The quasi-diffusive approximation in transport theory: Local solutions

Journal Article · Sun Jan 01 04:00:00 EST 1995 · Transport Theory and Statistical Physics

DOI:https://doi.org/10.1080/00411459508205120· OSTI ID:391351

Celaschi, M; Montagnini, B ^[1]

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1. Universita di Pisa, Pisa (Italy)

The one velocity, plane geometry integral neutron transport equation is transformed into a system of two equations, one of them being the equation of continuity and the other a generalized Fick`s law, in which the usual diffusion coefficient is replaced by a self-adjoint integral operator. As the kernel of this operator is very close to the Green function of a diffusion equation, an approximate inversion by means of a second order differential operator allows to transform these equations into a purely differential system which is shown to be equivalent, in the simplest case, to a diffusion-like equation. The method, the principles of which have been exposed in a previous paper, is here extended and applied to a variety of problems. If the inversion is properly performed, the quasi-diffusive solutions turn out to be quite accurate, even in the vicinity of the interface between different material regions, where elementary diffusion theory usually fails. 16 refs., 3 tabs.

• Sponsoring Organization: USDOE
• OSTI ID: 391351
• Journal Information: Transport Theory and Statistical Physics, Journal Name: Transport Theory and Statistical Physics Journal Issue: 1-3 Vol. 24; ISSN TTSPB4; ISSN 0041-1450
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CONTINUITY EQUATIONS
FICK LAWS
INTEGRAL EQUATIONS
NEUTRON DIFFUSION EQUATION
NEUTRON TRANSPORT THEORY
ONE-DIMENSIONAL CALCULATIONS