PLUTO  4.4-patch2
particles_distrib_regular.c File Reference

Assign particle coordinates from distribution function. More...

#include "pluto.h"

Detailed Description

Given the separable distribution functions $ f(x) = dN/dx,\,g(y) = dN/dy $ we use the cumulative distribution function

\[ F(x)G(y) = \frac{1}{N_x}\int_{x_b}^{x} f(x)\,dx\quad \frac{1}{N_x}\int_{y_b}^{y} g(y)\,dy \qquad\mathrm{where}\qquad N_x = \int_{x_b}^{x_e} f(x) dx,\, N_y = \int_{y_b}^{y_e} g(y) dy,\, \]

to solve

\[ F(x_i) - R_i = 0 \]

using a Newton-Raphson scheme:

\[ x_i^{(k+1)} = x_i^{(k)} - \frac{F(x_i) - R_i}{f(x)/N} \]

Authors
A. Mignone (migno.nosp@m.ne@p.nosp@m.h.uni.nosp@m.to.i.nosp@m.t)
References
  • "Title"
    Authors, Journal (year) vol, page
Date
Oct 15, 2015