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, which is working well enough provided that time steps in SPH are significantly small.

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.

The energy computation is based in the time integration of the variation rates, and therefore it is supposed that all components starts from $0[{\mathrm{J}}]$ , however, it can be modified after importing this preset. For instance, to set the initial potential energy as $1[{\mathrm{J}}]$ we can use the following XML code:

<Variables>
    <Variable name="energy_Epot" type="float" value="1.0" />
</Variables>

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	Total external forces work, $W$ .

Definitions

This preset is not adding new definitions (see Definitions).

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
Energy	kernel	Compute the energy components variation rate per particle (see the introduction).
dSdt	reduction	Compute the total entropy variation rate (see the introduction).
dEkindt	reduction	Compute the total kinetic energy variation rate (see the introduction).
dEpotdt	reduction	Compute the total potential energy variation rate (see the introduction).
dWdt	reduction	Compute the total external forces work variation rate (see the introduction).
dEintdt	set_scalar	Compute the total internal energy variation rate (see the introduction).
Eint	set_scalar	Integrate the total internal energy, i.e. $U_{{n+1}}=U_{n}+\Delta t\,{\frac{dU_{n}}{dt}}$ .
ES	set_scalar	Integrate the total entropy, i.e. $S_{{n+1}}=S_{n}+\Delta t\,{\frac{dS_{n}}{dt}}$ .
Ekin	set_scalar	Integrate the total kinetic energy, i.e. $E_{{n+1}}^{{kin}}=E_{n}^{{kin}}+\Delta t\,{\frac{dE_{n}^{{kin}}}{dt}}$ .
Epot	set_scalar	Integrate the total potential energy, i.e. $E_{{n+1}}^{{pot}}=E_{n}^{{pot}}+\Delta t\,{\frac{dE_{n}^{{pot}}}{dt}}$ .
EW	set_scalar	Integrate the total external forces work, i.e. $W_{{n+1}}=W_{n}+\Delta t\,{\frac{dW_{n}}{dt}}$ .

Reports

This preset is not adding new reports (see Reports).