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 GOVINDARAJU L December 24, 2005 01:17

Difference between FEM,FDM and FVM

I want to knw about the exact diffrence bet the FVM, FDM, and FEM, Thanki=s in advance

 apurva January 7, 2006 09:41

Re: Difference between FEM,FDM and FVM

i too am looking for difference between FEM,FDM and FVM if you can share with me what u know ,i say we both can get information.i am working on a project based on FVM

 Sangkwon Na January 12, 2006 11:32

Difference between FDM and FVM

I like to find difference between FDM and FVM in detail. Please could you help me to understand it. Thanks.

 Prabakaran M K January 19, 2006 02:38

Re: Difference between FEM,FDM and FVM

In Finite Differnece, the Dependant variable values are stored at the nodes only.

In FEM, The dependant values are stored at the element nodes.

But in FVM, the dependant values are stored in the center of the Finite volume.

In FV approach, Conservation of mass, momentum, energy is ensured at each cell/finite volume level. This NOT true in FD and FE approach.

It is always better to use Governing Equation in Conservative form with FV approach to solve any problem which ensures conservation of all the properties in each cells/control volume.

To get more understanding, go thro' CFD books.

All the best, M K P

 pooranimurugesan October 28, 2012 11:03

A finite difference method (FDM) discretization is based upon the differential form of the PDE to be solved. Each derivative is replaced with an approximate difference formula (that can generally be derived from a Taylor series expansion). The computational domain is usually divided into hexahedral cells (the grid), and the solution will be obtained at each nodal point. The FDM is easiest to understand when the physical grid is Cartesian, but through the use of curvilinear transforms the method can be extended to domains that are not easily represented by brick-shaped elements. The discretization results in a system of equation of the variable at nodal points, and once a solution is found, then we have a discrete representation of the solution.
A finite volume method (FVM) discretization is based upon an integral form of the PDE to be solved (e.g. conservation of mass, momentum, or energy). The PDE is written in a form which can be solved for a given finite volume (or cell). The computational domain is discretized into finite volumes and then for every volume the governing equations are solved. The resulting system of equations usually involves fluxes of the conserved variable, and thus the calculation of fluxes is very important in FVM. The basic advantage of this method over FDM is it does not require the use of structured grids, and the effort to convert the given mesh in to structured numerical grid internally is completely avoided. As with FDM, the resulting approximate solution is a discrete, but the variables are typically placed at cell centers rather than at nodal points. This is not always true, as there are also face-centered finite volume methods. In any case, the values of field variables at non-storage locations (e.g. vertices) are obtained using interpolation.
A finite element method (FEM) discretization is based upon a piecewise representation of the solution in terms of specified basis functions. The computational domain is divided up into smaller domains (finite elements) and the solution in each element is constructed from the basis functions. The actual equations that are solved are typically obtained by restating the conservation equation in weak form: the field variables are written in terms of the basis functions, the equation is multiplied by appropriate test functions, and then integrated over an element. Since the FEM solution is in terms of specific basis functions, a great deal more is known about the solution than for either FDM or FVM. This can be a double-edged sword, as the choice of basis functions is very important and boundary conditions may be more difficult to formulate. Again, a system of equations is obtained (usually for nodal values) that must be solved to obtain a solution.
Comparison of the three methods is difficult, primarily due to the many variations of all three methods. FVM and FDM provide discrete solutions, while FEM provides a continuous (up to a point) solution. FVM and FDM are generally considered easier to program than FEM, but opinions vary on this point. FVM are generally expected to provide better conservation properties, but opinions vary on this point also. If you are trying to decide which method to use, then the best path is probably found by consulting the literature in the specific problem area.

source: wiki

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