Optimal Prediction for Radiative Transfer: a New Perspective on Moment Closure
نویسندگان
چکیده
A direct numerical solution of the radiative transfer equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent system of infinitely many moments. A fundamental problem is how to truncate the system. Various closures have been presented in the literature. We formulate the method of optimal prediction, a strategy to approximate the mean solution of a large system by a smaller system, for radiation moment systems. To that end, the formalism is generalized to systems of partial differential equations. Using Gaussian measures, we re-derive linear closures, such as PN , diffusion, and diffusion correction closures. In addition, we propose a modification to existing closures. Although simple and with no extra cost, the newly derived crescendo-diffusion yields significantly better approximations in 1D and 2D tests.
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تاریخ انتشار 2008