diff --git a/theory/latex/sph.tex b/theory/latex/swift.tex similarity index 78% rename from theory/latex/sph.tex rename to theory/latex/swift.tex index f0cebab163637ff6a0bc6f8503ac48c58e5fdbc0..c8f1c9c8385be287f5f4c3b1eec08dc1a2c019f7 100755 --- a/theory/latex/sph.tex +++ b/theory/latex/swift.tex @@ -1,16 +1,120 @@ -\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}