Kinetic Description of Multiscale Phenomena
The Annual Kinetic FRG Meeting
September 21-25, 2009
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Boundary Conditions for Moment Closures
Dr. C. David Levermore
University of Maryland
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Abstract: Moment closures with asymptotically consistent boundary conditions are developed to describe monoenergetic, photon transport through a bounded, stationary, isotropic medium that scatters, absorbs, and emits as a blackbody. It is found that for traditional spherical harmonic closures (PN) asymptotically consistent boundary conditions generally overdetermine the moment equations. Traditional boundary conditions that make the PN system well-posed (like the Marshak conditions) are therefore inconsistent with an asymptotically decaying boundary layer. A notable exception to this inconsistency is the PN system in planar geometry when N is odd, for which asymptotically consistent boundary conditions were derived by Larsen and Pomraning. By adding a diffusive term to traditional spherical harmonic closures, one obtains a closure (DN) with asymptotically consistent boundary conditions that are well-posed. |
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