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Finite Volume
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 solutio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to Numerical methods for partial differential equations, numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematics, 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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Element Method
The 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. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are 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 numerical domain for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain. The sim ... [...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 simply 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 ... [...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 (french: link=no, Centre national de la recherche scientifique, CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 ... 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] |
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] |
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 thermodynamic terms ... References * External links The MITgcm home pageDepartment of Earth, Atmospheric and Planetary Science at MITThe ECCO2 consortium {{Atmospheric, Oceanographic and Climate Models Physical oceanography ... [...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] |
