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Rescuing 14 sources and tagging 1 as dead.) #IABot (v2.0.1

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'''लैटिस-बोल्ट्ज़मैन मैथड''' (एल.बी.एम) तरल सिमुलेशन के लिये कंप्यूटेश्नल तरल गतिकी का एक वर्ग होता है। नेवियर-स्टोल्स समीकरण हल करने के बजाय, डिस्क्रीट बोल्ट्ज़्मैन समीकरण को हल किया जाता है। इसके द्वारा न्यूटोनियन तरल का बहाव [[भटनागर-ग्रॉस-क्रुक ऑपरेटर]] समान कोलीज़न मॉडलों का सिमुलेशन करने हेतु किया जाता है।

== गणितीय ब्यौरे ==
बोल्ट्ज़्मैन समीकरण, एकल पार्टिकल प्रोबैब्लिटी वितरण फ़ंक्शन <math>f(x,v,t)</math> के लिये एवॉल्यूशन समीकरण होता है:

:<math>\partial_t f + v\partial_x f + F\partial_v f=\Omega</math>

जहां <math>F</math> बाहरी बल है एवं <math>\Omega</math> कोलीज़न समाकलक है। लैटिस बोल्ट्ज़्मैन मैथड इस समीकरण को डिस्क्रीटाइज़ कर देता है। इसके लिये ये स्पेस को एक लैटिस एवं वेलोसिटी स्पेस को वेलोसिटी सेट्स <math>v_i</math> में डिस्क्रीटाइज़ कर देता है। तब बोल्ट्ज़्मैन समीकरण, जो अब लैटिस बोल्ट्ज़्मैन समीकरण बन चुका है, बन जाता है:

:<math>f_i(x+v_i,t+1)-f_i(x,t) + F_i=\Omega</math>

The collision operator is often approximated by a BGK collision operator:

:<math>\Omega = \frac{1}{\tau} (f_i^0-f_i)</math>

where <math>f_i^0</math> is the local equilibrium distribution.

The moments of the <math>f_i</math> give the local conserved quantities. The density is given by

:<math>\rho=\sum_i f_i</math>

and the local momentum is given by

:<math>\rho u = \sum_i f_i v_i.</math>

For the popular isothermal lattice Boltzmann methods these are the only conserved quantities. Thermal models also conserve energy and therefore have an additional conserved quantity:

:<math>\rho \theta + \rho u u =\sum_i f_i v_i v_i.</math>

The collision operator has to respect the conservation laws. Therefore the equilibirum distribution <math>f_i^0</math> must have the same conserved moments as the <math>f_i</math>.

== सॉफ्टवेयर ==
* [https://web.archive.org/web/20100515115312/http://www.exa.com/pages/pflow/pflow_physics.html PowerFLOW]: commercial CFD code which uses LBM, created and distributed by [[Exa, Inc.|Exa Corp.]]
* [https://web.archive.org/web/20120624023755/http://www.openlb.net/ OpenLB]: Open source library based on LBM, parallel, C++
* [https://web.archive.org/web/20100421114849/http://elbeem.sourceforge.net/ El'Beem]: free CFD code (GPL) which uses LBM
* [https://web.archive.org/web/20090614195322/http://thomas-pohl.info/work/lba.html J-Lattice-Boltzmann]: interactive Java applet for experimenting with LBM
* [http://physics.ndsu.edu/people/faculty/wagner/lattice_boltzmann_codes/ C examples]{{Dead link|date=जून 2020 |bot=InternetArchiveBot }}: Some simple example LBM code in C.
* [https://web.archive.org/web/20100703161333/http://www.lbmethod.org/palabos/ Palabos]: Open source lattice Boltzmann code
* [https://web.archive.org/web/20100507030106/http://sailfish.us.edu.pl/ Sailfish]: Open Source LBM code (LGPL) for Graphics Processing Units (CUDA/OpenCL)
* [https://web.archive.org/web/20190129040329/http://walberla.net/ waLBerla]: Open Source HPC software framework for the LBM, massively parallel, C++

== विस्तृत पठन ==
* {{cite book|author=Succi, Sauro|title=The Lattice Boltzmann Equation for Fluid Dynamics and Beyond|publisher=[[ऑक्सफोर्ड यूनिवर्सिटी प्रेस]]|year=2001|isbn=0198503989}}
* {{cite book|author=Wolf-Gladrow, Dieter|title=Lattice-Gas Cellular Automata and Lattice Boltzmann Models|publisher=[[Springer Verlag]]|year=2000|isbn=9783540669739}}
* {{cite book|author=Sukop, Michael C. and Daniel T. Thorne, Jr.|title=Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers|publisher = [[Springer Science+Business Media|Springer]]|year=2007|isbn=9783540279815}}
* {{cite book|author=Jian Guo Zhou|title=Lattice Boltzmann Methods for Shallow Water Flows|publisher = [[Springer Science+Business Media|Springer]]|year=2004|isbn=3540407464}}

== सन्दर्भ ==
<references/>

== बाहरी कड़ियां ==
* [https://web.archive.org/web/20100112044000/http://www.lbmethod.org/ LBMethod.org]: A site with various resources related to LBM, including a forum.
* [https://web.archive.org/web/20081112022707/http://www.science.uva.nl/research/scs/projects/lbm_web/lbm.html LBM Method]
* [https://web.archive.org/web/20100215133932/http://physics.ndsu.edu/fileadmin/physics.ndsu.edu/Wagner/LBbook.pdf Lattice Boltzmann summary]
* [https://web.archive.org/web/20070614172334/http://www.lstm.uni-erlangen.de/lbm/lb-methods/ Erlangen Lattice Boltzmann mailing list]
* [https://web.archive.org/web/20110720013726/http://dsfd.physics.ndsu.nodak.edu/cgi-bin/mailman/listinfo/dsfd-announce DSFD mailing list: sends information about DSFD and related conferences, opportunities for doctoral, postdoctoral, faculty and industry positions for applicants who have experience with Lattice Boltzmann or other related methods.]
* [https://web.archive.org/web/20110226125135/http://dsfd.org/ dsfd.org: Website of the annual DSFD conference series (1986 -- now) where advances in theory and application of the lattice Boltzmann method are discussed]
* [https://web.archive.org/web/20091216131744/http://www.icmmes.org/ Website of the annual ICMMES conference on Lattice Boltzmann methods and their applications ]

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लैटिस-बोल्ट्ज़मैन मैथड - अवतरण इतिहास

imported>InternetArchiveBot: Rescuing 14 sources and tagging 1 as dead.) #IABot (v2.0.1