ANALYTIC DISCRETE-ORDINATES SOLUTION FOR TIME-DEPENDENT TRANSPORT IN FINITE MEDIA

Abstract

We present an extension of the Analytic Discrete-Ordinates method to time-dependent transport in finite media. The application of this technique to time-dependent transport is primarily accomplished through the use of a Laplace transform. In the case of finite media, a system of equations arises from enforcing boundary conditions. Instead of directly solving this system, we construct a solution in terms of a Neumann series. We then show that terms can be neglected when numerically evaluating the inverse Laplace transform such that the series reduces to a finite sum. With this extension, we use convergence acceleration to generate a high-precision benchmark.

Keywords

• analytic discrete-ordinates method
• time-dependent transport
• laplace transform
• neumann series
• talbot’s method
• wynn-epsilon convergence acceleration