INTERPOLATION SCHEMES AND FLUX LIMITERS IN FINITE VOLUME METHOD
INTERPOLATION SCHEMES AND FLUX LIMITERS IN FINITE VOLUME METHOD :
The finite volume is a method by which volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem. The terms in FVM are evaluated as fluxes at the surfaces of each finite volume. Also the flux entering a given volume is the same as that leaving the adjacent volume, hence making this method conservative.
Interpolation schemes: Interpolation is the method of estimating the value of a function for an intermediate value of the independent variable. In FVM, various interpolation schemes are used to estimate the solution. This is because, in FVM the face values appearing in the fluxes have to be computed by some form of interpolation from the centroid values of the control volumes as they are unknown.
Few of the popular interpolation schemes are;
- Central differencing scheme
- Upwind differencing scheme
- Total variation diminishing scheme
- Hybrid schemes etc
Flux limiter: Flux limiters are used in the presence of shocks or discontinuities. In high resolution schemes, Flux limiters are necessary to tune higher order and lower order in such a way as to maintain smooth flow in regions of discontinuity. They only come into action when sharp wavefronts are presence. In smooth changing waves they are not used.
Examples of flux limiter functions are given below;
- CHARM
- HQUICK
- HCUS
- KOREN