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4月25日 江松院士学术报告 (数学与统计学院)

编辑:时间:2019-04-23浏览:54设置

报 告 人:江松 院士

报告题目:Asymptotic preserving schemes for radiative transfer systems

报告时间:2019年4月25日(周四)下午16:30

报告地点:静远楼1506报告厅

主办单位:数学与统计学院、科学技术研究院

报告人概况:

  江松,应用数学家。1982年毕业于四川大学数学系,1984年在西安交通大学获硕士学位,1988年在德国波恩大学获博士学位。2015年当选中国科学院院士。 北京应用物理与计算数学研究所研究员,党委书记。

  主要从事可压缩流体力学数学理论、计算方法及应用研究。在理论方面,对任何绝热指数γ>1,与合编辑证明了具有大外力的三维定常可压缩Navier-Stokes (NS)方程弱解的存在性,以及具有大初值的高维非定常NS方程球/轴对称解的整体存在性。在应用方面,针对武器物理数值模拟的多介质大变形、网格畸变等计算难点,与同事一起提出了若干实用的新算法(如整体ALE局部欧拉自然耦合方法),并研制完成重大武器型号数值模拟App平台。曾获国家自然科学二等奖、军队科技进步一等奖、中国青年科技奖、求是杰出青年奖等。

报告摘要:

  Radiative transfer systems find a wide range of applications, for example, in the inertial constrained fusion research and in astrophysics. The solution of a radiative transport system can cover both optical thin and optical thick regimes due to the large variation of photon's mean-free path and its interaction with the material. In the small mean free path limit, a nonlinear time-dependent radiative transfer system can converge to an equilibrium diffusion equation due to the intensive interaction among radiation and material. In the optical thin limit, the photon free transport mechanism will emerge. In this talk, we are going to develop an asymptotic preserving unified gas kinetic scheme (AP-UGKS) for both grey and frequency-dependent radiative transfer systems, where the radiation transport equation is coupled with the material thermal energy equation. The newly developed scheme has the asymptotic preserving property in the optically thick regime to capture the diffusive solution without using a cell size being smaller than the photon’s mean free path and time step being less than the photon collision time. Besides the diffusion limit, the scheme can capture the exact solution in the optical thin regime as well. Due to the direct modeling for the time evolution of the interface radiative intensity, a smooth transition of the transport physics from optical thin to optical thick can be accurately recovered. Many numerical examples are included to validate the current approach. Extensions to more complex systems will be presented.      


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