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A moment closure based on a projection on the boundary of the realizability domain: 1D case. (English) Zbl 1458.35350

Summary: This work aims to develop and test a projection technique for the construction of closing equations of moment systems. One possibility to define such a closure consists in reconstructing an underlying kinetic distribution from a vector of moments, then expressing the closure based on this reconstructed function.
Exploiting the geometry of the realizability domain, i.e. the set of moments of positive distribution function, we decompose any realizable vectors into two parts, one corresponding to the moments of a chosen equilibrium function, and one obtain by a projection onto the boundary of the realizability domain in the direction of equilibrium function. A realizable closure of both of these parts are computed with standard techniques providing a realizable closure for the full system. This technique is tested for the reduction of a radiative transfer equation in slab geometry.

MSC:

35Q35 PDEs in connection with fluid mechanics
35Q79 PDEs in connection with classical thermodynamics and heat transfer
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76T10 Liquid-gas two-phase flows, bubbly flows
80A21 Radiative heat transfer
35L40 First-order hyperbolic systems
35B09 Positive solutions to PDEs
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
65F05 Direct numerical methods for linear systems and matrix inversion
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F20 Numerical solutions to overdetermined systems, pseudoinverses
35R06 PDEs with measure

Software:

NumPy; ATTILA
PDFBibTeX XMLCite
Full Text: DOI

References:

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