Editing Computational fluid dynamics (section)

==== Finite difference method ====

{{Main|Finite difference method}}

The finite difference method (FDM) has historical importance<ref name=":0" /> and is simple to program.  It is currently only used in few specialized codes, which handle complex geometry with high accuracy and efficiency by using embedded boundaries or overlapping grids (with the solution interpolated across each grid).{{Citation needed|date=November 2010}} 
:<math> 
\frac{\partial Q}{\partial t}+
\frac{\partial F}{\partial x}+
\frac{\partial G}{\partial y}+
\frac{\partial H}{\partial z}=0
</math>
where <math>Q</math> is the vector of conserved variables, and <math>F</math>, <math>G</math>, and <math>H</math> are the fluxes in the <math>x</math>, <math>y</math>, and <math>z</math> directions respectively.