# Investigation of Blood-Like Non-Newtonian Fluid Flow in Stenotic Arteries using the Lattice Boltzmann Method in 2D

## Main Article Content

## Abstract

The impact of non-Newtonian fluid properties on the mathematical modeling of flow in stenosed arteries is investigated. The main goal is to determine whether the Newtonian fluid model is sufficient for the flow modeling in the desired geometry. The magnitude of negative horizontal flux is used as a primary quantity for comparing Newtonian and non-Newtonian approaches. The comparison is performed for vessel geometries with gradually increasing severity of stenosis. The mathematical model is solved using the lattice Boltzmann method with a modification to include the non-Newtonian effects. The results show that the difference in fluid characteristics increases with the degree of stenosis. However, for the simulation of flow in the least stenosed artery, both models provide similar results and, thus, the Newtonian model can be employed.

## Article Details

How to Cite

Škardová, K., Eichler, P., Oberhuber, T., & Fučík, R.
(2020).
Investigation of Blood-Like Non-Newtonian Fluid Flow in Stenotic Arteries using the Lattice Boltzmann Method in 2D.

*Proceedings Of The Conference Algoritmy,*, 91 - 100. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1558/822
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Articles

## References

[1] J. Boyd, J. M. Buick, and S. Green. Analysis of the Casson and Carreau-Yasuda non-Newtonian blood models in steady and oscillatory flows using the lattice Boltzmann method. Physics of Fluids, 19(9):093103, 2007.

[2] S.S. Chikatamarla, S. Ansumali, and I. V. Karlin. Entropic lattice Boltzmann models for hydrodynamics in three dimensions. Physical review letters, 97(1):010201, 2006.

[3] D. d'Humieres. Generalized lattice-Boltzmann equations. Rarefied gas dynamics, 1992.

[4] R. Fučı́k, P. Eichler, R. Straka, P. Pauš, J. Klinkovský, and T. Oberhuber. On optimal node spacing for immersed boundary–lattice Boltzmann method in 2D and 3D. Computers & Mathematics with Applications, 77(4):1144–1162, 2019.

[5] R. Fučı́k, R. Galabov, P. Pauš, P. Eichler, J. Klinkovský, R. Straka, J. Tintěra, and R. Chabiniok. Investigation of phase-contrast magnetic resonance imaging underestimation of turbulent flow through the aortic valve phantom: Experimental and computational studyusing lattice Boltzmann method. Magnetic Resonance Materials in Physics, Biology and Medicine, pages 1–14, 2020.

[6] M. Geier, A. Greiner, and J. G. Korvink. Cascaded digital lattice Boltzmann automata for high Reynolds number flow. Physical Review E, 73(6):066705, 2006.

[7] M. Geier, A. Pasquali, and M. Schönherr. Parametrization of the cumulant lattice Boltzmann method for fourth order accurate diffusion Part I: Derivation and validation. J. Comput. Phys, 348:862–888, 2017.

[8] Z. Guo and C. Shu. Lattice Boltzmann method and its applications in engineering, volume 3. World Scientific, 2013.

[9] Payne Stephen J. Cerebral Blood Flow and Metabolism: A Quantitative Approach. World Scientific, 2017.

[10] Y. Kim, S. Lim, S. V. Raman, O. P. Simonetti, and A. Friedman. Blood flow in a compliant vessel by the immersed boundary method. Annals of biomedical engineering, 37(5):927–942, 2009.

[11] T. Krüger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva, and E. M. Viggen. The Lattice Boltzmann Method. Springer, 2017.

[12] K. N. Premnath and S. Banerjee. Incorporating forcing terms in cascaded lattice Boltzmann approach by method of central moments. Physical Review E, 80(3):036702, 2009.

[13] C.-H. Wang and J.-R. Ho. A lattice Boltzmann approach for the non-Newtonian effect in the blood flow. Computers & Mathematics with Applications, 62(1):75–86, 2011.

[2] S.S. Chikatamarla, S. Ansumali, and I. V. Karlin. Entropic lattice Boltzmann models for hydrodynamics in three dimensions. Physical review letters, 97(1):010201, 2006.

[3] D. d'Humieres. Generalized lattice-Boltzmann equations. Rarefied gas dynamics, 1992.

[4] R. Fučı́k, P. Eichler, R. Straka, P. Pauš, J. Klinkovský, and T. Oberhuber. On optimal node spacing for immersed boundary–lattice Boltzmann method in 2D and 3D. Computers & Mathematics with Applications, 77(4):1144–1162, 2019.

[5] R. Fučı́k, R. Galabov, P. Pauš, P. Eichler, J. Klinkovský, R. Straka, J. Tintěra, and R. Chabiniok. Investigation of phase-contrast magnetic resonance imaging underestimation of turbulent flow through the aortic valve phantom: Experimental and computational studyusing lattice Boltzmann method. Magnetic Resonance Materials in Physics, Biology and Medicine, pages 1–14, 2020.

[6] M. Geier, A. Greiner, and J. G. Korvink. Cascaded digital lattice Boltzmann automata for high Reynolds number flow. Physical Review E, 73(6):066705, 2006.

[7] M. Geier, A. Pasquali, and M. Schönherr. Parametrization of the cumulant lattice Boltzmann method for fourth order accurate diffusion Part I: Derivation and validation. J. Comput. Phys, 348:862–888, 2017.

[8] Z. Guo and C. Shu. Lattice Boltzmann method and its applications in engineering, volume 3. World Scientific, 2013.

[9] Payne Stephen J. Cerebral Blood Flow and Metabolism: A Quantitative Approach. World Scientific, 2017.

[10] Y. Kim, S. Lim, S. V. Raman, O. P. Simonetti, and A. Friedman. Blood flow in a compliant vessel by the immersed boundary method. Annals of biomedical engineering, 37(5):927–942, 2009.

[11] T. Krüger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva, and E. M. Viggen. The Lattice Boltzmann Method. Springer, 2017.

[12] K. N. Premnath and S. Banerjee. Incorporating forcing terms in cascaded lattice Boltzmann approach by method of central moments. Physical Review E, 80(3):036702, 2009.

[13] C.-H. Wang and J.-R. Ho. A lattice Boltzmann approach for the non-Newtonian effect in the blood flow. Computers & Mathematics with Applications, 62(1):75–86, 2011.