Editing Computational fluid dynamics (section)

==== Finite volume method ====

{{Main|Finite volume method}}

The finite volume method (FVM) is a common approach used in CFD codes, as it has an advantage in [[Random-access memory|memory]] usage and solution speed, especially for large problems, high [[Reynolds number]] turbulent flows, and source term dominated flows (like combustion).<ref>{{cite book|last=Patankar|first=Suhas V.|author-link=Suhas Patankar|title=Numerical Heat Transfer and Fluid FLow|year=1980|publisher=Hemisphere Publishing Corporation
|isbn=978-0891165224}}</ref>

In the finite volume method, the governing partial differential equations (typically the Navier-Stokes equations, the mass and energy conservation equations, and the turbulence equations) are recast in a conservative form, and then solved over discrete control volumes. This [[discretization]] guarantees the conservation of fluxes through a particular control volume. The finite volume equation yields governing equations in the form,
:<math>\frac{\partial}{\partial t}\iiint Q\, dV + \iint F\, d\mathbf{A} = 0,</math>
where <math>Q</math> is the vector of conserved variables, <math>F</math> is the vector of fluxes (see [[Euler equations (fluid dynamics)|Euler equations]] or [[Navier–Stokes equations]]), <math>V</math> is the volume of the control volume element, and <math>\mathbf{A}</math> is the surface area of the control volume element.