Project Details
Description
The radiative transfer equation can be used to describe the transport of light through optically thick or optically thin regimes. As a result, there is great interest in the solution of the radiative transfer equation from numerous scientific fields. The goal of this research is to develop a method connecting solutions of the radiative diffusion equation with solutions of the radiative transfer equation where optically thick and thin regimes coexist. The radiative transfer equation is notoriously difficult to solve in many real-world applications. As a result, the diffusion approximation is often used, as the resulting equation is easier to solve. In optically thick regimes, the diffusion approximation is appropriate; however, in optically thin regimes, the solution of the radiative transfer equation is needed. In collaboration with Professor Masayuki Umemura of the Center for Computational Sciences at the University of Tsukuba, Japan, a method connecting solutions of the radiative diffusion equation in optically thick regimes with solutions of the radiative transfer equation in optically thin regimes will be developed. This approach will result in a more efficient means of solving radiative transfer problems in regions where optically thick and thin regimes coexist.
More specifically, the radiative transfer equation is an integro-differential equation which mathematically describes the propagation of radiation within a medium that participates. Analytical solutions for the equation are known only for a small subset of situations, which necessitates its numerical solution. Yet numerically, due to the high dimension and integro-differential form of the equation, the computational demands are significant. The diffusion approximation is an extremely important approximation in radiative transfer. In comparison, the radiative diffusion equation is much easier to solve and is an accurate approximation in optically thick regimes. In order to develop a more efficient method for solving radiative transfer problems where optically thick and thin regimes coexist, we aim to develop a method capable of coupling solutions of the radiative diffusion equation with solutions of the radiative transfer equation.
This award under the East Asia and Pacific Summer Institutes program supports summer research by a U.S. graduate student and is jointly funded by NSF and the Japan Society for the Promotion of Science.
Status | Finished |
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Effective start/end date | 6/1/16 → 5/31/17 |
Funding
- National Science Foundation: $5,400.00