A nonlinear diffusion theory for particle transport in strong absorbers

The Minerboʹs maximum entropy Eddington factor (MEEF) method is attractive as a low-order approximation to transport theory due to its accuracy and simplicity for handling various degree of anisotropy in radiation fields. However, it has been demonstrated that certain commonly used implicit mesh schemes that have been tried for solving the MEEF equations are numerically unstable and may lead to anomalous solutions. An effective remedy for this numerical difficulty is to derive a nonlinear diffusion approximation from the MEEF description. The resulting nonlinear diffusion equation can be solved by the commonly used implicit mesh schemes and is almost as accurate as the MEEF description. Although primarily developed for time-dependent radiation-hydrodynamics and other high-energy physics problems that involve strong anisotropy of radiation field near radiation wave fronts, the nonlinear diffusion theory is demonstrated to be applicable to a variety of steady state particle transport problems, especially for problems with strong absorption. Overall, it predicts better results than other low-order approximations.