Week 9 - FVM Literature Review
Theory of understanding the concept of The difference between FDM and FVM, Interpolation schemes in FVM:
*In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences
* A finite difference is a mathematical expression of the form f (x + b) − f (x + a). If a finite difference is divided by b − a, one gets a difference quotient.
* However there is a drawback, we cannot use it directly when grids are not aligned along with XYZ directions
* In the Finite volume method, instead of writing the equation in a point we write it for a volume
* Write the governing equation in its integral form
* Apply gauss divergence theorem
* Come up with suitable methods to calculate flux terms.
Interpolation schemes :
Interpolation schemes are used to transform cell-centre quantities to face centres. The operation is used in many of the finite volume calculations, e.g. for the calculation of gradient, divergence, and Laplacian terms.
