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.
Highlights
Solving the discrete-ordinates equations — that is, approximating the angular dependence using quadrature solving the resulting space-dependent system of equations analytically — is a well-known technique for generating solutions to radiation-transport problems [1]
Is this series solution easier to develop than a direct solution, we show that terms can be neglected when numerically evaluating the inverse Laplace transform such that the series reduces to a finite sum
We have extended the Analytic Discrete-Ordinates (ADO) method to time-dependent transport in finite media
Summary
Solving the discrete-ordinates equations — that is, approximating the angular dependence using quadrature solving the resulting space-dependent system of equations analytically — is a well-known technique for generating solutions to radiation-transport problems [1]. We have extended the ADO method to time-dependent transport, for the case of semi-infinite media [5] This extension was primarily accomplished through the use of a Laplace transform in time. We investigated using convergence acceleration to generate a high-precision benchmark in the presence of ray effects, which are inherent in solutions of the discrete-ordinates equations when time dependence is included. With a properly chosen sequence of quadrature sets, we can use convergence acceleration with the ADO method to produce a high-precision benchmark for time-dependent transport, too. We continue our extension of the ADO method to time-dependent transport to include finite media We develop this extension in the context of solving an example problem. Our current extension of the ADO method to time-dependent transport in finite media complements this previous work
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