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Flux Limiters
Flux limiters are used in high resolution schemes – numerical schemes used to solve problems in science and engineering, particularly fluid dynamics, described by partial differential equations (PDEs). They are used in high resolution schemes, such as the MUSCL scheme, to avoid the spurious oscillations (wiggles) that would otherwise occur with high order spatial discretization schemes due to shocks, discontinuities or sharp changes in the solution domain. Use of flux limiters, together with an appropriate high resolution scheme, make the solutions total variation diminishing (TVD). Note that flux limiters are also referred to as slope limiters because they both have the same mathematical form, and both have the effect of limiting the solution gradient near shocks or discontinuities. In general, the term flux limiter is used when the limiter acts on system ''fluxes'', and slope limiter is used when the limiter acts on system ''states'' (like pressure, velocity etc.). How they wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
High Resolution Scheme
High-resolution schemes are used in the numerical solution of partial differential equations where high accuracy is required in the presence of shocks or discontinuities. They have the following properties: *Second- or higher-Order of accuracy, order spatial accuracy is obtained in smooth parts of the solution. *Solutions are free from spurious oscillations or wiggles. *High accuracy is obtained around shocks and discontinuities. *The number of mesh points containing the wave is small compared with a first-order scheme with similar accuracy. General methods are often not adequate for accurate resolution of steep gradient phenomena; they usually introduce non-physical effects such as ''smearing'' of the solution or ''spurious oscillations''. Since publication of ''Godunov's order barrier theorem'', which proved that linear methods cannot provide non-oscillatory solutions higher than first order (Godunov 1954, Godunov 1959), these difficulties have attracted much attention and a nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Karman Institute
The von Karman Institute for Fluid Dynamics (VKI) is a non-profit educational and scientific organization which specializes in three specific fields: aeronautics and aerospace, environment and applied fluid dynamics, turbomachinery and propulsion. Founded in 1956, it is located in Sint-Genesius-Rode, Belgium. About The von Karman Institute for Fluid Dynamics is a non-profit international, educational and scientific organization which is working in three specific fields: ''aeronautics and aerospace, environment and applied fluid dynamics, turbomachinery and Vehicle propulsion, propulsion''. The VKI provides education in these specific areas for students from all over the world. A hundred students come to the Institute each year to study fluid dynamics, for a PhD programme, a research master in Fluid Dynamics, a final year project and also to gather further knowledge while doing a work placement in a specific area. Each year, Lecture Series and events are being organized insi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Total Variation Diminishing
In numerical methods, total variation diminishing (TVD) is a property of certain discretization schemes used to solve hyperbolic partial differential equations. The most notable application of this method is in computational fluid dynamics. The concept of TVD was introduced by Ami Harten. Model equation In systems described by partial differential equations, such as the following hyperbolic advection equation, :\frac + a\frac = 0, the total variation (TV) is given by :TV(u(\cdot,t)) = \int \left, \frac \ \mathrmx , and the total variation for the discrete case is, :TV(u^n) = TV(u(\cdot,t^n)) = \sum_j \left, u_^n - u_j^n \ . where u_^n=u(x_,t^n). A numerical method is said to be total variation diminishing (TVD) if, :TV \left( u^\right) \leq TV \left( u^\right) . Characteristics A numerical scheme is said to be monotonicity preserving if the following properties are maintained: *If u^ is monotonically increasing (or decreasing) in space, then so is u^. proved the follow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sergei K
Sergius is a male given name of Ancient Roman origin after the name of the Latin ''gens'' Sergia or Sergii of regal and republican ages. It is a common Christian name, in honor of Saint Sergius, or in Russia, of Saint Sergius of Radonezh, and has been the name of four popes. It has given rise to numerous variants, present today mainly in the Romance (Serge, Sergio, Sergi) and Slavic languages (Serhii, Sergey, Serguei). It is not common in English, although the Anglo-French name Sergeant is possibly related to it. Etymology The name originates from the Roman ''nomen'' (patrician family name) ''Sergius'', after the name of the Roman ''gens'' of Latin origins Sergia or Sergii from Alba Longa, Old Latium, counted by Theodor Mommsen as one of the oldest Roman families, one of the original 100 ''gentes originarie''. It has been speculated to derive from a more ancient Etruscan name but the etymology of the nomen Sergius is problematic. Chase hesitantly suggests a connection with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
High Resolution Scheme
High-resolution schemes are used in the numerical solution of partial differential equations where high accuracy is required in the presence of shocks or discontinuities. They have the following properties: *Second- or higher-Order of accuracy, order spatial accuracy is obtained in smooth parts of the solution. *Solutions are free from spurious oscillations or wiggles. *High accuracy is obtained around shocks and discontinuities. *The number of mesh points containing the wave is small compared with a first-order scheme with similar accuracy. General methods are often not adequate for accurate resolution of steep gradient phenomena; they usually introduce non-physical effects such as ''smearing'' of the solution or ''spurious oscillations''. Since publication of ''Godunov's order barrier theorem'', which proved that linear methods cannot provide non-oscillatory solutions higher than first order (Godunov 1954, Godunov 1959), these difficulties have attracted much attention and a nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Godunov's Theorem
In numerical analysis and computational fluid dynamics, Godunov's theorem — also known as Godunov's order barrier theorem — is a mathematical theorem important in the development of the theory of high resolution schemes for the numerical solution of partial differential equations. The theorem states that: :''Linear numerical schemes for solving partial differential equations (PDE's), having the property of not generating new extrema (monotone scheme), can be at most first-order accurate.'' Professor Sergei K. Godunov originally proved the theorem as a Ph.D. student at Moscow State University. It is his most influential work in the area of applied and numerical mathematics and has had a major impact on science and engineering, particularly in the development of methods used in computational fluid dynamics (CFD) and other computational fields. One of his major contributions was to prove the theorem (Godunov, 1954; Godunov, 1959), that bears his name. The theorem We generally fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bram Van Leer
Bram van Leer is Arthur B. Modine Emeritus Professor of aerospace engineering at the University of Michigan, in Ann Arbor. He specializes in ''Computational fluid dynamics (CFD)'', ''fluid dynamics'', and ''numerical analysis.'' His most influential work lies in CFD, a field he helped modernize from 1970 onwards. An appraisal of his early work has been given by C. Hirsch (1979) An astrophysicist by education, van Leer made lasting contributions to CFD in his five-part article series “Towards the Ultimate Conservative Difference Scheme (1972-1979),” where he extended Godunov's finite-volume scheme to the second order (MUSCL). Also in the series, he developed non-oscillatory interpolation using limiters, an approximate Riemann solver, and discontinuous-Galerkin schemes for unsteady advection. Since joining the University of Michigan's Aerospace Engineering Department (1986), he has worked on convergence acceleration by local preconditioning and multigrid relaxation for Euler and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Dynamics
In physics 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'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). 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. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanley Osher
Stanley Osher (born April 24, 1942) is an American mathematician, known for his many contributions in shock capturing, level-set methods, and PDE-based methods in computer vision and image processing. Osher is a professor at the University of California, Los Angeles (UCLA), Director of Special Projects in the Institute for Pure and Applied Mathematics (IPAM) and member of the California NanoSystems Institute (CNSI) at UCLA. He has a daughter, Kathryn, and a son, Joel. Education * BS, Brooklyn College, 1962 * MS, New York University, 1964 * PhD, New York University, 1966 Research interests * Level-set methods for computing moving fronts * Approximation methods for hyperbolic conservation laws and Hamilton–Jacobi equations * Total variation (TV) and other PDE-based image processing techniques * Scientific computing * Applied partial differential equations * L1/TV-based convex optimization Osher is listed as an ISI highly cited researcher. Research contributions Osher was th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philip L
Philip, also Phillip, is a male given name, derived from the Greek (''Philippos'', lit. "horse-loving" or "fond of horses"), from a compound of (''philos'', "dear", "loved", "loving") and (''hippos'', "horse"). Prominent Philips who popularized the name include kings of Macedonia and one of the apostles of early Christianity. ''Philip'' has many alternative spellings. One derivation often used as a surname is Phillips. It was also found during ancient Greek times with two Ps as Philippides and Philippos. It has many diminutive (or even hypocoristic) forms including Phil, Philly, Lip, Pip, Pep or Peps. There are also feminine forms such as Philippine and Philippa. Antiquity Kings of Macedon * Philip I of Macedon * Philip II of Macedon, father of Alexander the Great * Philip III of Macedon, half-brother of Alexander the Great * Philip IV of Macedon * Philip V of Macedon New Testament * Philip the Apostle * Philip the Evangelist Others * Philippus of Croton (c. 6th centur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
