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Bhatnagar–Gross–Krook Operator
The Bhatnagar–Gross–Krook operator (abbreviated BGK operator) term refers to a collision operator used in the Boltzmann equation and in the lattice Boltzmann method, a computational fluid dynamics technique. It is given by the formula : \Omega_i = -\tau^(n_i - n_i^\text), where n_i^\text is a local equilibrium value for the population of particles in the direction of link \mathbf_i. The term \tau is a relaxation time and related to the viscosity. The operator is named after Prabhu L. Bhatnagar, Eugene P. Gross, and Max Krook, the three scientists who introduced it in an article in ''Physical Review ''Physical Review'' is a peer-reviewed scientific journal. The journal was established in 1893 by Edward Nichols. It publishes original research as well as scientific and literature reviews on all aspects of physics. It is published by the Ame ...'' in 1954. References * Statistical mechanics Computational fluid dynamics {{compu-physics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernstein–Greene–Kruskal Modes
Bernstein–Greene–Kruskal modes (a.k.a. BGK modes) are nonlinear electrostatic waves that propagate in a collisionless plasma. They are nonlinear solutions to the Vlasov- Poisson system of equations in plasma physics, and are named after physicists Ira B. Bernstein, John M. Greene, and Martin D. Kruskal, who solved and published the exact solution for the one-dimensional unmagnetized case in 1957. BGK modes have been studied extensively in numerical simulations for two- and three-dimensional cases, and are believed to be produced by the two-stream instability. They have been observed as electron phase space holes (electrostatic solitary structures). and double layers in space plasmas, as well as in scattering experiments in the laboratory. Small-amplitude limit: Van Kampen modes ? It is generally claimed that in the linear limit BGK modes (e.g. in the small amplitude approximation) reduce to what is known as Van Kampen modes, named after Nico van Kampen who derived t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator (mathematics)
In mathematics, an operator is generally a Map (mathematics), mapping or function (mathematics), function that acts on elements of a space (mathematics), space to produce elements of another space (possibly and sometimes required to be the same space). There is no general definition of an ''operator'', but the term is often used in place of ''function'' when the domain of a function, domain is a set of functions or other structured objects. Also, the domain of an operator is often difficult to characterize explicitly (for example in the case of an integral operator), and may be extended so as to act on related objects (an operator that acts on functions may act also on differential equations whose solutions are functions that satisfy the equation). (see Operator (physics) for other examples) The most basic operators are linear maps, which act on vector spaces. Linear operators refer to linear maps whose domain and range are the same space, for example from \mathbb^n to \mathbb^n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boltzmann Equation
The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium; it was devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G. Lerner, G. L. Trigg, VHC publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1, ISBN (VHC Inc.) 0-89573-752-3. The classic example of such a system is a fluid with temperature gradients in space causing heat to flow from hotter regions to colder ones, by the random but biased transport of the particles making up that fluid. In the modern literature the term Boltzmann equation is often used in a more general sense, referring to any kinetic equation that describes the change of a macroscopic quantity in a thermodynamic system, such as energy, charge or particle number. The equation arises not by analyzing the individual positions and momenta of each particle in the fluid but rather by considering a probability distribution for the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Boltzmann Methods
The lattice Boltzmann methods (LBM), originated from the lattice gas automata (LGA) method (Hardy- Pomeau-Pazzis and Frisch- Hasslacher- Pomeau models), is a class of computational fluid dynamics (CFD) methods for fluid simulation. Instead of solving the Navier–Stokes equations directly, a fluid density on a lattice is simulated with streaming and collision (relaxation) processes. The method is versatile as the model fluid can straightforwardly be made to mimic common fluid behaviour like vapour/liquid coexistence, and so fluid systems such as liquid droplets can be simulated. Also, fluids in complex environments such as porous media can be straightforwardly simulated, whereas with complex boundaries other CFD methods can be hard to work with. Algorithm Unlike CFD methods that solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy) numerically, LBM models the fluid consisting of fictive particles, and such particles perform consecutive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Fluid Dynamics
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 dynamics, 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 (liquids and gases) with surfaces defined by Boundary value problem#Boundary value conditions, 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 turbulence, turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed Closed-form solution, analytical or Empirical research, empirical analysis of a particular problem can be used for compa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prabhu Lal Bhatnagar
Prabhu Lal Bhatnagar (8 August 1912 – 5 October 1976), commonly addressed as P. L. Bhatnagar, was an Indian mathematician known for his contribution to the Bhatnagar–Gross–Krook operator used in Lattice Boltzmann methods (LBM). Early years and career He was born in Kota in Rajasthan and was the second of five sons. He did his schooling in Rampura and later at Herberter College in Kota. After schooling he went to Maharajah's College in Jaipur where in 1935 he completed BSc with first rank, followed by MSc. His research career started at the Allahabad University under the supervision of Prof. B. N. Prasad on summability theory but soon he joined Prof. Amiya Charan Banerjee to work in differential equations. The results of his work (with Prof. Banerji, published in Proceeding of National Academy of Sciences, 1938) are included in the book of Erich Kamke. He became interested in the area of astrophysics after coming in contact with Meghnad Saha. In 1939 he obtained ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eugene P
Eugene may refer to: People and fictional characters * Eugene (given name) Eugene is a common male given name that comes from the Greek language, Greek εὐγενής (''eugenēs''), "noble", literally "well-born", from εὖ (''eu''), "well" and γένος (''genos''), "race, stock, kin". [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
