A Test Problem for Codes Solving the Discretized Diffusion Equation in Cartesian Geometry Derived Via Discrete Green’s Functions

Journal Article · 10 November 2018 · Journal of Computational and Theoretical Transport

DOI: https://doi.org/10.1080/23324309.2018.1497992 · OSTI ID:1489467

Gentile, Nicholas A. ^[1]; Hayes, John C. ^[1]

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1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

We obtain here a solution to a zone-centered discretization of the one dimensional time-dependent diffusion equation with arbitrary initial conditions and source, constant absorption and scattering opacity, and constant zone size and time step. The solution is obtained using the discrete Green’s functions of the discretized equation. The solution of the discretized equation is useful in the testing of computer codes, because the code can be expected to agree with the solution to the discrete equation, to within small errors caused by roundoff. This is in contrast to solutions of the differential equation, with which the code results only approximately agree. Finally, the usefulness of the solution for tests of an inertial confinement fusion code is demonstrated.

• Research Organization: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC52-07NA27344
• OSTI ID: 1489467
• Report Number(s): LLNL-JRNL--753609; 940135
• Journal Information: Journal of Computational and Theoretical Transport, Journal Name: Journal of Computational and Theoretical Transport Journal Issue: 4-6 Vol. 47; ISSN 2332-4309
• Publisher: Taylor and FrancisCopyright Statement
• Country of Publication: United States
• Language: English