Lattice Boltzmann Method without Invoking the M << 1 Assumption

SO Ronald

doi:10.61927/igmin223

109 of 152

The Influence of Low Pesticide Doses on Fusarium Molds

Mihaela Ursan, Oana-Alina Boiu-Sicuia, Ioana Irina Crăinescu and Călina Petruța Cornea

111 of 152

Harnessing Microbes for the Benefit of Man

Sayan Bhattacharyya

Biology Group Review Article 記事ID: igmin223

Lattice Boltzmann Method without Invoking the M << 1 Assumption

Atmospheric Science

SO Ronald ^*

Affiliation

DOI10.61927/igmin223 全文HTML 全文PDF この記事を引用する

要約

When a Maxwellian distribution is assumed for the distribution function in the BGK-type modelled BE, it will give rise to the Euler equations if it is the first-order approximation in the Chapman-Enskog method. Then the second-order equations will yield the N-S equations. Most LBM developed to date are formulated based on the second-order equations. Consequently, the assumption of a flow Mach number M << 1 is inherent in this formulation. This approach creates an unnecessary restriction on the LBM that should be avoided if possible. An alternative approach is to formulate a new LBM by considering an equilibrium distribution function where the first-order approximations give rise to the N-S equations. Adopting this approach, a new LBM has been formulated. This new LBM gives reliable results when applied to simulate aeroacoustics, incompressible flows, and compressible flows with and without shocks. Good agreement with measurements and numerical data derived from DAS/DNA calculations is obtained.

参考文献

Chapman S, Cowling TG. The Mathematical Theory of Non-uniform Gases. Cambridge University Press; 1939. Chapter 12.
Mott-Smith HM. The solution of the Boltzmann equation for a shock wave. Phys Rev. 1951;82:885-892.
Wang-Chang CS, Uhlenbeck GE, deBoer J, editors. Studies in Statistical Mechanics. Wiley; 1964; 2.
Morse TF. Kinetic model for gases with internal degrees of freedom. Phys Fluids. 1964;7:159-169.
Salwen H, Grousch CE, Ziering S. Extension of the Mott-Smith method for a one-dimensional shock wave. Phys Fluids. 1964;7:180-189.
Holway LH. New statistical models for kinetic theory: methods of construction. Phys Fluids. 1966;9:1658-1673.
Bhatnagar PL, Gross EP, Krook M. A model for collision processes in gases: I. Small amplitude processes in charged and neutral one-component systems. Phys Rev. 1954;94:511-525.
Broadwell J. Study of rarefied shear flow by the discrete velocity method. Phys Fluids. 1964;7:1243.
Cao NS, Chen S, Jin S, Martinez D. Physical symmetry and lattice symmetry in the lattice Boltzmann method. Phys Rev E. 1997;55:R21-24.
Mei R, Shyy W. On the finite difference-based lattice Boltzmann method in curvilinear coordinates. J Comput Phys. 1998;143:426-448.
Wolf-Gladrow DA. Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction. Springer Verlag; 2000. Chapter 5.
Alexander FJ, Chen S, Sterling JD. Lattice Boltzmann thermohydrodynamics. Phys Rev E. 1993;47:R2249-R2252.
McNamara GR, Alder B. Analysis of the lattice Boltzmann treatment of hydrodynamics. Physica A. 1993;194:218-228.
Hu S, Yan G, Shi W. A lattice Boltzmann model for compressible perfect gas. Acta Mechanica Sinica (English Edition). 1997;13:218-226.
Kataoka T, Tsutahara M. Lattice Boltzmann model for the compressible Navier-Stokes equations with flexible specific-heat ratio. Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Mar;69(3 Pt 2):035701. doi: 10.1103/PhysRevE.69.035701. Epub 2004 Mar 25. PMID: 15089354.
Xu K. Gas-Kinetic Scheme for Unsteady Compressible Flow Simulations. von Karman Institute for Fluid Dynamics Lecture Series, Vol. 1998-03. von Karman Institute; 1998.
Li XM, Leung RCK, So RMC. One-step aeroacoustics simulation using lattice Boltzmann method. AIAA J. 2006;44:78-89.
Li XM. Computational Aeroacoustics Using Lattice Boltzmann Model. PhD thesis. Mechanical Engineering Department, Hong Kong Polytechnic University; 2006.
Eucken A. Über das Wärmeleitvermögen, die spezifische Wärme und die innere Reibung der Gase. Physikalische Zeitschrift. 1913;14:324-332.
Lallemand P, Luo LS. Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions. Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Sep;68(3 Pt 2):036706. doi: 10.1103/PhysRevE.68.036706. Epub 2003 Sep 23. PMID: 14524925.
Chen Y, Ohashi H, Akiyama M. Thermal lattice Bhatnagar-Gross-Krook model without nonlinear deviations in macrodynamic equations. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1994 Oct;50(4):2776-2783. doi: 10.1103/physreve.50.2776. PMID: 9962315.
McNamara GR, Garcia AL, Alder BJ. Stabilization of thermal lattice Boltzmann models. J Statistical Phys. 1995;81:395-408.
Teixeira C, Chen H, Freed DM. Multi-speed thermal lattice Boltzmann method stabilization via equilibrium under-relaxation. Comput Phys Commun. 2000;129:207-226.
Shan X. Simulation of Rayleigh-Bénard convection using a lattice Boltzmann method. Phys Rev E. 1997;55:2780-2788.
Leung RCK, Kam EWS, So RMC. Recovery of the transport coefficients in the Navier-Stokes equations from the modeled Boltzmann equation. AIAA J. 2007;45:737-739.
Aristov VV. Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows. Kluwer Academic Publishers; 2001. Chapter 7.
So RMC, Leung RCK, Kam EWS, Fu SC. Progress in the development of a new lattice Boltzmann method. Computers & Fluids. 2019;190:440-469.
Fu SC, So RMC, Leung RCK. Modeled Boltzmann equation and its application to direct aeroacoustics simulation. AIAA J. 2008;46:1651-1662.
So RMC, Leung RCK, Fu SC. Modeled Boltzmann equation and its application to shock-capturing simulation. AIAA J. 2008;46:3038-3048.
So RMC, Fu SC, Leung RCK. Finite Difference Lattice Boltzmann Method for Compressible Thermal Fluids. AIAA J. 2010;48(6):1059-1071.
Lele SK. Direct numerical simulations of compressible turbulent flows: fundamentals and applications. In: Hanifi A, et al., editors. Transition, Turbulence and Combustion Modeling. Kluwer Academic Publishers; 1998. pp. 424-429.
Brenner H. Kinematics of volume transport. Physica A. 2005;349:11-59.
Brenner H. Navier-Stokes revisited. Physica A. 2005;349:60-132.
Greenshields CJ, Reese JM. The structure of shock waves as a test of Brenner’s modifications to the Navier-Stokes equations. J Fluid Mech. 2007;580:407-429.
Kam EWS, So RMC, Leung RCK. Lattice Boltzmann method simulation of aeroacoustics and nonreflecting boundary conditions. AIAA J. 2007;45:1703-1712.
Li XM, So RMC, Leung RCK. Propagation speed, internal energy and direct aeroacoustics simulation using lattice Boltzmann method. AIAA J. 2006;44:2896-2903.
Leung RCK, Li XM, So RMC. Comparative Study of Nonreflecting Boundary Condition for One-Step Duct Aeroacoustics Simulation. AIAA J. 2006;44:664-667.
Tam CKW, Webb JC. Dispersion-relation-preserving finite difference schemes for computational aeroacoustics. J Comput Phys. 1993;107:262-281.
Gilbarg D, Paolucci D. The structure of shock waves in the continuum theory of fluids. J Rat. Mech. Analy. 1953;2:617-642.
Ohwada T. Structure of normal shock waves: direct numerical analysis of the Boltzmann equation for Hard-sphere molecules. Phys Fluids A. 1993;5:217-234.
Alsmeyer H. Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam. J Fluid Mech. 1976;74:497-513.
Thomas LH. Note on Becker’s theory of the shock front. J Chem Phys. 1944;12:449-453.
Chu CK. Kinetic-theoretic description of the formation of a shock wave. Phys Fluids. 1965;8:12-22.
Bird GA. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press; 1994.
Yang JY, Huang JC. Rarefied flow computations using nonlinear model Boltzmann equations. J Comput Phys. 1995;120:323-339.
Xu K, Tang L. Nonequilibrium Bhatnagar-Gross-Krook model for nitrogen shock structure. Phys Fluids. 2004;16:3824-3827.
Xu K, Josyula E. Gas-kinetic scheme for rarefied flow simulation. Math Comput Simul. 2006;72:253-256.
Weiss W. Continuous shock structure in extended thermodynamics. Phys Rev E. 1995;52:R5760-5763.

類似の記事

Potentially Toxic Metals in Cucumber Cucumis sativus Collected from Peninsular Malaysia: A Human Health Risk Assessment
Chee Kong Yap, Rosimah Nulit, Aziran Yaacob, Zaieka Shamsudin, Meng Chuan Ong, Wan Mohd Syazwan, Hideo Okamura, Yoshifumi Horie, Chee Seng Leow, Ahmad Dwi Setyawan, Krishnan Kumar, Wan Hee Cheng and Kennedy Aaron Aguol
DOI10.61927/igmin200

Atmospheric Fungal Spore Injection: A Promising Breakthrough for Challenging the Impacts of Climate Change Through Cloud Seeding and Weather Modification
Adam Ghebrezgiabher Ghebreyesus and Tedros Gebrezgiabhier Gebreyesus
DOI10.61927/igmin248

Revisit TBCK-A Pseudo Kinase or a True Kinase
Jin Wu and Jianjun Zhu
DOI10.61927/igmin238

Fred Vlès – Early Holistic Biophysicist and Pioneer of “Earthing”
Marco Bischof
DOI10.61927/igmin129

Diagnostic Challenges in Pancreatic Tumors
Ionuţ Simion Coman, Elena Violeta Coman, Costin George Florea, Teodora Elena Tudose, Cosmin Burleanu, Anwar Erchid and Valentin Titus Grigorean
DOI10.61927/igmin185

The Influence of Dynamical Downscaling and Boundary Layer Selection on Egypt’s Potential Evapotranspiration using a Calibrated Version of the Hargreaves-samani Equation: RegCM4 Approach
Samy A Anwar and Ankur Srivastava
DOI10.61927/igmin229

Peritoneal Carcinomatosis from Ovarian Cancer: A Case Report
Andrea González De Godos, Enrique Asensio Diaz, Pilar Pinto Fuentes, Baltasar Pérez Saborido and David Pacheco Sánchez
DOI10.61927/igmin181

Lifestyle and Well-being among Portuguese Firefighters
Laura Carmona, Raquel Pinheiro, Joana Faria-Anjos, Sónia Namorado and Maria José Chambel
DOI10.61927/igmin146

The use of FIKR (Facet, Insight, Knowledge, and Resilience) Personality as an Effective Assessment Tool to Select the Best Leadership in an Organization
Chee Kong Yap, Chee Seng Leow and Wing Sum Vincent Leong
DOI10.61927/igmin174

The Dibia in Igbo Traditional Socio-political and Metaphysical Economy: An Interrogation
Kingsley Okoro and Kenneth Igbo Nwokike
DOI10.61927/igmin176

ソーシャルアイコン

研究を公開する

私たちは、科学、技術、工学、医学に関する幅広い種類の記事を編集上の偏見なく公開しています。

提出する

見る原稿のガイドライン追加論文処理料

IgMin 科目を探索する

トップ10の記事をクリック

クイックリンク

原稿を提出する

研究論文

グーグルスカラー

Google Scholarは2004年11月にベータ版が発表され、幅広い学術領域を航海する学術ナビゲーターとして機能します。それは査読付きジャーナル、書籍、会議論文、論文、博士論文、プレプリント、要約、技術報告書、裁判所の意見、特許をカバーしています。 IgMin の記事を検索

[1] Chapman S, Cowling TG. The Mathematical Theory of Non-uniform Gases. Cambridge University Press; 1939. Chapter 12.

[2] Mott-Smith HM. The solution of the Boltzmann equation for a shock wave. Phys Rev. 1951;82:885-892.

[3] Wang-Chang CS, Uhlenbeck GE, deBoer J, editors. Studies in Statistical Mechanics. Wiley; 1964; 2.

[4] Morse TF. Kinetic model for gases with internal degrees of freedom. Phys Fluids. 1964;7:159-169.

[5] Salwen H, Grousch CE, Ziering S. Extension of the Mott-Smith method for a one-dimensional shock wave. Phys Fluids. 1964;7:180-189.

[6] Holway LH. New statistical models for kinetic theory: methods of construction. Phys Fluids. 1966;9:1658-1673.

[7] Bhatnagar PL, Gross EP, Krook M. A model for collision processes in gases: I. Small amplitude processes in charged and neutral one-component systems. Phys Rev. 1954;94:511-525.

[8] Broadwell J. Study of rarefied shear flow by the discrete velocity method. Phys Fluids. 1964;7:1243.

[9] Cao NS, Chen S, Jin S, Martinez D. Physical symmetry and lattice symmetry in the lattice Boltzmann method. Phys Rev E. 1997;55:R21-24.

[10] Mei R, Shyy W. On the finite difference-based lattice Boltzmann method in curvilinear coordinates. J Comput Phys. 1998;143:426-448.

[11] Wolf-Gladrow DA. Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction. Springer Verlag; 2000. Chapter 5.

[12] Alexander FJ, Chen S, Sterling JD. Lattice Boltzmann thermohydrodynamics. Phys Rev E. 1993;47:R2249-R2252.

[13] McNamara GR, Alder B. Analysis of the lattice Boltzmann treatment of hydrodynamics. Physica A. 1993;194:218-228.

[14] Hu S, Yan G, Shi W. A lattice Boltzmann model for compressible perfect gas. Acta Mechanica Sinica (English Edition). 1997;13:218-226.

[15] Kataoka T, Tsutahara M. Lattice Boltzmann model for the compressible Navier-Stokes equations with flexible specific-heat ratio. Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Mar;69(3 Pt 2):035701. doi: 10.1103/PhysRevE.69.035701. Epub 2004 Mar 25. PMID: 15089354.

[16] Xu K. Gas-Kinetic Scheme for Unsteady Compressible Flow Simulations. von Karman Institute for Fluid Dynamics Lecture Series, Vol. 1998-03. von Karman Institute; 1998.

[17] Li XM, Leung RCK, So RMC. One-step aeroacoustics simulation using lattice Boltzmann method. AIAA J. 2006;44:78-89.

[18] Li XM. Computational Aeroacoustics Using Lattice Boltzmann Model. PhD thesis. Mechanical Engineering Department, Hong Kong Polytechnic University; 2006.

[19] Eucken A. Über das Wärmeleitvermögen, die spezifische Wärme und die innere Reibung der Gase. Physikalische Zeitschrift. 1913;14:324-332.

[20] Lallemand P, Luo LS. Theory of the lattice Boltzmann method: acoustic and thermal properties in two and three dimensions. Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Sep;68(3 Pt 2):036706. doi: 10.1103/PhysRevE.68.036706. Epub 2003 Sep 23. PMID: 14524925.

[21] Chen Y, Ohashi H, Akiyama M. Thermal lattice Bhatnagar-Gross-Krook model without nonlinear deviations in macrodynamic equations. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1994 Oct;50(4):2776-2783. doi: 10.1103/physreve.50.2776. PMID: 9962315.

[22] McNamara GR, Garcia AL, Alder BJ. Stabilization of thermal lattice Boltzmann models. J Statistical Phys. 1995;81:395-408.

[23] Teixeira C, Chen H, Freed DM. Multi-speed thermal lattice Boltzmann method stabilization via equilibrium under-relaxation. Comput Phys Commun. 2000;129:207-226.

[24] Shan X. Simulation of Rayleigh-Bénard convection using a lattice Boltzmann method. Phys Rev E. 1997;55:2780-2788.

[25] Leung RCK, Kam EWS, So RMC. Recovery of the transport coefficients in the Navier-Stokes equations from the modeled Boltzmann equation. AIAA J. 2007;45:737-739.

[26] Aristov VV. Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows. Kluwer Academic Publishers; 2001. Chapter 7.

[27] So RMC, Leung RCK, Kam EWS, Fu SC. Progress in the development of a new lattice Boltzmann method. Computers & Fluids. 2019;190:440-469.

[28] Fu SC, So RMC, Leung RCK. Modeled Boltzmann equation and its application to direct aeroacoustics simulation. AIAA J. 2008;46:1651-1662.

[29] So RMC, Leung RCK, Fu SC. Modeled Boltzmann equation and its application to shock-capturing simulation. AIAA J. 2008;46:3038-3048.

[30] So RMC, Fu SC, Leung RCK. Finite Difference Lattice Boltzmann Method for Compressible Thermal Fluids. AIAA J. 2010;48(6):1059-1071.

[31] Lele SK. Direct numerical simulations of compressible turbulent flows: fundamentals and applications. In: Hanifi A, et al., editors. Transition, Turbulence and Combustion Modeling. Kluwer Academic Publishers; 1998. pp. 424-429.

[32] Brenner H. Kinematics of volume transport. Physica A. 2005;349:11-59.

[33] Brenner H. Navier-Stokes revisited. Physica A. 2005;349:60-132.

[34] Greenshields CJ, Reese JM. The structure of shock waves as a test of Brenner’s modifications to the Navier-Stokes equations. J Fluid Mech. 2007;580:407-429.

[35] Kam EWS, So RMC, Leung RCK. Lattice Boltzmann method simulation of aeroacoustics and nonreflecting boundary conditions. AIAA J. 2007;45:1703-1712.

[36] Li XM, So RMC, Leung RCK. Propagation speed, internal energy and direct aeroacoustics simulation using lattice Boltzmann method. AIAA J. 2006;44:2896-2903.

[37] Leung RCK, Li XM, So RMC. Comparative Study of Nonreflecting Boundary Condition for One-Step Duct Aeroacoustics Simulation. AIAA J. 2006;44:664-667.

[38] Tam CKW, Webb JC. Dispersion-relation-preserving finite difference schemes for computational aeroacoustics. J Comput Phys. 1993;107:262-281.

[39] Gilbarg D, Paolucci D. The structure of shock waves in the continuum theory of fluids. J Rat. Mech. Analy. 1953;2:617-642.

[40] Ohwada T. Structure of normal shock waves: direct numerical analysis of the Boltzmann equation for Hard-sphere molecules. Phys Fluids A. 1993;5:217-234.

[41] Alsmeyer H. Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam. J Fluid Mech. 1976;74:497-513.

[42] Thomas LH. Note on Becker’s theory of the shock front. J Chem Phys. 1944;12:449-453.

[43] Chu CK. Kinetic-theoretic description of the formation of a shock wave. Phys Fluids. 1965;8:12-22.

[44] Bird GA. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press; 1994.

[45] Yang JY, Huang JC. Rarefied flow computations using nonlinear model Boltzmann equations. J Comput Phys. 1995;120:323-339.

[46] Xu K, Tang L. Nonequilibrium Bhatnagar-Gross-Krook model for nitrogen shock structure. Phys Fluids. 2004;16:3824-3827.

[47] Xu K, Josyula E. Gas-kinetic scheme for rarefied flow simulation. Math Comput Simul. 2006;72:253-256.

[48] Weiss W. Continuous shock structure in extended thermodynamics. Phys Rev E. 1995;52:R5760-5763.

Lattice Boltzmann Method without Invoking the M << 1 Assumption

Affiliation

要約