompressible fluid-flow problems. It was originally introduced by Alexandre Chorin in 1967 as an efficient means of solving the incompressible Navier-Stokes equations. The key advantage of the projection method is that the computations of the velocity and the pressure fields are decoupled.
Roger Meyer Temam is a French applied mathematician working in numerical analysis, nonlinear partial differential equations and fluid mechanics. He graduated from the University of Paris – the Sorbonne in 1967, completing a doctorate under the direction of Jacques-Louis Lions. He has published over 400 articles, as well as 12 books.
Roland Glowinski was a French-American mathematician. He obtained his PhD in 1970 from Jacques-Louis Lions and was known for his work in applied mathematics, in particular numerical solution and applications of partial differential equations and variational inequalities. He was a member of the French Academy of Sciences and held an endowed chair at the University of Houston from 1985. Glowinski wrote many books on the subject of mathematics. In 2012, he became a fellow of the American Mathematical Society.
In fluid dynamics, vortex stretching is the lengthening of vortices in three-dimensional fluid flow, associated with a corresponding increase of the component of vorticity in the stretching direction—due to the conservation of angular momentum.
Mohammed Yousuff Hussaini is an Indian born American applied mathematician. He is the Sir James Lighthill Professor of Mathematics and Computational Science & Engineering at the Florida State University, United States. Hussaini is also the holder of the TMC Eminent Scholar Chair in High Performance Computing at FSU. He is widely known for his research in scientific computation, particularly in the field of computational fluid dynamics (CFD) and Control and optimization. Hussaini co-authored the popular book Spectral Methods in Fluid Dynamics with Claudio Canuto, Alfio Quarteroni, and Thomas Zang. He is the editor-in-chief of the journal Theoretical and Computational Fluid Dynamics.
Phillip Colella is an American applied mathematician and a member of the Applied Numerical Algorithms Group at the Lawrence Berkeley National Laboratory. He has also worked at Lawrence Livermore National Laboratory. He is known for his fundamental contributions in the development of mathematical methods and numerical tools used to solve partial differential equations, including high-resolution and adaptive mesh refinement schemes. Colella is a member of the US National Academy of Sciences.
In applied mathematics, the name finite pointset method is a general approach for the numerical solution of problems in continuum mechanics, such as the simulation of fluid flows. In this approach the medium is represented by a finite set of points, each endowed with the relevant local properties of the medium such as density, velocity, pressure, and temperature.
The viscous vortex domains (VVD) method is a mesh-free method of computational fluid dynamics for directly numerically solving 2D Navier-Stokes equations in Lagrange coordinates. It doesn't implement any turbulence model and free of arbitrary parameters. The main idea of this method is to present vorticity field with discrete regions (domains), which travel with diffusive velocity relatively to fluid and conserve their circulation. The same approach was used in Diffusion Velocity method of Ogami and Akamatsu, but VVD uses other discrete formulas
High-order compact finite difference schemes are used for solving third-order differential equations created during the study of obstacle boundary value problems. They have been shown to be highly accurate and efficient. They are constructed by modifying the second-order scheme that was developed by Noor and Al-Said in 2002. The convergence rate of the high-order compact scheme is third order, the second-order scheme is fourth order.
Thomas Yizhao Hou is the Charles Lee Powell Professor of Applied and Computational Mathematics in the Department of Computing and Mathematical Sciences at the California Institute of Technology. He is known for his work in numerical analysis and mathematical analysis.
The finite point method (FPM) is a meshfree method for solving partial differential equations (PDEs) on scattered distributions of points. The FPM was proposed in the mid-nineties in, and with the purpose to facilitate the solution of problems involving complex geometries, free surfaces, moving boundaries and adaptive refinement. Since then, the FPM has evolved considerably, showing satisfactory accuracy and capabilities to deal with different fluid and solid mechanics problems.
Lian-Ping Wang is a mechanical engineer and academic, most known for his work on computational fluid dynamics, turbulence, particle-laden flow, and immiscible multiphase flow, and their applications to industrial and atmospheric processes. He is the Chair Professor of Mechanics and Aerospace Engineering at the Southern University of Science and Technology in China, Professor of Mechanical Engineering, and Joint Professor of Physical Ocean Science and Engineering at University of Delaware.
