Commit 4a58893a authored by Matthieu Schaller's avatar Matthieu Schaller
Browse files

Corrected a few typos in the latex document.


Former-commit-id: e9567f4ffdde605b320736473eea9d16d40e93c1
parent 41c8de38
......@@ -71,7 +71,7 @@ Coming back to the simplest case, the derivatives of the kernel function are giv
\begin{eqnarray*}
\vec\nabla W(\vec{x},h) &=& \frac{1}{h^4}f'\left(\frac{|\vec{x}|}{h}\right) \frac{\vec{x}}{|\vec{x}|} \\
\frac{\partial W(\vec{x},h)}{\partial h} &=&- \frac{1}{h^4}\left[3\left(\frac{|\vec{x}|}{h}\right) +
\frac{\partial W(\vec{x},h)}{\partial h} &=&- \frac{1}{h^4}\left[3f\left(\frac{|\vec{x}|}{h}\right) +
\frac{|\vec{x}|}{h}f'\left(\frac{|\vec{x}|}{h}\right)\right]
\end{eqnarray*}
......@@ -163,11 +163,16 @@ The time step is then given by the Courant relation:
\Delta t_i = C_{CFL} \frac{h_i}{c_i}
\end{equation}
where the CFL parameter usually takes a value between $0.1$ and $0.3$. The integration in time can then take place. The
where the CFL parameter usually takes a value between $0.2$ and $0.3$. The integration in time can then take place. The
leapfrog integrator is usually used as it behaves well when coupled to gravity. \\
In the case where only one global timestep is used for all particles, the minimal timestep of all particles is reduced
and used.
and used. \\
Notice that $h$ has to be recomputed through the iterative process
presented in the previous section at every timestep. The time
derivative of the smoothing length only give a rough estimate of its
change. It only provides a good guess for the Newton-Raphson (or
bissection) scheme.
\section{Conserved quantities}
......
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