Commit f1119be4 authored by Matthieu Schaller's avatar Matthieu Schaller
Browse files

Updated and reorganised the theory file to describe the different loops used in the code.


Former-commit-id: 1826806b945282941348e9fa14889dd3b0be38ec
parent d86fc798
\documentclass[a4paper,10pt]{article}
\documentclass[a4paper,10pt]{report}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{color}
\newcommand{\swift}{\textsc{swift }}
\newcommand{\eagle}{\textsc{eagle }}
\newcommand{\gadget}{\textsc{gadget-2 }}
%opening
\title{SPH equations}
\title{SWIFT - Theory and equations}
\author{Matthieu}
\begin{document}
\maketitle
This document does not follow the GADGET notation.\\
\chapter{General properties}
\label{chap:intro}
The \swift code follows the model of \eagle and uses four different types of particles to represent the different
objects present in the Universe. These different types with their \gadget names are summarized in table
\ref{tab:parttypes}.
\begin{table}[h]
\centering
\label{tab:parttypes}
\begin{tabular}{|l|l|l|}
\hline
\textbf{Object} & \textbf{\gadget name} & \textbf{Description} \\
\hline
Gas & PartType0 & Particles representing the gas.\\
DM & PartType1 & Particles representing the dark matter.\\
Star & PartType4 & Paricles representing the stars.\\
BH & PartType5 & Particles representing the Black Holes.\\
\hline
\end{tabular}
\caption{The four types of particles present in the \swift code.}
\end{table}
All of these particles are affected by the gravitation force but additional interactions will exit for the non-DM
particles. The number of DM particles is a constant but the number of gas, star and BH particles will vary
over the simulation time. The latter two will tipically increase while the number of gas particles will usually
decrease. \\
Depending on the exact variation of the \eagle physics used, the total number of particles will be a
constant, implying that particles will change type but none will be spawned. \\
In a typical cosmological simulation, 50\% of the particles are DM particles, 46\% are gas particles, 4\% are star
particles and less than 0.001\% are BH particles. These numbers can change slightly when doing a ``zoom'' simulation.\\
The gas particles interact throught SPH forces which are computed through two loops over the neighbouring particles
(Chapter \ref{chap:SPH}). The first of these loop is over all the particles within a range $h_i$ of the particle $i$
whereas the second on is over all particles within $h_i$ and over all particles that see particle $i$ within their
search radius $h_j$. This second loop is in principle more expensive as more neighbours have to be found. \\
Gas particles also interact gravitationally and can take part in more complex \eagle interactions. The first of these
\eagle modules is the cooling which affects the particles on an individual basis. Depending on the age of the
Universe, the chemical composition of the gas and its density, some internal energy is added or removed to the gas.
This is done by interpolating ``cooling tables'' which have been pre-computed and yield the change of energy as a
function of all the relevant quantities. This is a very cheap module in terms of computing.
The star particles (Chapter \ref{chap:stars}) are created from gas particles when the right gas density and pressure
criteria are met. This does not require any loop over neighbours as it is a particle by particle effect. Depdending on
the options chosen, a gas particle can be transformed into a star particle or it can spawn one or more star particles.\\
Once they have been created, these star particles cease to interact via SPH forces and only obey the gravity forces. \\
The star particles evolve with time in order to reflect the change in chemical element composition of their cores.
They dispatch elements to their gas neighbours through a loop of the same kind than the 1st SPH loop. There are in fact
two loops performed, one to compute the weights of the neighbours and the second one to actually dispatch the elements
and the mass. This is called ``enrichment''\\
Finally, star particles also do feedback in the form of a packet of thermal energy given randomly to one of their
neighbours. This process occurs only once in the lifetime of the star, shortly after its creation. The calculation of
the weights in the enrichment parts is useful here as well. In the latest \eagle version, the amount of energy
dispatched is a function of the velocity spread of the DM particles surrounding the star. This quantity is computed
using, once again, a loop over the neighbours. \\
The Black Hole particles (Chapter \ref{chap:BHs}) are created from gas particles when they hit the bottom of a potential
well of a given depth. These particles will then do feedback in the same way that stars do it, i.e. by dumping a certain
amount of energy to one or more neighbouring gas particles. The black hole also swallowa (i.e. destroys) gas particles
passing by under some circumstances. This is achieved in the same loop over the neighbouring gas particles. There is no
interaction between the BHs and the stars or DM particles. \\
In summary, the various loops over different particles can be written in a short table. The
exact equations happening in these loops are given in the corresponding sections of this document.
\begin{table}[h]
\centering
\begin{tabular}{|l|c|c|c|c|}
\hline
$ \nearrow$&\textbf{DM} & \textbf{Gas} & \textbf{Stars} & \textbf{BHs} \\
\hline
\textbf{DM} & & & &\\
\hline
\textbf{Gas} & \textbullet & \textbullet & &\\
\hline
\textbf{Stars} &\textbullet & \textbullet & &\\
\hline
\textbf{BHs} & & \textbullet& &\\
\hline
\end{tabular}
\label{tab:interactions}
\caption{The various loops over neighbours required by the \eagle model. For instance, gas particles are looping over
their gas neighbours and (in another loop) over their DM neighbours. This table does not show the frequency of the
loops. Only the gas-gas loop occurs at every time step.}
\end{table}
\textcolor{red}{DISCUSS UNIT SYSTEM !!}
\chapter{Dark Matter particles}
\label{chap:DMs}
This section describes the physics of the DM particles but as all particles are affected by gravity, the equations
apply to all four types.
\chapter{Gas particles - SPH}
\label{chap:SPH}
\section{Particle definition}
Every particle contains the following information:
......@@ -207,7 +311,7 @@ h_j$. In general, the equations are more involved as they will contain terms to
thermal conduction. These terms are pure functions of the properties of particles $i$ and $j$ and are thus very simple
to insert once the code is stabilized.\\
The time step is given by the Courant relation where the cell size is the smoothing length and the velocitiy is the
The time step is given by the Courant relation where the cell size is the smoothing length and the velocity is the
signal speed:
\begin{equation}
......@@ -484,4 +588,16 @@ computed in the density loop and reads
\end{equation}
\chapter{Stars - EAGLE}
\label{chap:stars}
Blabla \eagle blablabla
\chapter{Black Holes - EAGLE}
\label{chap:BHs}
Blabla \eagle blablabla
\end{document}
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