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Shock Capturing Methods
In computational fluid dynamics, shock-capturing methods are a class of techniques for computing inviscid flows with shock waves. The computation of flow containing shock waves is an extremely difficult task because such flows result in sharp, discontinuous changes in flow variables such as pressure, temperature, density, and velocity across the shock. Method In shock-capturing methods, the governing equations of inviscid flows (i.e. Euler equations) are cast in conservation form and any shock waves or discontinuities are computed as part of the solution. Here, no special treatment is employed to take care of the shocks themselves, which is in contrast to the shock-fitting method, where shock waves are explicitly introduced in the solution using appropriate shock relations ( Rankine–Hugoniot relations). The shock waves predicted by shock-capturing methods are generally not sharp and may be smeared over several grid elements. Also, classical shock-capturing methods have the disadvan ... [...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 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 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. CFD is applie ... [...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 an ... [...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 cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Björn Engquist
Björn Engquist (also ''Bjorn Engquist''; born 2 June 1945 in Stockholm) has been a leading contributor in the areas of multiscale modeling and scientific computing, and a productive educator of applied mathematicians. Life He received his PhD in numerical analysis from University of Uppsala in 1975, and taught there during the following years while also holding a professorship at the University of California, Los Angeles. In 2001, he moved to Princeton University as the Michael Henry Stater University Professor of Mathematics and served as the director of the Program in Applied and Computational Mathematics. He has also been professor at the Royal Institute of Technology in Stockholm since 1993, and is director of the Parallel and Scientific Computing Institute. Engquist currently holds the Computational and Applied Mathematics Chair I at the Institute for Computational Engineering and Sciences at the University of Texas at Austin, after leaving Princeton in 2005. Research ... [...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] |
Dale A
Dale or dales may refer to: Locations * Dale (landform), an open valley * Dale (place name element) Geography ;Australia * The Dales (Christmas Island), in the Indian Ocean ;Canada * Dale, Ontario ;Ethiopia * Dale (woreda), district ;Norway * Dale, Fjaler, the administrative centre of Fjaler municipality, Vestland county * Dale, Sel, a village in Sel municipality in Innlandet county * Dale, Vaksdal, the administrative centre of Vaksdal municipality, Vestland county * Dale, Vaksdal, the administrative bop on the head * Dale Church (Fjaler), a church in Fjaler municipality, Vestland county * Dale Church (Luster), a church in Luster municipality, Vestland county *Dale Church (Vaksdal), a church in Vaksdal municipality, Vestland county *Dale Church (also known as Norddal Church), a church in Fjord municipality, Møre og Romsdal county ;Poland * Dale, Lesser Poland Voivodeship (south Poland) ;Sweden *The Dales, English exonym for Dalarna province ;United Kingdom * Dale, Cumbr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randall J
Randall may refer to the following: Places United States *Randall, California, former name of White Hall, California, an unincorporated community * Randall, Indiana, a former town *Randall, Iowa, a city *Randall, Kansas, a city * Randall, Minnesota, a city * Randall, West Virginia, an unincorporated community *Randall, Wisconsin, a town * Randall, Burnett County, Wisconsin, an unincorporated community *Randall County, Texas * Randall Creek, in Nebraska and South Dakota *Randall's Island, part of New York City *Camp Randall, Madison, Wisconsin, a former army camp, on the National Register of Historic Places * Fort Randall, South Dakota, a former military base, on the National Register of Historic Places Elsewhere * Mount Randall, Victoria Land, Antarctica * Randall Rocks, Graham Land, Antarctica *Randall, a community in the town of New Tecumseth, Ontario, Canada Businesses *Randall Amplifiers, a manufacturer of guitar amplifiers *Randall House Publications, American publisher * Ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John D
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died c. AD 30), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (lived c. AD 30), one of the twelve apostles of Jesus * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antony Jameson
Guy Antony Jameson, Fellow of the Royal Society, FRS, FREng (born 20 November 1934, Gillingham, Kent) is Professor in the Department of Aerospace Engineering at Texas A&M University. Jameson is known for his pioneering work in the field of computational fluid dynamics. He has published more than 300 scientific papers (authored or co-authored) in a wide range of areas including computational fluid dynamics, aerodynamics, and control theory. Jameson was elected a member of the National Academy of Engineering in 1997 for contributions to aircraft through the development of computational fluid dynamics. He was awarded the 2005 Elmer A. Sperry Award and received the 2015 AIAA/ASME/SAE/AHS Daniel Guggenheim Medal for lifetime achievement. He is an Honorary Fellow of the AIAA. Early life Born in Gillingham, Kent, UK Jameson spent much of his early childhood in India where his father was stationed as a British Army Officer. He first attended school at St. Edward's School, Shimla. Subse ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roe Solver
The Roe approximate Riemann solver, devised by Phil Roe, is an approximate Riemann solver based on the Godunov scheme and involves finding an estimate for the intercell numerical flux or Godunov flux F_ at the interface between two computational cells U_ and U_, on some discretised space-time computational domain. Roe scheme Quasi-linear hyperbolic system A non-linear system of hyperbolic partial differential equations representing a set of conservation laws in one spatial dimension can be written in the form : \frac + \frac = 0. Applying the chain rule to the second term we get the quasi-linear hyperbolic system : \frac + A(\boldsymbol)\frac = 0, where A is the Jacobian matrix of the flux vector \boldsymbol(\boldsymbol). Roe matrix The Roe method consists of finding a matrix \tilde(\boldsymbol_i,\boldsymbol_) that is assumed constant between two cells. The Riemann problem can then be solved as a truly linear hyperbolic system at each cell interface. The Roe matrix must obey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann Solver
A Riemann solver is a numerical method used to solve a Riemann problem. They are heavily used in computational fluid dynamics and computational magnetohydrodynamics. Definition Generally speaking, Riemann solvers are specific methods for computing the numerical flux across a discontinuity in the Riemann problem. They form an important part of high-resolution schemes; typically the right and left states for the Riemann problem are calculated using some form of nonlinear reconstruction, such as a flux limiter or a WENO method, and then used as the input for the Riemann solver. Exact solvers Sergei K. Godunov is credited with introducing the first exact Riemann solver for the Euler equations, by extending the previous CIR (Courant-Isaacson-Rees) method to non-linear systems of hyperbolic conservation laws. Modern solvers are able to simulate relativistic effects and magnetic fields. More recent research shows that an exact series solution to the Riemann problem exists, which may ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
