On the Stability of the Finite Difference based Lattice Boltzmann Method

Handle URI:
http://hdl.handle.net/10754/552433
Title:
On the Stability of the Finite Difference based Lattice Boltzmann Method
Authors:
El-Amin, Mohamed ( 0000-0002-1099-2299 ) ; Sun, Shuyu ( 0000-0002-3078-864X ) ; Salama, Amgad ( 0000-0002-4463-1010 )
Abstract:
This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.
KAUST Department:
Physical Sciences and Engineering (PSE) Division
Citation:
On the Stability of the Finite Difference based Lattice Boltzmann Method 2013, 18:2101 Procedia Computer Science
Publisher:
Elsevier BV
Journal:
Procedia Computer Science
Conference/Event name:
13th Annual International Conference on Computational Science, ICCS 2013
Issue Date:
1-Jun-2013
DOI:
10.1016/j.procs.2013.05.380
Type:
Conference Paper
ISSN:
18770509
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S1877050913005231
Appears in Collections:
Conference Papers; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorEl-Amin, Mohameden
dc.contributor.authorSun, Shuyuen
dc.contributor.authorSalama, Amgaden
dc.date.accessioned2015-05-07T13:54:21Zen
dc.date.available2015-05-07T13:54:21Zen
dc.date.issued2013-06-01en
dc.identifier.citationOn the Stability of the Finite Difference based Lattice Boltzmann Method 2013, 18:2101 Procedia Computer Scienceen
dc.identifier.issn18770509en
dc.identifier.doi10.1016/j.procs.2013.05.380en
dc.identifier.urihttp://hdl.handle.net/10754/552433en
dc.description.abstractThis paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.en
dc.publisherElsevier BVen
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S1877050913005231en
dc.rightsArchived with thanks to Procedia Computer Science. http://creativecommons.org/licenses/by-nc-nd/3.0/en
dc.subjectLBMen
dc.subjectFinite difference LBMen
dc.subjectStability anylasisen
dc.titleOn the Stability of the Finite Difference based Lattice Boltzmann Methoden
dc.typeConference Paperen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalProcedia Computer Scienceen
dc.conference.date2013-06-05 to 2013-06-07en
dc.conference.name13th Annual International Conference on Computational Science, ICCS 2013en
dc.conference.locationBarcelona, ESPen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Mathematics, Faculty of Science, Aswan University, Aswan 81528, Egypten
kaust.authorEl-Amin, Mohameden
kaust.authorSun, Shuyuen
kaust.authorSalama, Amgaden
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