{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T10:30:36Z","timestamp":1764239436438},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"1-4","license":[{"start":{"date-parts":[[2007,5,10]],"date-time":"2007-05-10T00:00:00Z","timestamp":1178755200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2007,8]]},"DOI":"10.1007\/s11075-007-9087-1","type":"journal-article","created":{"date-parts":[[2007,5,9]],"date-time":"2007-05-09T07:51:12Z","timestamp":1178697072000},"page":"389-408","source":"Crossref","is-referenced-by-count":1,"title":["Stable simulation of fluid flow with high-Reynolds number using Ehrenfests\u2019 steps"],"prefix":"10.1007","volume":"45","author":[{"given":"R.","family":"Brownlee","sequence":"first","affiliation":[]},{"given":"A. N.","family":"Gorban","sequence":"additional","affiliation":[]},{"given":"J.","family":"Levesley","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2007,5,10]]},"reference":[{"issue":"2","key":"9087_CR1","doi-asserted-by":"crossref","first-page":"026311.1","DOI":"10.1103\/PhysRevE.66.026311","volume":"66","author":"S. Ansumali","year":"2002","unstructured":"Ansumali, S., Karlin, I.V.: Kinetic boundary conditions in the lattice Boltzmann method. Phys. Rev., E 66(2), 026311.1\u2013026311.6 (2002)","journal-title":"Phys. Rev., E"},{"issue":"6","key":"9087_CR2","doi-asserted-by":"crossref","first-page":"798","DOI":"10.1209\/epl\/i2003-00496-6","volume":"63","author":"S.S. Ansumali","year":"2003","unstructured":"Ansumali, S.S, Karlin, I.V., Ottinger, H.C.: Minimal entropic kinetic models for hydrodynamics. Europhys. Lett. 63(6), 798\u2013804 (2003)","journal-title":"Europhys. Lett."},{"key":"9087_CR3","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1142\/S012918310400584X","volume":"15","author":"S. Ansumali","year":"2004","unstructured":"Ansumali, S., Chikatamarla, S.S., Frouzakis, C.E., Boulouchos, K.: Entropic lattice Boltzmann simulation of the flow past square-cylinder. Int. J. Mod. Phys. C 15, 435\u2013445 (2004)","journal-title":"Int. J. Mod. Phys. C"},{"key":"9087_CR4","first-page":"2004","volume-title":"34th AIAA Fluid Dynamics Conference and Exhibit","author":"G. Baskar","year":"2004","unstructured":"Baskar, G., Babu, V.: Simulation of the unsteady flow around rectangular cylinders using the ISLB method. In: 34th AIAA Fluid Dynamics Conference and Exhibit, pp.\u00a02004\u20132651. AIAA, Washington, DC (2004)"},{"issue":"3","key":"9087_CR5","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1103\/PhysRev.94.511","volume":"94","author":"P.L. Bhatnagar","year":"1954","unstructured":"Bhatnagar, P.L., Gross, E.P., Krook, M.: A model for collision processes in gases I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94(3), 511\u2013525 (1954)","journal-title":"Phys. Rev."},{"key":"9087_CR6","doi-asserted-by":"crossref","first-page":"037703","DOI":"10.1103\/PhysRevE.74.037703","volume":"74","author":"R.A. Brownlee","year":"2006","unstructured":"Brownlee, R.A., Gorban, A.N., Levesley, J.: Stabilisation of the lattice-Boltzmann method using the Ehrenfests\u2019 coarse-graining. Phys. Rev., E 74, 037703 (2006)","journal-title":"Phys. Rev., E"},{"issue":"3","key":"9087_CR7","doi-asserted-by":"crossref","first-page":"036711","DOI":"10.1103\/PhysRevE.75.036711","volume":"75","author":"R.A. Brownlee","year":"2007","unstructured":"Brownlee, R.A., Gorban, A.N., Levesley, J.: Stability and stabilization of the lattice Boltzmann method. Phys. Rev., E 75(3), 036711 (2007)","journal-title":"Phys. Rev., E"},{"key":"9087_CR8","doi-asserted-by":"crossref","first-page":"R5339","DOI":"10.1103\/PhysRevA.45.R5339","volume":"45","author":"H. Chen","year":"1992","unstructured":"Chen, H., Chen, S., Matthaeus, W.: Recovery of the Navier\u2013Stokes equation using a lattice\u2013gas Boltzmann method. Phys. Rev., A 45, R5339\u2013R5342 (1992)","journal-title":"Phys. Rev., A"},{"key":"9087_CR9","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1017\/S0022112082000561","volume":"116","author":"R.W. Davis","year":"1982","unstructured":"Davis, R.W., Moore, E.F.: A numerical study of vortex shedding from rectangles. J. Fluid Mech. 116, 475\u2013506 (1982)","journal-title":"J. Fluid Mech."},{"key":"9087_CR10","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1209\/epl\/i2002-00518-y","volume":"57","author":"P.J. Dellar","year":"2002","unstructured":"Dellar, P.J.: Compound waves in a thermohydrodynamic lattice BGK scheme using non-perturbative equilibria. Europhys. Lett. 57, 690\u2013696 (2002)","journal-title":"Europhys. Lett."},{"key":"9087_CR11","volume-title":"The conceptual foundations of the statistical approach in mechanics","author":"P. Ehrenfest","year":"1990","unstructured":"Ehrenfest, P., Ehrenfest, T.: The conceptual foundations of the statistical approach in mechanics. Dover, New York (1990)"},{"key":"9087_CR12","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/3-540-35888-9_7","volume-title":"Model Reduction and Coarse-graining Approaches for Multiscale Phenomena","author":"A.N. Gorban","year":"2006","unstructured":"Gorban, A.N.: Basic types of coarse-graining. In: Gorban, A.N., Kazantzis, N., Kevrekidis, I.G., \u00d6ttinger, H.-C., Theodoropoulos, C. (eds.) Model Reduction and Coarse-graining Approaches for Multiscale Phenomena, pp.\u00a0117\u2013176. Springer, Berlin (cond-mat\/0602024) (2006)"},{"key":"9087_CR13","volume-title":"Thermodynamic Equilibria and Extrema: Analysis of Attainability Regions and Partial Equilibrium","author":"A. Gorban","year":"2006","unstructured":"Gorban, A., Kaganovich, B., Filippov, S., Keiko, A., Shamansky, V., Shirkalin, I.: Thermodynamic Equilibria and Extrema: Analysis of Attainability Regions and Partial Equilibrium. Springer, Berlin (2006)"},{"key":"9087_CR14","volume-title":"Lecture Notes in Physics, vol.\u00a0660","author":"A.N. Gorban","year":"2005","unstructured":"Gorban, A.N., Karlin, I.V.: Invariant manifolds for physical and chemical kinetics. In: Lecture Notes in Physics, vol.\u00a0660. Springer, Berlin (2005)"},{"key":"9087_CR15","doi-asserted-by":"crossref","first-page":"066124","DOI":"10.1103\/PhysRevE.63.066124","volume":"62","author":"A.N. Gorban","year":"2001","unstructured":"Gorban, A.N., Karlin, I.V., \u00d6ttinger, H.C., Tatarinova, L.L.: Ehrenfest\u2019s argument extended to a formalism of nonequilibrium thermodynamics. Phys. Rev., E 62, 066124 (2001)","journal-title":"Phys. Rev., E"},{"key":"9087_CR16","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1209\/0295-5075\/9\/4\/008","volume":"9","author":"F. Higuera","year":"1989","unstructured":"Higuera, F., Succi, S., Benzi, R.: Lattice gas \u2013 dynamics with enhanced collisions. Europhys. Lett. 9, 345\u2013349 (1989)","journal-title":"Europhys. Lett."},{"key":"9087_CR17","first-page":"616","volume":"1","author":"I.V. Karlin","year":"2006","unstructured":"Karlin, I.V., Ansumali, S., Frouzakis, C.E., Chikatamarla, S.S.: Elements of the lattice Boltzmann method I: linear advection equation. Commun. Comput. Phys. 1, 616\u2013655 (2006)","journal-title":"Commun. Comput. Phys."},{"key":"9087_CR18","first-page":"196","volume":"2","author":"I.V. Karlin","year":"2007","unstructured":"Karlin, I.V., Chikatamarla, S.S., Ansumali, S.: Elements of the lattice Boltzmann method II: Kinetics and hydrodynamics in one dimension. Commun. Comput. Phys. 2, 196\u2013238 (2007)","journal-title":"Commun. Comput. Phys."},{"key":"9087_CR19","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1209\/epl\/i1999-00370-1","volume":"47","author":"I.V. Karlin","year":"1999","unstructured":"Karlin, I.V., Ferrante, A., \u00d6ttinger, H.C.: Perfect entropy functions of the lattice Boltzmann method. Europhys. Lett. 47, 182\u2013188 (1999)","journal-title":"Europhys. Lett."},{"key":"9087_CR20","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1103\/PhysRevLett.81.6","volume":"81","author":"I.V. Karlin","year":"1998","unstructured":"Karlin, I.V., Gorban, A.N., Succi, S., Boffi, V.: Maximum entropy principle for lattice kinetic equations. Phys. Rev. Lett. 81, 6\u20139 (1998)","journal-title":"Phys. Rev. Lett."},{"key":"9087_CR21","volume-title":"Information Theory and Statistics","author":"S. Kullback","year":"1959","unstructured":"Kullback, S.: Information Theory and Statistics. Wiley, New York (1959)"},{"key":"9087_CR22","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1017\/S0022112082003115","volume":"123","author":"A. Okajima","year":"1982","unstructured":"Okajima, A.: Strouhal numbers of rectangular cylinders. J. Fluid Mech. 123, 379\u2013398 (1982)","journal-title":"J. Fluid Mech."},{"key":"9087_CR23","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1103\/PhysRevLett.80.65","volume":"80","author":"X. Shan","year":"1998","unstructured":"Shan, X., He, X.: Discretization of the velocity space in the solution of the Boltzmann equation. Phys. Rev. Lett. 80, 65\u201368 (1998)","journal-title":"Phys. Rev. Lett."},{"key":"9087_CR24","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198503989.001.0001","volume-title":"The Lattice Boltzmann Equation for Fluid Dynamics and Beyond","author":"S. Succi","year":"2001","unstructured":"Succi, S.: The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. OUP, New York (2001)"},{"key":"9087_CR25","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1209\/0295-5075\/17\/6\/001","volume":"17","author":"Y.H. Qian","year":"1992","unstructured":"Qian, Y.H., D. d\u2019Humieres, Lallemand, P.: Lattice BGK models for Navier\u2013Stokes equation. Europhys. Lett. 17, 479\u2013484 (1992)","journal-title":"Europhys. Lett."},{"key":"9087_CR26","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1017\/S002211206600020X","volume":"25","author":"B.J. Vickery","year":"1966","unstructured":"Vickery, B.J.: Fluctuating lift and drag on a long cylinder of square cross-section in a smooth and in a turbulent stream. J. Fluid Mech. 25, 481\u2013494 (1966)","journal-title":"J. Fluid Mech."},{"key":"9087_CR27","volume-title":"Series Comprehensive Chemical Kinetics, vol.\u00a032","author":"G.S. Yablonskii","year":"1991","unstructured":"Yablonskii, G.S., Bykov, V.I., Gorban, A.N., Elokhin, V.I.: Kinetic models of catalytic reactions. In: Compton, R.G. (ed.) Series Comprehensive Chemical Kinetics, vol.\u00a032. Elsevier, Amsterdam (1991)"},{"key":"9087_CR28","first-page":"144","volume-title":"Selected Works of Yakov Borisovich Zeldovich, vol.\u00a01","author":"Y.B. Zeldovich","year":"1996","unstructured":"Zeldovich, Y.B.: Proof of the uniqueness of the solution of the equations of the law of mass action. In: Ostriker, J.P. (ed.) Selected Works of Yakov Borisovich Zeldovich, vol.\u00a01, pp.\u00a0144\u2013148. Princeton University Press, Princeton, NJ (1996)"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-007-9087-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-007-9087-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-007-9087-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,14]],"date-time":"2024-02-14T04:35:03Z","timestamp":1707885303000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-007-9087-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,5,10]]},"references-count":28,"journal-issue":{"issue":"1-4","published-print":{"date-parts":[[2007,8]]}},"alternative-id":["9087"],"URL":"https:\/\/doi.org\/10.1007\/s11075-007-9087-1","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,5,10]]}}}