Week 9 - FVM Literature Review

Finite Volume method (FVM) :

1. In finite volume method , the fluid domain is divided into finite number of cells where each cell is having a control volume.
2. The grid defines the boundary of the cell and the computational node lies at the centre of the cell
3. FVM is used for solving complex geometry as it uses integral form for governing equations.
4. FVM uses Gauss divergence theorem for solving Gauss divergence equations.

Major differences between FDM and FVM :

Finite Difference Method	Finite Volume Method
In finite difference method the fluid domain is divided into a regular grid.	In finite volume method , the fluid domain is divided into finite number of cells where each cell is having a control volume
In FDM, the governing equations are in integral form	In FVM, the governing equations are in differential form
Computational node present at the intersection of the boundary	Computational node present at the centre of the cell
Due to its use of structured grid, solving complex geometry is difficult	As the FVM uses integral form for solving complex geometry is easy
FDM is unsuitable for handling discontinuities	FDM can handle discontinuities due to the nature of integral equations
FDM does not ensure conservation	FVM ensures conservation at both cell and domain level

The need for interpolation schemes and flux limiters in FVM :

1. Gradient schemes are used to solve gradient terms in the governing equations.
2. The interpolation schemes are used for calculating the face values of the computaional node.
3. The use of gradient schemes create values greater then local maximum/minimum.
4. So to control these overshooting of values flux limiters are used to limits the higher order interpolations into single order interpolations which prevents the formation of new local maximum/minimun.