Computational attributes of the integral form of the equation of transfer

Details Computational attributes of the integral form of the equation of transfer Computational attributes of the integral form of the equation of transfer

Oct 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991jqsrt..46..329f&link_type=abstract

Journal of Quantitative Spectroscopy and Radiative Transfer (ISSN 0022-4073), vol. 46, Oct. 1991, p. 329-342.

Statistics

Computation

2

Anisotropic Media, Boltzmann Transport Equation, Heat Transfer, Radiative Transfer, Scattering Functions, Transport Theory, Boundary Conditions, Computer Programs, Fast Neutrons, Finite Difference Theory, Legendre Functions, Radiative Heat Transfer

Scientific paper

Difficulties can arise in radiative and neutron transport calculations when a highly anisotropic scattering phase function is present. In the presence of anisotropy, currently used numerical solutions are based on the integro-differential form of the linearized Boltzmann transport equation. This paper, departs from classical thought and presents an alternative numerical approach based on application of the integral form of the transport equation. Use of the integral formalism facilitates the following steps: a reduction in dimensionality of the system prior to discretization, the use of symbolic manipulation to augment the computational procedure, and the direct determination of key physical quantities which are derivable through the various Legendre moments of the intensity. The approach is developed in the context of radiative heat transfer in a plane-parallel geometry, and results are presented and compared with existing benchmark solutions. Encouraging results are presented to illustrate the potential of the integral formalism for computation. The integral formalism appears to possess several computational attributes which are well-suited to radiative and neutron transport calculations.

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