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 zonecentered discretization of the one dimensional timedependent 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:

 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):
 LLNLJRNL753609
Journal ID: ISSN 23324309; 940135
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational and Theoretical Transport
 Additional Journal Information:
 Journal Volume: 47; Journal Issue: 46; Journal ID: ISSN 23324309
 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 zonecentered discretization of the one dimensional timedependent 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 = 46,
volume = 47,
place = {United States},
year = {2018},
month = {11}
}