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Interpolation schemes in FVM:

The flux terms in FVM are calculated using the values at the cell centres. For example, heat flux is calculated using temperature values at cell centres (E,P and W). But the flux is obtained when we multiply this by thermal diffusivity. Thermal diffusivity depends on temperature and the value will be different at each finite volume. As we are interested in calculating the flux at the surfaces (e,w), we take the interpolated values from both the neighbouring cells.

Flux Limiters in FVM:

Some schemes when used to solve some problems, deviate from the exact value by a large factor. One of the examples is artificial viscosity in a pure convection problem. To obtain more accurate solution, a factor total variation (TV) is calculated. In order for the oscillations to be eliminated or supressed, the value of TV must decrease with timestep. Hence, this method is called total variation decomposition (TVD). The TVD is acheived by multiplying flux derivatives with a non- linear function. This non-linear function is know as flux limiter.