Week 9 - FVM Literature Review

Finite Difference Method (FDM):

FDM is one of the discretizing techniques in which we discretize the domain into individual grid points and then solve the governing equations on those points.

Finite Volume Method (FVM):

FVM is the most commonly used discretizing technique where the governing equations are derived using the integral approach by considering the domain into a small 'n' number of control volumes.

We consider the flow as having the conserved fluid properties, energy, mass and momentum over the particular control volume.

Drawback of FDM over FVM:

FDM is not suitable for the geometry that was not discretized along the x, y or z-axis

Need for different numerical schemes:

Gradient scheme:

A gradient scheme is the way how we numerically represent the gradient of the variables to evaluate the variables from the existing data in neighbouring cells.

Interpolation scheme:

An Interpolation scheme is primarily used to derive the field variables at the face centre by the interpolations of cell centre values.

Flux Limiter:

A flux limiter is important to specify the bound for the gradient which may exceed due to some flow behaviour and helps in avoiding the discontinuity in the gradient.