Abstract
It is known that classic diffusion theory can lead to negative scalar fluxes if the external source of particles is anisotropic. The usual derivation of diffusion theory, via a truncated spherical harmonics expansion, gives no consistent way of dealing with this lack of positivity. In this paper we show that asymptotic methods can be used to derive a positive diffusion equation. These same ideas can be used to produce alternate diffusion theories which should be more accurate than classic diffusion theory for diffusive problems. A specific such modified diffusion theory is developed in some detail.
Presented as a tribute to Kenneth M. Case on the occasion of his 65th birthday and to Paul F. Zweifel on the occasion of his 60th birthday
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References
J.J. Duderstadt and W.R. Martin, Transport Theory, Wiley-Interscience, New York, 1979, pp. 219–222.
G.C. Pomraning, “Diffusion Theory Via Asymptotics,” Transport Theory and Statistical Physics, submitted for publication.
E.W. Larsen and J.B. Keller, J. Math. Phys. 15, 75 (1974).
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© 1991 Springer Basel AG
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Pomraning, G.C. (1991). Diffusion Theory via Asymptotics. In: Greenberg, W., Polewczak, J. (eds) Modern Mathematical Methods in Transport Theory. Operator Theory: Advances and Applications, vol 51. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5675-1_23
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DOI: https://doi.org/10.1007/978-3-0348-5675-1_23
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5677-5
Online ISBN: 978-3-0348-5675-1
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