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Finite Volume Method
The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations. In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite volume. Because the flux entering a given volume is identical to that leaving the adjacent volume, these methods are conservative. Another advantage of the finite volume method is that it is easily formulated to allow for unstructured meshes. The method is used in many computational fluid dynamics packages. "Finite volume" refers to the small volume surrounding each node point on a mesh. Finite volume methods can be compared and contrasted with the finite difference methods, which approximate derivatives using nodal values, or finite element methods, which create local approximations of a so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equation
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to how is thought of as an unknown number solving, e.g., an algebraic equation like . However, it is usually impossible to write down explicit formulae for solutions of partial differential equations. There is correspondingly a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity and stability. Among the many open questions are the existence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Element Method
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. Computers are usually used to perform the calculations required. With high-speed supercomputers, better solutions can be achieved and are often required to solve the largest and most complex problems. FEM is a general numerical method for solving partial differential equations in two- or three-space variables (i.e., some boundary value problems). There are also studies about using FEM to solve high-dimensional problems. To solve a problem, FEM subdivides a large system into smaller, simpler parts called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Differential Equations
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Numerical may refer to: * Number * Numerical digit * Numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GNU Free Document License
The GNU Free Documentation License (GNU FDL or GFDL) is a copyleft license for free documentation, designed by the Free Software Foundation (FSF) for the GNU Project. It is similar to the GNU General Public License, giving readers the rights to copy, redistribute, and modify (except for "invariant sections") a work and requires all copies and derivatives to be available under the same license. Copies may also be sold commercially, but, if produced in larger quantities (greater than 100), the original document or source code must be made available to the work's recipient. The GFDL was designed for manuals, textbooks, other reference and instructional materials, and documentation which often accompanies GNU software. However, it can be used for any text-based work, regardless of subject matter. For example, the free online encyclopedia Wikipedia uses the GFDL (coupled with the Creative Commons Attribution Share-Alike License) for much of its text, excluding text that was impor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raphaèle Herbin
Raphaèle Herbin is a French applied mathematician; she is known for her work on the finite volume method. Herbin has been a professor at Aix-Marseille University since 1995, and directs the Institut de Mathématiques de Marseille. She earned her doctorate in 1986 at Claude Bernard University Lyon 1, with the dissertation ''Approximation numérique d'inéquations variationnelles non linéaires par des méthodes de continuation'' supervised by Francis Conrad. Herbin is a co-author of the books ''Mesure, intégration, probabilités'' (Ellipses, 2013) and ''The gradient discretisation method'' (Springer, 2018). In 2017 the CNRS The French National Centre for Scientific Research (, , CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 eng ... gave Herbin their CNRS medal of innovation. References External linksHome page* {{DEFAULTSORT:Herbin, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Volume Method For Unsteady Flow
Unsteady flows are characterized as flows in which the properties of the fluid are time dependent. It gets reflected in the governing equations as the time derivative of the properties are absent. For Studying Finite-volume method for unsteady flow there is some governing equations > Governing Equation The conservation equation for the transport of a scalar in unsteady flow has the general form as \frac + \operatorname\left(\rho \phi \upsilon\right) = \operatorname\left(\Gamma \operatorname \phi\right) + S_\phi \rho is density and \phi is conservative form of all fluid flow, \Gamma is the Diffusion coefficient and S is the Source term. \operatorname\left(\rho \phi \upsilon\right) is Net rate of flow of \phi out of fluid element(convection), \operatorname\left(\Gamma \operatorname \phi\right) is Rate of increase of \phi due to diffusion, S_\phi is Rate of increase of \phi due to sources. \frac is Rate of increase of \phi of fluid element(transient), The first ter ... [...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 honour of Saint Sergius, or in Kyivan Rus', of Sergius of the Holy Caves (Saint Sergius the Obedient of the Kiev Caves), one of saint Fathers of Kyiv, 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, Srđan). It is not common in English, although the Anglo-French name Sargent 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 originaria''. It has been speculated to derive from a more ancien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MIT General Circulation Model
The MIT General Circulation Model (MITgcm) is a numerical computer code that solves the equations of motion governing the ocean or Earth's atmosphere using the finite volume method. It was developed at the Massachusetts Institute of Technology and was one of the first non-hydrostatic models of the ocean. It has an automatically generated adjoint that allows the model to be used for data assimilation. The MITgcm is written in the programming language Fortran. History See also * Physical oceanography * Global climate model A general circulation model (GCM) is a type of climate model. It employs a mathematical model of the general circulation of a planetary atmosphere or ocean. It uses the Navier–Stokes equations on a rotating sphere with thermodynamics, thermod ... References * External links The MITgcm home pageDepartment of Earth, Atmospheric and Planetary Science at MITThe ECCO2 consortium Physical oceanography Numerical climate and weather models {{ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
KIVA (software)
KIVA is a family of Fortran-based computational fluid dynamics software developed by Los Alamos National Laboratory (LANL). The software predicts complex fuel and air flows as well as ignition, combustion, and pollutant-formation processes in engines. The KIVA models have been used to understand combustion chemistry processes, such as auto-ignition of fuels, and to optimize diesel engines for high efficiency and low emissions. General Motors has used KIVA in the development of direct-injection, stratified charge gasoline engines as well as the fast burn, homogeneous-charge gasoline engine. Cummins reduced development time and cost by 10%–15% using KIVA to develop its high-efficiency 2007 ISB 6.7-L diesel engine that was able to meet 2010 emission standards in 2007. At the same time, the company realized a more robust design and improved fuel economy while meeting all environmental and customer constraints. History LANL's Computational Fluid Dynamics expertise hails from the ver ... [...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 Order, ORDER or Orders may refer to: * A socio-political or established or existing order, e.g. World order, Ancien Regime, Pax Britannica * Categorization, the process in which ideas and objects are recognized, differentiated, and understood ... 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 pu ... [...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: Professor Sergei 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 follow Wesseling (2001). Aside Assume a continuum problem described by a PDE is to be computed using a numerical scheme based upon a uniform computational grid and a one-step, constant step ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
