{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T10:30:51Z","timestamp":1758709851331},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2009,12,31]],"date-time":"2009-12-31T00:00:00Z","timestamp":1262217600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput. Visual Sci."],"published-print":{"date-parts":[[2010,3]]},"DOI":"10.1007\/s00791-009-0132-6","type":"journal-article","created":{"date-parts":[[2009,12,30]],"date-time":"2009-12-30T09:46:00Z","timestamp":1262166360000},"page":"129-143","source":"Crossref","is-referenced-by-count":2,"title":["Efficient monolithic simulation techniques for the stationary Lattice Boltzmann equation on general meshes"],"prefix":"10.1007","volume":"13","author":[{"given":"T.","family":"H\u00fcbner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"Turek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,12,31]]},"reference":[{"issue":"3","key":"132_CR1","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1209\/epl\/i2006-10138-1","volume":"75","author":"A. Bardow","year":"2006","unstructured":"Bardow A., Karlin I.V., Gusev A.A.: General characteristic-based algorithm for off-lattice Boltzmann simulations. Europhys. Lett. 75(3), 434\u2013440 (2006)","journal-title":"Europhys. Lett."},{"key":"132_CR2","first-page":"222","volume-title":"Graph Theory with Applications to Engineering and Computer Science","author":"N. Deo","year":"1974","unstructured":"Deo N.: Graph Theory with Applications to Engineering and Computer Science, pp. 222\u2013333. Prentice Hall International, Englewood Cliffs, NJ (1974)"},{"key":"132_CR3","unstructured":"d\u2019Humi\u00e8res, D.: Generalized lattice-Boltzmann equations. In: Shizgal, B.D., Weaver, D.P. (eds.) Rarefied Gas Dynamics: Theory and Simulations, Prog Aeronaut Astronaut 159, pp. 450\u2013458. (1992)"},{"key":"132_CR4","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1098\/rsta.2001.0955","volume":"360","author":"D. d\u2019Humi\u00e8res","year":"2002","unstructured":"d\u2019Humi\u00e8res D., Ginzburg I., Krafczyk M., Lallemand P., Luo L.-S.: Multiple-relaxation-time Lattice Boltzmann models in three-dimensions. Philos. Trans. R. Soc. Lond. 360, 437\u2013451 (2002)","journal-title":"Philos. Trans. R. Soc. Lond."},{"key":"132_CR5","doi-asserted-by":"crossref","first-page":"066702","DOI":"10.1103\/PhysRevE.63.066702","volume":"63","author":"D. d\u2019Humi\u00e8res","year":"2001","unstructured":"d\u2019Humi\u00e8res D., Bouzidi M., Lallemand P.: Thirteen-velocity three-dimensional Lattice Boltzmann model. Phys. Rev. E 63, 066702 (2001)","journal-title":"Phys. Rev. E"},{"key":"132_CR6","doi-asserted-by":"crossref","first-page":"1094","DOI":"10.1002\/nme.1657","volume":"67","author":"A. D\u00fcster","year":"2006","unstructured":"D\u00fcster A., Demkowicz L., Rank E.: High-order finite elements applied to the discrete Boltzmann equation. Int. J. Numer. Methods Eng. 67, 1094\u20131121 (2006)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"132_CR7","first-page":"75","volume":"1","author":"U. Frisch","year":"1987","unstructured":"Frisch U., d\u2019Humi\u00e8res D., Hasslacher B., Lallemand P.: Lattice gas hydrodynamics in two and three dimensions. Complex Syst. 1, 75\u2013136 (1987)","journal-title":"Complex Syst."},{"key":"132_CR8","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1023\/B:JOSS.0000015179.12689.e4","volume":"88","author":"X. He","year":"1997","unstructured":"He X., Luo L.S.: Lattice Boltzmann model for the incompressible Navier-Stokes equation. J. Stat. Phys. 88, 927\u2013944 (1997)","journal-title":"J. Stat. Phys."},{"key":"132_CR9","doi-asserted-by":"crossref","first-page":"066709","DOI":"10.1103\/PhysRevE.67.066709","volume":"67","author":"Z. Guo","year":"2003","unstructured":"Guo Z., Zhao T.S.: Explicit finite-difference Lattice Boltzmann method for curvilinear coordinates. Phys. Rev. E 67, 066709 (2003)","journal-title":"Phys. Rev. E"},{"key":"132_CR10","unstructured":"H\u00fcbner, T.: Spezielle Diskretisierungs- und L\u00f6sungsmethoden f\u00fcr Integro-Differentialgleichungen am Beispiel der Strahlungstransportgleichung. Diploma Thesis http:\/\/www.mathematik.uni-dortmund.de\/lsiii\/static\/showpdffile_Huebner2005.pdf , Dortmund. (2005)"},{"key":"132_CR11","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/s00607-007-0250-2","volume":"81","author":"T. H\u00fcbner","year":"2007","unstructured":"H\u00fcbner T., Turek S.: An efficient and accurate short-characterisctics solver for radiative transfer problems. Computing 81, 281\u2013296 (2007)","journal-title":"Computing"},{"key":"132_CR12","unstructured":"H\u00fcbner, T.: Monolithische L\u00f6sungsmethoden f\u00fcr die Lattice-Boltzmann Gleichung. PhD Thesis (2010, to appear)"},{"key":"132_CR13","unstructured":"H\u00fcbner, T., Turek, S.: Efficient monolithic Lattice Boltzmann solver for nonstationary flow problems. (2010, to appear)"},{"key":"132_CR14","doi-asserted-by":"crossref","first-page":"3535","DOI":"10.1063\/1.869426","volume":"9","author":"T. Inamuro","year":"1997","unstructured":"Inamuro T., Yoshino M., Ogino F.: Accuracy of the Lattice Boltzmann method for small Knudsen number with finite Reynolds number. Phys. Fluids 9, 3535 (1997)","journal-title":"Phys. Fluids"},{"key":"132_CR15","unstructured":"Junk, M.: LBM-discrete dynamics and finite difference method. In: Proceedings of the GAMM Workshop on Discrete Modelling and Discrete Algorithms in Continuum Mechanics. Logos, Berlin (2001)"},{"key":"132_CR16","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1017\/S0022112094001771","volume":"271","author":"A. Ladd","year":"1994","unstructured":"Ladd A.: Numerical simulations of particulate suspensions via a discretized Boltzmann equation. J. Fluid Mech. 271, 285\u2013309 (1994)","journal-title":"J. Fluid Mech."},{"issue":"6","key":"132_CR17","doi-asserted-by":"crossref","first-page":"6546","DOI":"10.1103\/PhysRevE.61.6546","volume":"61","author":"P. Lallemand","year":"2000","unstructured":"Lallemand P., Luo L.S.: Theory of the Lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E 61(6), 6546\u20136562 (2000)","journal-title":"Phys. Rev. E"},{"key":"132_CR18","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1016\/j.compfluid.2005.07.020","volume":"35","author":"D.J. Mavriplis","year":"2006","unstructured":"Mavriplis D.J.: Multigrid solution of the steady-state Lattice Boltzmann equation. Comput. Fluids 35, 573\u2013591 (2006)","journal-title":"Comput. Fluids"},{"key":"132_CR19","doi-asserted-by":"crossref","first-page":"041203","DOI":"10.1103\/PhysRevE.65.041203","volume":"65","author":"R. Mei","year":"2002","unstructured":"Mei R., Yu D., Shyy W., Luo L.-S.: Force evaluation in the Lattice Boltzmann method involving curved geometry. Phys. Rev. E 65, 041203 (2002)","journal-title":"Phys. Rev. E"},{"issue":"4","key":"132_CR20","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1142\/S0129183107010905","volume":"18","author":"D. Noble","year":"2007","unstructured":"Noble D., Holdych D.: Full Newton Lattice Boltzmann Method for Time-Steady Flows using a Direct Linear Solver. Int. J. Mod. Phys. C 18(4), 652\u2013660 (2007)","journal-title":"Int. J. Mod. Phys. C"},{"key":"132_CR21","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\u2019Humi\u00e8res D., Lallemand P.: Lattice BGK models for Navier-Stokes equation. Europhys. Lett. 17, 479\u2013484 (1992)","journal-title":"Europhys. Lett."},{"key":"132_CR22","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1016\/0045-7930(94)00037-Y","volume":"24","author":"M. Reider","year":"1995","unstructured":"Reider M., Sterling J.: Accuracy of discrete velocity BGK models for the simulation of the incompressible Navier Stokes equations. Comput. Fluids 24, 459\u2013467 (1995)","journal-title":"Comput. Fluids"},{"issue":"3","key":"132_CR23","doi-asserted-by":"crossref","first-page":"856","DOI":"10.1137\/0907058","volume":"7","author":"Y. Saad","year":"1986","unstructured":"Saad Y., Schultz M.H.: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7(3), 856\u2013869 (1986)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"132_CR24","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1007\/978-3-322-89849-4_39","volume":"52","author":"M. Sch\u00e4fer","year":"1996","unstructured":"Sch\u00e4fer M., Turek S.: Benchmark computations of laminar flow around cylinder. Notes Numer. Fluid Mech. 52, 547\u2013566 (1996)","journal-title":"Notes Numer. Fluid Mech."},{"issue":"1\/2","key":"132_CR25","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1023\/A:1014551813787","volume":"107","author":"J. T\u00f6lke","year":"2002","unstructured":"T\u00f6lke J., Krafczyk M., Rank E.: A multigrid-solver for the discrete boltzmann-equation. J. Stat. Phys. 107(1\/2), 573\u2013591 (2002)","journal-title":"J. Stat. Phys."},{"issue":"8","key":"132_CR26","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1142\/S0129183198001059","volume":"9","author":"J. T\u00f6lke","year":"1998","unstructured":"T\u00f6lke J., Krafczyk M., Schulz M., Rank E., Berrios R.: Implicit discretization and non-uniform mesh refinement approaches for FD discretizations of LBGK Models. Int. J. Mod. Phys. C 9(8), 1143\u20131157 (1998)","journal-title":"Int. J. Mod. Phys. C"},{"key":"132_CR27","unstructured":"Turek, S.: FEATFLOW finite element software for the incompressible Navier-Stokes equations: User Manual ( www.featflow.de ). Release 1.2, University of Dortmund (2000)"},{"key":"132_CR28","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/BF02238078","volume":"54","author":"S. Turek","year":"1995","unstructured":"Turek S.: A Generalized Mean Intensity Approach for the Numerical Solution of the Radiative Transfer Equation. Computing 54, 27\u201338 (1995)","journal-title":"Computing"},{"issue":"4","key":"132_CR29","first-page":"299","volume":"14","author":"S. Turek","year":"2007","unstructured":"Turek S., Ouazzi A.: Unified edge\u2013oriented stabilization of nonconforming FEM for incompressible flow problems: numerical investigations. J. Numer. Math. 14(4), 299\u2013322 (2007)","journal-title":"J. Numer. Math."},{"key":"132_CR30","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1137\/0913035","volume":"13","author":"H. Van der Vorst","year":"1992","unstructured":"Van der Vorst H.: BI\u2013CGSTAB: A fast and smoothly converging variant of BI\u2013CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 13, 631\u2013644 (1992)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"132_CR31","first-page":"29","volume":"1","author":"H. Wobker","year":"2009","unstructured":"Wobker H., Turek S.: Numerical Studies of Vanka-type Smoothers in Computational Solid Mechanics. Adv. Appl. Math. Mech. 1, 29\u201355 (2009)","journal-title":"Adv. Appl. Math. Mech."},{"issue":"6","key":"132_CR32","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1063\/1.869307","volume":"9","author":"Q. Zou","year":"1997","unstructured":"Zou Q., He X.: On pressure and velocity boundary conditions for the Lattice Boltzmann BGK model. Phys. Fluids 9(6), 1591\u20131598 (1997)","journal-title":"Phys. Fluids"}],"container-title":["Computing and Visualization in Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00791-009-0132-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00791-009-0132-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00791-009-0132-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T06:46:09Z","timestamp":1559112369000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00791-009-0132-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12,31]]},"references-count":32,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,3]]}},"alternative-id":["132"],"URL":"https:\/\/doi.org\/10.1007\/s00791-009-0132-6","relation":{},"ISSN":["1432-9360","1433-0369"],"issn-type":[{"value":"1432-9360","type":"print"},{"value":"1433-0369","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,12,31]]}}}