View source for Presets/cfd

== Introduction ==

cfd.xml is the main preset to be loaded in order to perform Fluid Dynamics simulations.

=== Governing equations ===

The following governing equations are approximately solved with this preset:

<math>
\frac{d\rho}{dt} = - \rho \mathrm{div}\left(\mathbf{u}\right),
</math>

<math>
\frac{d\mathbf{u}}{dt} = \mathbf{g} + \frac{\mathrm{div}\left(\mathbb{T}\right)}{\rho},
</math>

<math>
p = p \left( \rho \right);
</math>

where <math>\rho</math> and <math>\mathbf{u}</math> are the density and the velocity respectively, <math>\mathbf{g}</math> is an external volumetric force field, <math>p</math> is the pressure, and <math>\mathbb{T}</math> is the stress tensor for a Newtonian fluid:

<math>
\mathbb{T} = \left(-p + \lambda \mathrm{tr}\left(\mathbb{D}\right)\right) \mathbb{1} + 2 \mu \mathbb{D},
</math>

with <math>\lambda</math> and <math>\mu</math> the viscous coefficients and <math>\mathbb{D}</math> the rate of strain tensor:

<math>
\mathbb{D} = \frac{\nabla\mathbf{u} + \nabla\mathbf{u}^T}{2}.
</math>

As it has been stated in the 3<sup>rd</sup> governing equation (formerly Equation Of State, or EOS), we need to stablish a relation between the density and the pressure:

<math>
p = \frac{c_s^2 \rho_0}{\gamma}\left(\left(\frac{\rho}{\rho_0}\right)^gamma + 1\right),
</math>

where <math>c_s</math> is the sound speed (at least 10 times the maximum speed expected during the simulation), <math>\rho_0</math> the density of reference of the fluid, and <math>\gamma</math> an incompressibility factor (1 is recommended, but it can be increased to get better incompressibility properties).

== Using cfd.xml ==

To use it just use the include tag:

<syntaxhighlight lang="xml">
<Include file="/usr/share/aquagpusph/resources/Presets/domain.xml" />
</syntaxhighlight>

Where <tt>/usr/share/aquagpusph/</tt> should be conveniently modified. For backguard compatibility you can include <tt>/usr/share/aquagpusph/resources/OpenCLMain.xml</tt> instead (it is just including cfd.xml).

This preset should be included before any other one.

== Variables defined ==

[[Category:Presets]]