Week 9 - FVM Literature Review

Finite Volume Method(FVM)

The finite volume method is a discretization technique for partial differential equation, especially those arise from physical conservation laws. FVM uses a volume integral formulation of the problem with a finite partitioning set of volumes to discrete the equation.

Differences between FDM & FVM

• In Finite Difference, the Dependant variable values are stored at the nodes only.But in FVM, the dependant values are stored in the centre of the Finite volume.
• In FV approach, Conservation of mass, momentum, energy is ensured at each cell/finite volume level. This not true in FDM
  

INTERPOLATION SCHEMES

Interpolation is the process of using points with known values or sample points to estimate values at other unknown points.In FVM interpolation schemes are used to find the values of volume integrals required at the points other than nodes.Some of the used methods are central differencing scheme, hybrid scheme, upwind scheme and Quick scheme

Flux limiters

Flux limiters are used in high resolution schemes – numerical schemes used to solve problems in science and engineering, particularly fluid dynamics, described by partial differential equations (PDE's). They are used in high resolution schemes, such as the MUSCL scheme, to avoid the spurious oscillations (wiggles) that would otherwise occur with high order spatial discretization schemes due to shocks, discontinuities or sharp changes in the solution domain. Use of flux limiters, together with an appropriate high resolution scheme, make the solutions total variation diminishing (TVD).

Note that flux limiters are also referred to as slope limiters because they both have the same mathematical form, and both have the effect of limiting the solution gradient near shocks or discontinuities.like (pressure,velocity,etc)