摘要
利用隐式蒙特卡罗方法模拟热辐射输运问题时,辐射源粒子的抽样对结果的正确性很重要.在球几何热辐射输运隐式蒙特卡罗模拟中,通常的做法是假设单个网格(球壳)的温度不随空间变化,即源粒子在球壳内均匀分布.对于网格内部温度分布梯度不大的情况,这种处理不会造成太大误差,然而当物质的吸收系数很大或球壳较厚时,那么单个网格内温度的空间变化也可能较大,这种处理将导致模拟的热辐射传播速度比实际的要快.本文分析了导致这种偏差的原因,并基于辐射能量密度分布,推导了球几何下辐射源粒子发射位置的概率密度函数,提出了两种辐射源粒子空间抽样方法,设计了抽样流程,计算了典型的热辐射输运问题.数值计算表明,这两种新的源粒子空间抽样方法均能修正辐射传播速度与参考值的偏差,解决计算结果过分依赖于网格剖分的问题.同时,在网格数较少、模拟粒子数较少的情况下新方法仍能得到较准确的结果,有效提高了计算效率.
Sampling of radiation source particles is important for obtaining a correct result in the thermal radiative transfer simulation with implicit Monte Carlo.When conducting the implicit Monte Carlo simulation of spherical geometry,temperature in a cell(a spherical shell)is generally treated as a spatially independent value.That means that the particles of radiative source are uniformly distributed in a spherical shell.In some cases where the gradient of temperature inside a cell is relatively small,the treatment does not cause too many errors.However,when the opacity of material becomes large enough or the spherical shell becomes thick enough,the temperature of thermal wave head will change sharply and there will be a great temperature gradient even in a single spherical shell.The treatment will make the thermal radiation propagate much faster than the practical one,which is unacceptable in physics.We investigate the physical and numerical reasons for this violation,finding that the simulation results strongly rely on the separation of cell and that the thermal wave propagates faster with the cell number decreasing.In order to yield an accurate result,the cell number has to increase up to a large enough value.Unfortunately,more cells need more particles to reduce the numerical variance,and more particles will cost more computation time and thus causing the simulation efficiency to lower.In our work,temperature is not treated as a constant in space any more.Instead,it is treated as a linear function in a cell.Based on a new temperature function and radiative energy density distribution,a probability density distribution function of emitting position of radiation source particle in spherical geometry is obtained.Then two new spatial sampling methods are proposed and the sampling procedures of radiation source particle are designed.To verify our new sampling methods,we test several typical thermal radiative problems and compare the result with a reference solution.Numerical experiments show that both two new sampling methods can correct the errors of thermal radiative propagation speed and overcome the difficulty that simulation result is strongly dependent on cell number.In addition,both new sampling methods can obtain an accurate result even with less cells and less particles,which can saves plenty of computation time and improves the simulation efficiency.
作者
许育培
李树
Xu Yu-Pei;Li Shu(Institute of Applied Physics and Computational Mathematics,Beijing 100094,China;Graduate School of China Academy of Engineering Physics,Beijing 100088,China)
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2020年第11期326-334,共9页
Acta Physica Sinica
基金
中国工程物理研究院于敏基金(批准号:FZ025)
国家自然科学基金(批准号:11775033,11775030)资助的课题.
关键词
隐式蒙特卡罗
热辐射输运
球几何
空间抽样
implicit Monte Carlo
thermal radiation transport
spherical geometry
spatial sampling
