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

Abstract

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.

Authors:
 [1];  [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1489467
Report Number(s):
LLNL-JRNL-753609
Journal ID: ISSN 2332-4309; 940135
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational and Theoretical Transport
Additional Journal Information:
Journal Name: Journal of Computational and Theoretical Transport; Journal ID: ISSN 2332-4309
Publisher:
Taylor and Francis
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; diffusion equation; deterministic method; radiation transport

Citation Formats

Gentile, Nicholas A., and Hayes, John C. A Test Problem for Codes Solving the Discretized Diffusion Equation in Cartesian Geometry Derived Via Discrete Green’s Functions. United States: N. p., 2018. Web. doi:10.1080/23324309.2018.1497992.
Gentile, Nicholas A., & Hayes, John C. A Test Problem for Codes Solving the Discretized Diffusion Equation in Cartesian Geometry Derived Via Discrete Green’s Functions. United States. doi:10.1080/23324309.2018.1497992.
Gentile, Nicholas A., and Hayes, John C. Sun . "A Test Problem for Codes Solving the Discretized Diffusion Equation in Cartesian Geometry Derived Via Discrete Green’s Functions". United States. doi:10.1080/23324309.2018.1497992. https://www.osti.gov/servlets/purl/1489467.
@article{osti_1489467,
title = {A Test Problem for Codes Solving the Discretized Diffusion Equation in Cartesian Geometry Derived Via Discrete Green’s Functions},
author = {Gentile, Nicholas A. and Hayes, John C.},
abstractNote = {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.},
doi = {10.1080/23324309.2018.1497992},
journal = {Journal of Computational and Theoretical Transport},
number = ,
volume = ,
place = {United States},
year = {2018},
month = {11}
}

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