Abstract
It has recently been proved that solutions of nonlinear radiative transfer problems satisfy a maximum principle (Andreev, Kozmanov, and Rachilov, U.S.S.R. Comput. Math. Math. Phys. 23, 104 (1983); Mercier, SIAM J. Math. Anal., in press). In this article it is shown that Monte Carlo solutions of such problems, obtained using the method of Fleck and Cummings ( J. Comput. Phys. 8, 313 (1971)), must satisfy this maximum principle for sufficiently small time-steps, but can violate it for sufficiently large time-steps. Analyses of the frequency-dependent and grey cases are given, and a numerical solution violating the maximum principle is discussed.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
