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:

${\displaystyle{\frac{d\rho}{dt}}=-\rho{\mathrm{div}}\left({\mathbf{u}}\right),}$

${\displaystyle{\frac{d{\mathbf{u}}}{dt}}={\mathbf{g}}+{\frac{{\mathrm{div}}\left({\mathbb{T}}\right)}{\rho}},}$

$p=p\left(\rho\right);$

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

${\displaystyle{\mathbb{T}}=\left(-p+\lambda{\mathrm{tr}}\left({\mathbb{D}}\right)\right){\mathbb{1}}+2\mu{\mathbb{D}},}$

with ${\displaystyle\lambda}$ and ${\displaystyle\mu}$ the viscous coefficients and ${\displaystyle{\mathbb{D}}}$ the rate of strain tensor:

${\displaystyle{\mathbb{D}}={\frac{\nabla{\mathbf{u}}+\nabla{\mathbf{u}}^{T}}{2}}.}$

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

$p={\frac{c_{s}^{2}\rho_{0}}{\gamma}}\left(\left({\frac{\rho}{\rho_{0}}}\right)^{\gamma}+1\right),$

where $c_{s}$ is the sound speed (at least 10 times the maximum speed expected during the simulation), ${\displaystyle\rho_{0}}$ the density of reference of the fluid, and ${\displaystyle\gamma}$ 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:

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

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

This preset should be included before any other one.