EAPSI: A Method Connecting Radiation Diffusion and Radiation Transfer Along Resonant Lines

EAPSI：一种沿着共振线连接辐射扩散和辐射传输的方法

• 批准号: 1613777
• 负责人: Kenneth Czuprynski
• 金额: $ 0.54万
• 依托单位: Czuprynski Kenneth D
• 依托单位国家: 美国
• 项目类别: Fellowship Award
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-06-01 至 2017-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1613777&HistoricalAwards=false
• 关键词: EAPSI; Method; Connecting; Radiation; Diffusion

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.

辐射传输方程可以用来描述光通过光学厚或光学薄区域的传输。 因此，辐射传输方程的求解引起了众多科学领域的极大兴趣。本研究的目标是开发一种将辐射扩散方程的解与光学厚区和光学薄区共存的辐射传输方程的解联系起来的方法。 众所周知，辐射传递方程在许多实际应用中很难求解。因此，经常使用扩散近似，因为所得方程更容易求解。在光学厚的区域，扩散近似是合适的;然而，在光学薄的区域，需要辐射传输方程的解。与日本筑波大学计算科学中心的Masayuki Umemura教授合作，将开发一种将光学厚区域中的辐射扩散方程的解与光学薄区域中的辐射传递方程的解联系起来的方法。这种方法将导致一个更有效的手段来解决在光学厚和薄regimes. More共存的区域中的辐射传递问题，更具体地说，辐射传递方程是一个积分微分方程，它在数学上描述了辐射在参与的介质中的传播。该方程的解析解仅在一小部分情况下是已知的，这需要其数值解。然而，数值上，由于高的维度和积分微分形式的方程，计算需求是显着的。扩散近似是辐射传递中一个非常重要的近似。相比之下，辐射扩散方程更容易求解，并且是光学厚区域的精确近似。 为了开发一种更有效的方法来解决光学厚和薄制度共存的辐射传输问题，我们的目标是开发一种方法，能够耦合的辐射扩散方程的解决方案与辐射传输方程的解决方案。东亚和太平洋夏季研究所计划下的这个奖项支持美国研究生的夏季研究，由NSF和日本科学促进会共同资助。