On the approximate solution of the multi-group time-dependent transport equation by P L -method

Stanislav Míka

Aplikace matematiky (1979)

  • Volume: 24, Issue: 2, page 133-154
  • ISSN: 0862-7940

Abstract

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This paper concerns l -velocity model of the general linear time-dependent transport equation. The assumed probability of the collision (scattering, fission) depends only on the angle of the directions of the moving neutron before and after the collision. The weak formulation of the problem is given and a priori estimates are obtained. The construction of an approximate problem by bad hbox-method is given. In the symmetric hyperbolic system obtained by bad hbox-method dissipativity and 𝒜 -orthogonality of the relevant boundary spaces are proved and the connection with the mono-velocity model of the transport equation studied in papers by U.M. Sultangazin and S.K. Godunov is shown. The work is concluded by the proof of the weak convergence of the bad hbox-method.

How to cite

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Míka, Stanislav. "On the approximate solution of the multi-group time-dependent transport equation by $P_L$-method." Aplikace matematiky 24.2 (1979): 133-154. <http://eudml.org/doc/15088>.

@article{Míka1979,
abstract = {This paper concerns $l$-velocity model of the general linear time-dependent transport equation. The assumed probability of the collision (scattering, fission) depends only on the angle of the directions of the moving neutron before and after the collision. The weak formulation of the problem is given and a priori estimates are obtained. The construction of an approximate problem by $\text\{P_L\}$-method is given. In the symmetric hyperbolic system obtained by $\text\{P_L\}$-method dissipativity and $\mathcal \{A\}$-orthogonality of the relevant boundary spaces are proved and the connection with the mono-velocity model of the transport equation studied in papers by U.M. Sultangazin and S.K. Godunov is shown. The work is concluded by the proof of the weak convergence of the $\text\{P_L\}$-method.},
author = {Míka, Stanislav},
journal = {Aplikace matematiky},
keywords = {spherical-harmonics method; neutron transport equation; approximation of solution; spherical-harmonics method; neutron transport equation; approximation of solution},
language = {eng},
number = {2},
pages = {133-154},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the approximate solution of the multi-group time-dependent transport equation by $P_L$-method},
url = {http://eudml.org/doc/15088},
volume = {24},
year = {1979},
}

TY - JOUR
AU - Míka, Stanislav
TI - On the approximate solution of the multi-group time-dependent transport equation by $P_L$-method
JO - Aplikace matematiky
PY - 1979
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 24
IS - 2
SP - 133
EP - 154
AB - This paper concerns $l$-velocity model of the general linear time-dependent transport equation. The assumed probability of the collision (scattering, fission) depends only on the angle of the directions of the moving neutron before and after the collision. The weak formulation of the problem is given and a priori estimates are obtained. The construction of an approximate problem by $\text{P_L}$-method is given. In the symmetric hyperbolic system obtained by $\text{P_L}$-method dissipativity and $\mathcal {A}$-orthogonality of the relevant boundary spaces are proved and the connection with the mono-velocity model of the transport equation studied in papers by U.M. Sultangazin and S.K. Godunov is shown. The work is concluded by the proof of the weak convergence of the $\text{P_L}$-method.
LA - eng
KW - spherical-harmonics method; neutron transport equation; approximation of solution; spherical-harmonics method; neutron transport equation; approximation of solution
UR - http://eudml.org/doc/15088
ER -

References

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