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	Finite volume method - Wikipedia, the free encyclopedia
		The finite volume method is a method for representing and evaluating partial differential equations as 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.
		Finite volume schemes are conservative as cell averages change through the edge fluxes.
	en.wikipedia.org /wiki/Finite_volume_method (440 words)

	Finite element method - Wikipedia, the free encyclopedia
		The method was provided with a rigorous mathematical foundation in 1973 with the publication of Strang and Fix's An Analysis of The Finite Element Method, and has since been generalized into a branch of applied mathematics for numerical modeling of physical systems in a wide variety of engineering disciplines, e.g., electromagnetism and fluid dynamics.
		The development of the finite element method in structural mechanics is often based on an energy principle, e.g., the virtual work principle or the minimum total potential energy principle, which provides a general, intuitive and physical basis that has a great appeal to structural engineers.
		Methods that use higher degree piecewise polynomial basis functions are often called spectral element methods, especially if the degree of the polynomials increases as the triangulation size h goes to zero.
	en.wikipedia.org /wiki/Finite_element_method (2159 words)

	FPSO Roll Motions
		The Euler method seemed to predict, qualitatively, the separated flow patterns in the case of the bilge keels, and the expected increase in the hydrodynamic roll coefficients with the size of the bilge keel.
		Our preliminary studies have indicated that a finite volume method (developed in the past to predict the flow around propulsors or thrusters) that solves for the unsteady flow in the time domain is the most computationally efficient, yet accurate method, in dealing with the separated flow behind the bilge keels of a hull.
		The method was validated extensively and systematically, by first recovering the well known solution of a plane progressive wave, and then by comparisons of the added mass and damping coefficients with those of Vugts in the case of heave motions of a rectangular hull section (without bilge keels), for a wide range of reduced frequencies.
	otrc.tamu.edu /Pages/fpsoroll.htm (5054 words)

	Multi-scale finite-volume method for use in subsurface flow simulation patent invention (Site not responding. Last check: 2007-10-19)
		The method of claim 3 wherein: the solving of the pressure equation of step (ii) to obtain fine-scale pressures is performed on a system with larger support.
		The method of claim 4 wherein: the solving of the pressure equation of step (ii) may be performed by over-sampling around the coarse cells.
		The method of claim 3 wherein: the solving of the pressure equation of step (ii) may be performed by over-sampling around the coarse cells.
	www.freshpatents.com /Multi-scale-finite-volume-method-for-use-in-subsurface-flow-simulation-dt20050915ptan20050203725.php?type=claims (290 words)

	Songlin Zhu: Research3
		This paper presents the application of a finite-volume method for 3D fluid flow and heat transfer using non-orthogonal coordinates and a nonstaggered grid.
		Over all method is applied to predict the laminar flow through a 90 degree banded square duct and the natural convection in the LHRE''s cooling passage.
		The transport equation (1) was discrete d using a finite-volume method based on a nonstaggered grid system, where all variables are stored at their geometrical centers.
	www.unc.edu /~slzhu/research/CFD/method.html (716 words)

	Finite Volume Methods
		In [P-03], Section 3, a finite volume scheme is formulated in a very general setting consisting of a system of nonlinear evolution equations in arbitrary finite space dimension, each evolution equation living on a different polytope domain.
		In [KP-05], the finite volume scheme is specialized to the case of a nonlinear heat equation with piecewise constant diffusion coefficient.
		In [GKP-05], a finite volume scheme is devised for the case of anisotropic thermal conductivities, which was not covered in [P-03].
	www.wias-berlin.de /people/philip/projects/fvm (2023 words)

	FPSO Roll Motions
		The latter method was used for comparison of the hull pressures and roll moment as predicted from the viscous and the inviscid methods.
		The non-linear panel method should be much less computer intensive than the finite volume method, and will allow us to compare the effects of viscosity on the hydrodynamic coefficients in the case of large roll motions.
		Our viscous method (NS-2D) was tested with the commercial viscous flow code (Fluent) in the absence of a free-surface, in the case of a hull (without or with bilge keels) subject to a sinusoidal horizontal inflow, and our results (pressure distributions and forces) were found to be in good agreement with those of Fluent.
	otrc.tamu.edu /Pages/05fpsoroll.htm (6864 words)

	Finite volume -- CFD-Wiki, the ultimate free CFD reference
		Based on the control volume formulation of analytical fluid dynamics, the first step in the FVM is to divide the domain into a number of control volumes (aka cells, elements) where the variable of interest is located at the centroid of the control volume.
		FVM is the ideal method for computing discontinuous solutions arising in compressible flows.
		Since finite volume methods are conservative they automatically satisfy the jump conditions and hence give physically correct weak solutions.
	www.cfd-online.com /Wiki/Finite_volume (408 words)

	2.10.2 The finite volume method: finite volumes versus finite difference
		The finite volume method is used to discretize the equations in space.
		The expression ``finite volume'' actually has two meanings; one is the method of embedded or intersecting boundaries (shaved or lopped cells in our terminology) and the other is non-linear interpolation methods that can deal with non-smooth solutions such as shocks (i.e.
		This happens because the each direction is discretized independently in the finite difference method while the integrating over finite volume implicitly treats all directions simultaneously.
	mitgcm.org /sealion/online_documents/node44.html (278 words)

	Finite Volume Methods
		Among several possibilities to generate such approximations, it is the finite volume method which lies in the focus of research of the group.
		This method basically assumes that the computational domain is partitioned into a finite number of control volumes, open polygonal boxes around the discretization points, which in some way are similar to representative elementary volumes (REV) used in the derivation of a large class of physical models.
		In cooperation with R. Eymard (Univ. Marne la Vallee), the group studies a finite volume discretization of a wide class of nonlinear convection-diffusion equations.
	www.wias-berlin.de /research-groups/nummath/new-fv.html (228 words)

	FEM1D_PMETHOD - P-Method Finite Element Method for 1D problem.
		FEM1D_ADAPTIVE is a C++ program that applies the finite element method to a linear two point boundary value problem in a 1D region, using adaptive refinement to improve the solution.
		FREE_FEM_HEAT is a C++ program which uses the finite element method and the backward Euler method to solve the time-dependent heat equation on an arbitrary triangulated region in 2D.
		PLTMG_SINGLE is a FORTRAN77 library of routines for solving elliptic partial differential equations using the finite element method with piecewise linear triangles and the multigrid approach.
	www.csit.fsu.edu /~burkardt/cpp_src/fem1d_pmethod/fem1d_pmethod.html (864 words)

	Finite Volume Methods (Site not responding. Last check: 2007-10-19)
		Moreover, this interpretation leads to a heuristic method for calculating the force on each node, which is as simple to implement and comprehend as masses and springs.
		In the finite volume spirit, we also present a geometric rather than interpolating function definition of strain.
		We use the FVM and a quasi-incompressible, transversely isotropic, hyperelastic constitutive model to simulate contracting muscle tissue.
	graphics.stanford.edu /papers/fvm_sig03 (137 words)

	» Finite Volume Method (Site not responding. Last check: 2007-10-19)
		Analysis of the Cell Vertex Finite Volume Method for the Cauchy--Riemann Equations...
		Analysis of the Cell-Vertex Finite Volume Method for Hyperbolic...
		A Second-Order Finite Volume Method for the Incompressible Navier-Stokes Equations on Staggered Unstructured Grids...
	www.finitedifference.info /info/Finite-Volume-Method (157 words)

	syllabus04.htm (Site not responding. Last check: 2007-10-19)
		finite difference, finite volume, spectral methods) and consequently tend to be large in size, less detailed in the respective treatments and/or painfully lacking in examples.
		Finally, and perhaps most importantly, the finite volume technique is the numerical method upon which the FLUENT software package is based.
		By concentrating on the finite volume method, many of the numerical options available in the software will be nicely addressed in the text (in addition to the user manuals!).
	www.uvm.edu /~dhitt/me249/syllabus04.htm?tp=true (1855 words)

	Finite Volume Method (Site not responding. Last check: 2007-10-19)
		In finite volume approach, this integral is applied to each control volume, and the equation is turned into a set of equations for the inventory in each control volume.
		The accuracy of a finite volume scheme depends on the accuracy to which the surface integral can be evaluated.
		In particular, if the control volumes are all boxes of the same size, then the average concentration between two adjacent boxes is a second-order accurate estimate of the concentration at the center of the face in between.
	www.ocean.washington.edu /people/faculty/kawase/NumericalModeling/Lecture_5_Slide_2.html (524 words)

	finite (Site not responding. Last check: 2007-10-19)
		An Introduction".) The present volume is an elementary introduction to the study of stress and strain field by use of finite element analysis, FEA.
		This volume is based on the 1st edition of the book "Fields of Physics on the PC by Finite Element Analysis", published in 1994., by the same author, followed by a 2nd edition in 1996.
		Nonconforming and other methods (refers to: abstract lemmas and a simple boundary approximation, isoparametric elements, further tools from functional analysis, saddle point problems, the Stokes equation, finite elements for the Stokes problem, a posteriori error estimates).
	www.library.tuiasi.ro /ipm/vol11no34/finite.html (1868 words)

	A Finite-Volume Particle Method for Compressible Flows - Hietel, Steiner, Struckmeier (ResearchIndex) (Site not responding. Last check: 2007-10-19)
		Abstract: We derive a new class of particle methods for conservation laws, which are based on numerical flux functions to model the interactions between moving particles.
		The derivation is similar to that of classical Finite--Volume methods; except that the fixed grid structure in the Finite--Volume method is substituted by so--called mass packets of particles.
		In fact, we are going to embed this method into a more general framework which also includes classical finite volume schemes.
	citeseer.ist.psu.edu /140256.html (550 words)

	Kunert, Gerd; Mghazli, Zoubida; Nicaise, Serge : A posteriori error estimation for a finite volume discretization on ...
		The problem is discretized by a vertex-centered finite volume method.
		The estimator is also robust with respect to the mesh anisotropy as long as the anisotropic mesh sufficiently reflects the anisotropy of the solution (which is almost always the case for sensible discretizations).
		Altogether, reliable and efficient \emph{a posteriori} error estimation is achieved for the finite volume method on anisotropic meshes.
	www.mathematik.tu-chemnitz.de /preprint/2003/SFB393_16.html (384 words)

	ipedia.com: Numerical analysis Article (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-10-19)
		Numerical analysis is that branch of applied mathematics which studies the methods and algorithms to find (approximate) numerical solutions to various mathematical problems, using a finite sequence of arithmetic and logical operations.
		A very simple method is to use linear interpolation, which assumes that the unknown function is linear between every pair of successive points.
		This can be done by a finite element method, a finite difference method, or (particularly in engineering) a finite volume method.
	www.ipedia.com.cob-web.org:8888 /numerical_analysis_1.html (1418 words)

	NC State NA Seminar, Fall 2003
		Such a smearing may be unacceptable in certain circumstances, especially when a system of conservation or balance laws is coupled with a nonlinear transport equation as, for instance, in numerical simulations of transport of a passive pollutant or compressible inviscid reacting gases.
		We introduce a new hybrid finite-volume-particle method whose core idea is to use a finite-volume method to numerically integrate a system of conservation (balance) laws and a particle method to solve transport equations coupled with the system.
		Particle methods applied to transport equations, can ameliorate most of the problems posed by the presence of numerical viscosity since particles provide a non-dissipative approximation of the convection.
	www2.ncsu.edu /math/Announcements/NAS/SPRING_2005/chertock.html (283 words)

	Bill Morton's Home Page
		Development of FVEG (Finite Volume Evolution-Galerkin) methods for approximating systems of hyperbolic PDEs in several space dimensions, such as the Euler equations of compressible fluid dynamics or Maxwell's equations of electro-magnetic waves; collaboration is with Prof Warnecke in Magdeburg and Prof Lukacova-Medvidova in Hamburg --- see recent publications below.
		Application of the box finite difference scheme (more generally, the cell-vertex finite volume method) to problems of groundwater flow; collaboration is with Sarah Mitchell and Alastair Spence.
		Use of the energy method to analyse the stability of finite difference and finite volume methods.
	www.bath.ac.uk /math-sci/staff/kwmweb.html (287 words)

	Old Meetings: CHT97
		Most methods that are applicable to participating-medium radiation are applied to regular geometries, where the surfaces of the enclosure coincide with coordinate surfaces.
		A method of determination of distribution of the radiative heat flux, based on two-zone thermodynamic model and integral equation of radiative heat transfer, has been proposed by Furmañski et al.
		The number of these subdomains has been varied with the temporary volumes of both the chamber and the burn zone, dependent on the actual crank angle, in accordance with the rule that all finite elements are of a comparable length.
	www.ichmt.org /abstracts/CHT-97/session7.html (1743 words)

	An Error Estimate for Finite Volume Methods for the Stokes Equations (Site not responding. Last check: 2007-10-19)
		In the present paper, we study an error estimate for finite volume methods for the stokes equations.
		The result is new even for the finite volume method.
		Finite volume method, Stokes equations, Discrete Poincaré inequality, Error estimate.
	www.maths.tcd.ie /EMIS/journals/JIPAM/v3n2/045_01.html (252 words)

	index
		Introduction to the finite volume method for the fluid flow prediction.
		To understand the basic characteristics of numerical methods as a basis for competent usage of commercial CFD codes.
		An Example of Finite Volume Method for the One-Dimensional Unsteady Conduction.
	www.fsb.hr /hydro/web_sites/Popis%20predmeta/Computational%20Fluid%20Mechanics.htm (195 words)

	Recherche bibliographique (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-10-19)
		Convergence of finite volume schemes for a degenerate convection-diffusion equation arising in flow in porous media.
		A comparison of methods for calculating the matrix block source term in a double porosity model for contaminant transport.
		A numerical upscaling method for an elliptic equation with heterogenous tensorial coefficients.
	www.gdrmomas.org.cob-web.org:8888 /pubsmomas.html (1741 words)

	MEDM Home (Site not responding. Last check: 2007-10-19)
		The irregular bottom slope is represented using a s-coordinate transformation, and the horizontal grids are comprised of unstructured triangular cells.
		The finite-volume method (FVM) used in this model combines the advantages of a finite element method (FEM) for geometric flexibility and a finite-difference method (FDM) for simple discrete computation.
		Currents, temperature and salinity in the model are computed in the integral form of the equations, which provides a better representation of the conservative laws for mass, momentum and heat in the coastal region with complex geometry.
	fvcom.smast.umassd.edu /FVCOM (190 words)

	TxSpace at Texas A&M University Libraries: Item 1969.1/2242 (Site not responding. Last check: 2007-10-19)
		The numerical method presented is intended to capture the small scales eand#64256;ect on the large scale solution without resolving the small scale details, which is done through the construction of a multiscale map.
		Analysis of the multiscale method is separately done for cases of linear and nonlinear coeand#64259;cients.
		For linear coeand#64259;cients, the multiscale and#64257;nite volume element method is viewed as a perturbation of multiscale and#64257;nite element method.
	txspace.tamu.edu /handle/1969.1/2242 (267 words)

	Spectral (finite) volume method
		Sun, Wang, Liu "Spectral (finite) volume method for conservation laws on unstructured grids.
		Spectral (finite) volume method - Max, Thu, 13 Apr 2006, 8:15 a.m.
		Re: Spectral (finite) volume method - opaque, Thu, 13 Apr 2006, 9:11 a.m.
	www.cfd-online.com /Forum/main_archive.cgi?read=44762 (93 words)

	The finite volume method
		The finite volume method evolved in the early seventies via the finite difference
		method has been shown to be a special case of the finite element method with non-
		The finite element method consists of representing a given domain by an
	www.tpub.com /content/nasa2001/NASA-2001-tm211046/NASA-2001-tm2110460057.htm (198 words)

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