Week 9 - FVM Literature Review

Finite Volume Method:

• Finite volume method is introduced for Complex geometry's
• so here instead of writing Equations for single point we are writing for Entire Volume.
• We have volume ,may be cube, tetrahedral,polyhedral etc., inside this particular volume the flow is conserved,the flow quantity is conserved,Energy is conserved,mass conserved and so on and this called FV representation.
• Instead of writing equations in apoint we write it for volume
• Then we apply few mathematical techniques to help us to solve these equations for any type of grids
• Also Finite volume representation preserves the concept of conservation
• In FVM ,the domain is made of arbitary control volumes (internal& Boundary)
• Solutions sought in each of the volumes are stored in the cell centriods

Differnces:

FDM:

• Governing equations are in the differntial form
• Solutions are computed at each node ie., intersection of mesh lines
• Requires the use of unstructured grid,difficult to implement for complex Geometrys
• Easy to obtain high order schmes,so preferable for applications that required high accuracy
• All flow variables need to be differntialable & continious over the entire Domain ,unsuitable for handling discontinious
• Does not ensure conservation

FVM

• Governing Equations are in the form of integral .
• Solution computed at the cell centroids.
• Can handled Unstructed grid and hence complex geometries with ease.
• Deriving high than second order is next to impossible due to complexicity involved.
• Can handle discontinuities due to nature of integral equations.
• Imposes and ensures at both cell and domain levels.