Energy conservation in radiation hydrodynamics. Application to the Monte Carlo method used for photon transport in the fluid frame

Abstract

The advantage of a formulation of the radiative transfer equation in the fluid frame has recently been shown by R.BUCHLER and D. MIHALAS. The equations obtained with this formulation clearly show that the Doppler shift should not be neglected, even in cases where the material velocity is much smaller than the speed of light, in order to keep energy balance.

We analyze some consequences of this remark in the case where the radiative transfer equation is solved via the Monte-Carlo Method : we show that the energy loss of a Monte Carlo photon in a cell is composed of two parts, one due to absorption, the other (which may be negative) to the Doppler shift. We also show that the latter can be used in order to get an estimation of the work of the radiative pressure, and the radiative pressure itself. Finally we show that, with such a modification of the standard procedure, one can get energy conservation, even in some relatively high (though non relativistic) speed flows.