PLUTO: /home/Andrea/PLUTO/Src/States/hancock.c File Reference

MUSCL-Hancock predictor step. More...

#include "pluto.h"

Detailed Description

Use time-extrapolation to compute interface states and cell-centered value at the half-time step, $V_{i,\pm}^{n+\HALF} = V_{i,\pm}^n + \partial_t V \Delta t^n/2$

This is done using the one-dimensional primitive form ot the equations for the HD, RHD and MHD modules since we have at disposal $\partial_t V = -A\partial V_x + S$ .

Conversely, for relativistic MHD, we adopt the one-dimensional conservative form of the equations (conservative Hancock predictor) and compute the primitive values using $\partial_t V \approx (V^{n+\HALF}_i-V^n_i)/(\Delta t/2)$ . This requires taking the following steps:

convert to conservative: vp -> up, vm -> um
Evolve u(n+1/2) = u(n) - dt/(2dx)*[F(vp) - F(vm)]
convert to primitive u(n+1/2) -> v(n+1/2)
add time incerement v(n+1/2)-v(n) to left/right states

Author: A. Mignone (migno.nosp@m.ne@p.nosp@m.h.uni.nosp@m.to.i.nosp@m.t)

Date: Oct 1, 2012