Analytical Solutions for Testing Ray-Effect Errors in Numerical Solutions of the Transport Equation

Chang, B

Lawrence Livermore National Laboratory

关键词: Numerical Solution;    Origin;    Lawrence Livermore National Laboratory;    Testing;    Absorption;   

DOI  :  10.2172/15004539
RP-ID  :  UCRL-ID-153272
RP-ID  :  W-7405-ENG-48
RP-ID  :  15004539

美国|英语

来源: UNT Digital Library

【 摘 要 】

This paper contains three analytical solutions of transport problems which can be used to test ray-effect errors in the numerical solutions of the Boltzmann Transport Equation (BTE). We derived the first two solutions and the third was shown to us by M. Prasad [2]. Since this paper is intended to be an internal LLNL report, no attempt was made to find the original derivations of the solutions in the literature in order to cite the authors for their work. Before we embarked on this project, the only analytical solution known to us which could serve as a diagnostic test for ray-effects is the solution of an isotropic point source in a homogeneous non-scattering medium. However this solution is not an accurate test, because a point source is difficult to represent numerically. Thus it is useful for testing purposes to have an analytical solution of a localized volume source. The sources in the three problems below are isotropic spheres centered at the origin. Since ray-effect oscillations are the most pronounced for the transport in a vacuum (because the oscillations are not damped out by absorption), the absorption is set to zero in the regions exterior of the sources in the three problems. Since these problems are spherically symmetric, they are solved in the 1-D spherical coordinate system.