Numerical methods in fluid mechanics: Difference between revisions

Revision as of 22:09, 5 December 2013

Revision as of 19:44, 12 December 2013

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==Computational cost==

The [[CPU]] time to solve the system of equations differs substantially from method to method. Finite differences are usually the cheapest on a per grid point basis followed by the finite element method and spectral method. However, a per grid point basis comparison is a little like comparing apple and oranges. Spectral methods deliver more accuracy on a per grid point basis than either [[Finite element method|FEM]] or [[Finite difference method|FDM]]. The comparison is more meaningful if the question is recast as ”what is the computational cost to achieve a given error tolerance?”. The problem becomes one of defining the error measure which is a complicated task in general situations.

==Application of finite differences to [[ordinary differential equation]]s==