Line-sampling-based Monte Carlo method

Overview & Synopsis

Null-collision Monte Carlo algorithms [1, 2, 3, 4] consist in adding a virtual null-collision coefficient to the real extinction one. These collisions, corresponding to pure forward scattering events, have no effect on the radiative transfer equation. A direct consequence of their introduction is that the resulting extinction coefficientˆβcoefficientˆ coefficientˆβ (defined as the sum of absorption, scattering and null-collision coefficients) can be defined arbitrarily. It can then be chosen as simple as desired to guarantee a rigorous free path sampling whatever the heterogeneity of the medium properties (pressure, temperature, mole fractions). The intermediate step of producing meshes, that can be the source of unquantifiable bias, is no longer required. In more formal terms, the exponential extinction term does not depend on the real extinction coefficient anymore, but only on the arbitrary fieldˆβfieldˆ fieldˆβ. Thereby, the absorption coefficient appears only in a linear form in the recursive integral formulation of radiative transfer equation. Then it becomes possible when studying thermal radiation in a gaseous mixture to decompose the absorption coefficient as the sum of contributions of each molecular transition (or line) for each considered species. This opens the door to the development of reference methods for which the costly step of producing numerous high-resolution absorption spectra vanishes. The absorption coefficient evaluation is no more required, only some molecular transitions are sampled during the Monte Carlo simulation and their exact contribution to absorption coefficient (for a given wavenum-ber and a given location) are computed from parameters gathered in molecular spectroscopic databases [5, 6, 7]. Nevertheless, it implies that probabilities must be associated to each molecular species and to each transition. The choice of these probabilities is fully arbitrary and has only an influence on the convergence rate of the algorithm. Such a probabilistic model is proposed, and the considered Monte Carlo approach is tested and validated against six unidimensional and non-scattering configurations gathered by André and Vaillon in [8]. The description of these cases, that cover a wide variety of high-temperature applications, is depicted in Fig. 1.