## 10.1. Comparison of the Radiation Models

In problems where thermal radiation is significant, the proper choice of the thermal radiation will affect not only the quality of the solution, but also the computational time it requires. Detailed thermal radiation calculations are time consuming, so proper selection must be made from physical considerations.

For problems in the diffusion or thick limit (), all the modeling options will produce nearly the same results. Then, the best alternative is a balance between Rosseland and P1 models. As the optical thickness decreases and approaches 1, the P1 model becomes the least expensive alternative. Finally, in the thin limit and for purely transparent cases only the Monte Carlo and Discrete Transfer model should be used. For details, see Optical Thickness in the CFX-Solver Theory Guide.

For gray models, where the radiation field is expected to be reasonably homogeneous everywhere (at least on a local basis), and high spatial resolution is required, the discrete transfer method is much more efficient and provides very accurate results if sufficient angular resolution is used.

A major advantage of the discrete transfer method is its fixed sampling in situations where the same mesh is to be used again and again, as in the case of a combined flow-radiation calculation for modeling a combustion chamber. In this case, the ray paths can be calculated once and stored giving a large improvement in efficiency. This is impossible with Monte Carlo because the photon trajectories depend on the absorption coefficient and walls emissivity.

A major problem with discrete transfer is the lack of error information. It is possible to perform angular sub-sampling for surface fluxes, for example, but this does not help with ray effects. If a source contribution has been missed by the complete ray sample, it will also be missed by the sub-sample. This can be dealt with by running a crude Monte Carlo simulation to detect any large errors.

The actual computational time needed by the discrete transfer method can also be very difficult to assess if iterations are needed to converge to the solution, as will be the case if scattering is present. The efficiency advantage of discrete transfer over Monte Carlo also rapidly disappears when non-gray models with a large number of spectral bands are to be computed. Discrete transfer treats each band independently and so the computational time increases in proportion to the number of bands used. Effectively N separate models are computed for an N-band model. The ray tracking is only done once, however. Because it is the radiative heat transfer that is computed, and the actual spectrum is of no interest, a Monte Carlo simulation is hardly affected by the number of bands as the spectrum is just another independent parameter to be sampled.

Unlike Monte Carlo, all the physical quantities of interest are found at fixed points (due to the fixed sampling and ray discretization), not as surface or volume averages.

Release 18.2 - © ANSYS, Inc. All rights reserved.