Unexpected convergence of lattice Boltzmann schemes
| Autor: | Tekitek, Mohamed-Mahdi, Boghosian, Bruce, Dubois, François, Graille, Benjamin, Lallemand, Pierre, Tekitek, Mohamed Mahdi |
|---|---|
| Přispěvatelé: | Faculté des Sciences Mathématiques, Physiques et Naturelles de Tunis (FST), Université de Tunis El Manar (UTM), Tufts University [Medford], Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mécanique des Structures et des Systèmes Couplés (LMSSC), Conservatoire National des Arts et Métiers [CNAM] (CNAM), Beijing Computational Science Research Center [Beijing] (CSRC) |
| Rok vydání: | 2018 |
| Předmět: |
General Computer Science
Scalar (mathematics) Lattice Boltzmann methods Time step Thermal diffusivity 01 natural sciences damped acoustic 010305 fluids & plasmas Dispersion relation 0103 physical sciences FOS: Mathematics 4710+g AMS (MSC2010) classification: 76M28 Mathematics - Numerical Analysis 0101 mathematics dispersion equation Scaling Physics Partial differential equation heat equation Mathematical analysis General Engineering Numerical Analysis (math.NA) Taylor expansion method PACS numbers: 0270Ns 0520Dd 010101 applied mathematics Heat equation [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] |
| Zdroj: | Computers and Fluids Computers and Fluids, Elsevier, 2020, 172, pp.301-311. ⟨10.1016/j.compfluid.2018.04.029⟩ |
| ISSN: | 0045-7930 |
| DOI: | 10.1016/j.compfluid.2018.04.029 |
| Popis: | International audience; In this work, we study numerically the convergence of the scalar D2Q9 lattice Boltzmann scheme with multiple relaxation times when the time step is proportional to the space step and tends to zero. We do this by a combination of theory and numerical experiment. The classical formal analysis when all the relaxation parameters are fixed and the time step tends to zero shows that the numerical solution converges to solutions of the heat equation, with a constraint connecting the diffusivity, the space step and the coefficient of relaxation of the momentum. If the diffusivity is fixed and the space step tends to zero, the relaxation parameter for the momentum is very small, causing a discrepency between the previous analysis and the numerical results. We propose a new analysis of the method for this specific situation of evanescent relaxation, based on the dispersion equation of the lattice Boltzmann scheme. A new asymptotic partial differential equation, the damped acoustic system, is emergent as a result of this formal analysis. Complementary numerical experiments establish the convergence of the scalar D2Q9 lattice Boltzmann scheme with multiple relaxation times and acoustic scaling in this specific case of evanescent relaxation towards the numerical solution of the damped acoustic system. |
| Databáze: | OpenAIRE |
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