| Title:
|
On the approximate solution of the multi-group time-dependent transport equation by $P_L$-method (English) |
| Author:
|
Míka, Stanislav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
24 |
| Issue:
|
2 |
| Year:
|
1979 |
| Pages:
|
133-154 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\Cal A$-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. (English) |
| Keyword:
|
spherical-harmonics method |
| Keyword:
|
neutron transport equation |
| Keyword:
|
approximation of solution |
| MSC:
|
45K05 |
| MSC:
|
45L05 |
| MSC:
|
82A77 |
| MSC:
|
82C70 |
| idZBL:
|
Zbl 0424.45008 |
| idMR:
|
MR0523229 |
| DOI:
|
10.21136/AM.1979.103789 |
| . |
| Date available:
|
2008-05-20T18:11:27Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103789 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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[11] K. O. Friedrichs: Symmetric positive linear differential equations.Comm. Pure Appl. Math. 11 (1958), 333-418. Zbl 0083.31802, MR 0100718 |
| Reference:
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| Reference:
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| Reference:
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[14] P. Lesaint: Finite Element Method for Symmetric Hyperbolic Equations.Numerische Mathematik 21 (1973), 244-255. MR 0341902, 10.1007/BF01436628 |
| Reference:
|
[15] А. Ш. Акишев У. M. Султангазин: О сильной сходимости метода сферических гармоник для кинетического уравнения переноса в случае сферической симметрии.Сборник ,,Математика и механика 8, Алма-Ата 1974, 12-18. Zbl 1235.49003 |
| Reference:
|
[16] S. Mika: Approximation of the solution of the multi-group time-dependent neutron transport equation by $P_L$-method.KMA VŠSE Plzeň 1976 (Dissertation - in Czech). |
| Reference:
|
[17] A. Douglis: The Solutions of Multidimensional Generalized Transport Equation and Their Calculation by Difference Methods.Numerical Solution of Partial Differential Equations ed. by Bramble. Academic Press, New York 1965, 197-256. MR 0205026 |
| Reference:
|
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| Reference:
|
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| . |
