Presets/energy.xml

Introduction

energy.xml is a preset used to compute the fluid energy components. If you wish to print the results in the screen and in an output file include energy_report.xml as well.

This tool is computing the following energy components variation rates for each particle:

${\displaystyle{\frac{dE_{a}^{{kin}}}{dt}}=m_{a}{\mathbf{u}}_{a}\cdot{\frac{d{\mathbf{u}}_{a}}{dt}},}$

${\displaystyle{\frac{dE_{a}^{{pot}}}{dt}}=-m_{a}{\mathbf{g}}\cdot{\mathbf{u}}_{a},}$

${\displaystyle{\frac{dW_{a}}{dt}}=-{\frac{m_{a}}{\rho_{a}}}\nabla p_{a}\cdot{\mathbf{u}}_{a}-{\frac{m_{a}}{\rho_{a}}}p_{a}\nabla\cdot{\mathbf{u}}_{a},}$

$T{\frac{dS_{a}}{dt}}=-\mu{\frac{m_{a}}{\rho_{a}}}{\mathbf{u}}_{a}\cdot\Delta{\mathbf{u}}_{a}-\delta{\frac{p_{a}m_{a}\Delta t}{\rho_{0}\rho_{a}}}\Delta p_{a},$

where $E_{a}^{{kin}}$ , $E_{a}^{{pot}}$ are the kinetic and the potential energy components for a generic particle a, $W_{a}$ is the work of the external forces, and $S_{a}$ is the entropy. These values per particle are later reduced to the total fluid variation:

${\displaystyle{\frac{dE^{{kin}}}{dt}}=\sum_{{a\in{\mathrm{Fluid}}}}{\frac{dE_{a}^{{kin}}}{dt}},}$

${\displaystyle{\frac{dE^{{pot}}}{dt}}=\sum_{{a\in{\mathrm{Fluid}}}}{\frac{dE_{a}^{{pot}}}{dt}},}$

${\displaystyle{\frac{dW}{dt}}=\sum_{{a\in{\mathrm{Fluid}}}}{\frac{dW_{a}}{dt}},}$

$T{\frac{dS}{dt}}=\sum_{{a\in{\mathrm{Fluid}}}}T{\frac{dS_{a}}{dt}}.$

The total internal energy variation can be then computed as:

${\displaystyle{\frac{dU}{dt}}={\frac{dW}{dt}}-{\frac{dE^{{pot}}}{dt}}-{\frac{dE^{{kin}}}{dt}}.}$

Finally these variables are numerically integrated by a simple Euler scheme.

Usage

To use it the following tag should be added to include the preset:

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

Where /usr/share/aquagpusph/ should be conveniently modified.

This preset should be loaded after cfd.xml.

Variables defined

When this preset is loaded some variables are generated (on top of the default variables of AQUAgpusph):

NAME	TYPE	LENGTH	DESCRIPTION
energy_dEintdt	float	1	Total internal energy variation rate, ${\displaystyle{\frac{dU}{dt}}}$ .
energy_Eint	float	1	Total internal energy, $U$ .
energy_dsdt	float*	N	Entropy variation rate, $T{\frac{dS_{a}}{dt}}$ .
energy_dSdt	float	1	Total entropy variation rate, $T{\frac{dS}{dt}}$ .
energy_S	float	1	Total entropy, $TS$ .
energy_dekindt	float*	N	Kinetic energy variation rate, ${\displaystyle{\frac{dE_{a}^{{kin}}}{dt}}}$ .
energy_dEkindt	float	1	Total kinetic energy variation rate, ${\displaystyle{\frac{dE^{{kin}}}{dt}}}$ .
energy_Ekin	float	1	Total kinetic energy, $E^{{kin}}$ .
energy_depotdt	float*	N	Potential energy variation rate, ${\displaystyle{\frac{dE_{a}^{{pot}}}{dt}}}$ .
energy_dEpotdt	float	1	Total potential energy variation rate, ${\displaystyle{\frac{dE^{{pot}}}{dt}}}$ .
energy_Epot	float	1	Total potential energy, $E^{{pot}}$ .
energy_dwdt	float*	N	External forces work variation rate, ${\displaystyle{\frac{dW_{a}}{dt}}}$ .
energy_dWdt	float	1	Total external forces work variation rate, ${\displaystyle{\frac{dW}{dt}}}$ .
energy_W	float	1	External forces work, $W$ .

Tools

The following tools are set to be executed each time step, just before the "t = t + dt" tool. (see Tools and cfd.xml to learn more about this):

NAME	TYPE	DESCRIPTION
tool	kernel	desc.