Numerical simulations for viscous reactive micropolar real gas flow. (English) Zbl 07925368
Pinto, Carla M. A. (ed.) et al., Computational and mathematical models in biology. Cham: Springer. Nonlinear Syst. Complex. 38, 1-33 (2023).
Summary: Micropolar fluids represent a fluid model that, unlike the classic model, does not only describe behavior at the macro level but also deals with fluid behavior at the microlevel. Describing microphenomena in this case was achieved through the introduction of a new hydrodynamic variable called microrotation. This work describes the micropolar gas model with special emphasis on the reactive micropolar gas, focusing on the initial boundary value problem describing the behavior of the micropolar reactive real gas in tubes with solid and thermally insulated walls. In other words, homogeneous boundary conditions for velocity, microrotation, and heat flux are studied. For the mentioned initial boundary value problem, the construction of the Faedo-Galerkin approximations and the corresponding numerical method for obtaining a numerical solution are described. The given numerical method was additionally analyzed with respect to the complexity of the initial conditions in terms of the number of terms in their Fourier expansions.
For the entire collection see [Zbl 1531.92008].
For the entire collection see [Zbl 1531.92008].
Keywords:
micropolar fluid; microstructure; microeffects; material modeling; microrotation; real gas; reactive gas; initial boundary value problem; Navier-Stokes equations; Lagrangian description; generalized solution; local existence; Faedo-Galerkin approximations; Fourier expansion; numerical solution; simulation; stabilizationReferences:
| [1] | R. Abreu, J. Kamm, A.S. Reiss, Micropolar modelling of rotational waves in seismology. Geophys. J. Int. 210 (2017). doi:10.1093/gji/ggx211 |
| [2] | Antontsev, SN; Kazhikhov, AV; Monakhov, VN, Boundary Value Problems in Mechanics of Nonhomogeneous Fluids, Studies in Mathematics and Its Applications, 1990, Amsterdam: North-Holland Publishing, Amsterdam · Zbl 0696.76001 |
| [3] | Bašić-Šiško, A.; Dražić, I., Global solution to a one-dimensional model of viscous and heat-conducting micropolar real gas flow, J. Math. Analy. Appl., 495, 124690, 2021 · Zbl 1462.35281 · doi:10.1016/j.jmaa.2020.124690 |
| [4] | Bašić-Šiško, A.; Dražić, I., Uniqueness of generalized solution to micropolar viscous real gas flow with homogeneous boundary conditions, Math. Methods Appl. Sci., 44, 6, 4330-4341, 2021 · Zbl 1473.76044 · doi:10.1002/mma.7032 |
| [5] | Bašić-Šiško, A.; Dražić, I., Local existence for viscous reactive micropolar real gas flow and thermal explosion with homogeneous boundary conditions, J. Math. Analy. Appl., 509, 125988, 2022 · Zbl 1509.35207 · doi:10.1016/j.jmaa.2022.125988 |
| [6] | A. Bašić-Šiško, I. Dražić, One-dimensional model and numerical solution to the viscous and heat-conducting reactive micropolar real gas flow and thermal explosion. Iranian J. Sci. Technol. Trans. Mech. Eng. (2022). doi:10.1007/s40997-022-00498-w |
| [7] | Bašić-Šiško, A.; Dražić, I.; Simčić, L., One-dimensional model and numerical solution to the viscous and heat-conducting micropolar real gas flow with homogeneous boundary conditions, Math. Comput. Simul., 195, 71-87, 2022 · Zbl 1540.76177 · doi:10.1016/j.matcom.2021.12.024 |
| [8] | Baidya, U.; Das, S.; Das, S., Analysis of misaligned hydrodynamic porous journal bearings in the steady- state condition with micropolar lubricant, ARCHIVE Proc. Instit. Mech. Eng. Part J J. Eng. Tribol., 208-210, 1994-1996, 2020 |
| [9] | Bebernes, J.; Bressan, A., Global a priori estimates for a viscous reactive gas, Proc. R. Soc. Edinburgh Sect. A Math., 101, 321-333, 1985 · Zbl 0614.76076 · doi:10.1017/S0308210500020862 |
| [10] | M. Benes, I. Pažanin, M. Radulović, Leray’s problem for the nonstationary micropolar fluid flow. Mediterran. J. Math. 17 (2020). doi:10.1007/s00009-020-1493-9 · Zbl 1437.35566 |
| [11] | Bhattacharjee, B.; Chakraborti, P.; Choudhuri, K., Evaluation of the performance characteristics of double-layered porous micropolar fluid lubricated journal bearing, Tribol. Int., 138, 415-423, 2019 · doi:10.1016/j.triboint.2019.06.025 |
| [12] | Bonnivard, M.; Pažanin, I.; Suárez-Grau, FJ, Effects of rough boundary and nonzero boundary conditions on the lubrication process with micropolar fluid, Euro. J. Mech. - B/Fluids, 72, 501-518, 2018 · Zbl 1408.76187 · doi:10.1016/j.euromechflu.2018.07.013 |
| [13] | Borgnakke, C.; Sonntag, RE, Fundamentals of Thermodynamics, SI Version, 2019, Hoboken: Wiley, Hoboken |
| [14] | Y.A. Çengel, R.H. Turner, Fundamentals of Thermal-Fluid Sciences (McGraw-Hill Companies, New York City, 2004) |
| [15] | Chen, Z.; Wang, D., Global stability of rarefaction waves for the 1d compressible micropolar fluid model with density-dependent viscosity and microviscosity coefficients, Nonlinear Analy. Real World Appl., 58, 103226, 2021 · Zbl 1455.35190 · doi:10.1016/j.nonrwa.2020.103226 |
| [16] | É. Clapeyron, Mémoire sur la puissance motrice de la chaleur. Journal de l’École Polytechnique, XIV(23), 153-191 (1834) |
| [17] | E. Cosserat, F. Cosserat, A. Hermann et forie des Corps déformables. A. Hermann et fils, Paris (1909) |
| [18] | Črnjarić Žic, N., Upwind numerical approximations of a compressible 1d micropolar fluid flow, J. Comput. Appl. Math., 303, 81-92, 2016 · Zbl 1337.35117 · doi:10.1016/j.cam.2016.02.022 |
| [19] | Črnjarić-Žic, N.; Mujaković, N., Numerical analysis of the solutions for 1d compressible viscous micropolar fluid flow with different boundary conditions, Math. Comput. Simul., 126, 45-62, 2016 · Zbl 1540.76130 · doi:10.1016/j.matcom.2016.03.001 |
| [20] | Cui, H.; Yao, ZA, Asymptotic behavior of compressible p-th power newtonian fluid with large initial data, J. Differ. Equ., 258, 3, 919-953, 2015 · Zbl 1305.35114 · doi:10.1016/j.jde.2014.10.011 |
| [21] | Dražić, I., Three-dimensional flow of a compressible viscous micropolar fluid with cylindrical symmetry: a global existence theorem, Math. Methods Appl. Sci., 40, 13, 4785-4801, 2017 · Zbl 1373.35241 |
| [22] | I. Dražić, A. Bašić-Šiško, Local existence theorem for micropolar viscous real gas flow with homogeneous boundary conditions. Math. Methods Appl. Sci. (2022). doi:10.1002/mma.8841 |
| [23] | I. Dražić, N. Mujaković, 3-d flow of a compressible viscous micropolar fluid with spherical symmetry: a local existence theorem. Boundary Value Prob. 2012 (2012). doi:10.1186/1687-2770-2012-69 |
| [24] | I. Dražić, N. Mujaković, 3-d flow of a compressible viscous micropolar fluid with spherical symmetry: a global existence theorem. Boundary Value Prob. 2015(98) (2015). doi:10.1186/s13661-015-0357-x |
| [25] | I. Dražić, N. Mujaković, 3-d flow of a compressible viscous micropolar fluid with spherical symmetry: large time behavior of the solution. J. Math. Analy. Appl. 431 (2015). doi:10.1016/j.jmaa.2015.06.002 · Zbl 1319.35184 |
| [26] | I. Dražić, N. Mujaković, Local existence of the generalized solution for three-dimensional compressible viscous flow of micropolar fluid with cylindrical symmetry. Boundary Value Prob. 2019 (2019). doi:10.1186/s13661-019-1131-2 |
| [27] | Dražić, I.; Mujaković, N.; Simčić, L., 3-d flow of a compressible viscous micropolar fluid with spherical symmetry: regularity of the solution, Math. Analy. Appl., 438, 1, 162-183, 2016 · Zbl 1382.35215 · doi:10.1016/j.jmaa.2016.01.071 |
| [28] | Dražić, I.; Mujaković, N.; Črnjarić Žic, N., Three-dimensional compressible viscous micropolar fluid with cylindrical symmetry: derivation of the model and a numerical solution, Math. Comput. Simul., 140, 107-124, 2017 · Zbl 1540.76218 · doi:10.1016/j.matcom.2017.03.006 |
| [29] | Dražić, I.; Čnjarić Žic, N.; Simčić, L., A shear flow problem for compressible viscous micropolar fluid: derivation of the model and numerical solution, Math. Comput. Simul., 162, 249-267, 2019 · Zbl 1540.76181 · doi:10.1016/j.matcom.2019.01.013 |
| [30] | Eringen, CA, Simple microfluids, Int. J. Eng. Sci., 2, 2, 205-217, 1964 · Zbl 0136.45003 · doi:10.1016/0020-7225(64)90005-9 |
| [31] | Feireisl, E.; Novotný, A., Large time behaviour of flows of compressible, viscous, and heat conducting fluids, Math. Methods Appl. Sci., 29, 1237-1260, 2006 · Zbl 1105.35075 · doi:10.1002/mma.722 |
| [32] | L. Huang, I. Dražić, Exponential stability for the compressible micropolar fluid with cylinder symmetry in \(\text{R}^3\). J. Math. Phys. 60, 021507 (2019). doi:10.1063/1.5017652 · Zbl 1409.76008 |
| [33] | Karvelas, EG; Tsiantis, A.; Papathanasiou, TD, Effect of micropolar fluid properties on the hydraulic permeability of fibrous biomaterials, Comput. Methods Program. Biomed., 185, 105135, 2020 · doi:10.1016/j.cmpb.2019.105135 |
| [34] | Khanukaeva, D.; Filippov, A., Isothermal flows of micropolar liquids: formulation of problems and analytical solutions, Colloid J., 80, 14-36, 2018 · doi:10.1134/S1061933X18010040 |
| [35] | M. Lewicka, P. Mucha, On temporal asymptotics for the pth power viscous reactive gas. Nonlinear Analy. Theory, Methods Appl. 57, 951-969 (2004). doi:10.1016/j.na.2003.12.001 · Zbl 1094.76052 |
| [36] | G. Lukaszewicz, Micropolar Fluids: Theory and Applications. Modeling and Simulation in Science, Engineering and Technology (Birkhäuser, Boston, 1999) · Zbl 0923.76003 |
| [37] | Lukaszewicz, G.; Pažanin, I.; Radulović, M., Asymptotic analysis of the thermomicropolar fluid flow through a thin channel with cooling, Appl. Analy., 101, 1-29, 2020 |
| [38] | Maltese, D.; Michálek, M.; Mucha, PB; Novotný, A.; Pokorný, M.; Zatorska, E., Existence of weak solutions for compressible navier-stokes equations with entropy transport, J. Differ. Equ., 261, 4448-4485, 2016 · Zbl 1351.35106 · doi:10.1016/j.jde.2016.06.029 |
| [39] | Mekheimer, K.; Elnaqeeb, T.; El Kot, M.; Alghamdi, F., Simultaneous effect of magnetic field and metallic nanoparticles on a micropolar fluid through an overlapping stenotic artery: blood flow model, Phys. Essays, 29, 272-283, 2016 · doi:10.4006/0836-1398-29.2.272 |
| [40] | Mujaković, N., One-dimensional flow of a compressible viscous micropolar fluid: a global existence theorem, Glasnik matematički, 33, 53, 199-208, 1998 · Zbl 0917.76004 |
| [41] | N. Mujaković, One-dimensional flow of a compressible viscous micropolar fluid: a local existence theorem. Glas. Mat., III. Ser. 33(1), 71-91 (1998) · Zbl 0912.35135 |
| [42] | Mujaković, N., One-dimensional flow of a compressible viscous micropolar fluid regularity of the solution, Radovi Matematički, 10, 181-193, 2001 · Zbl 1071.35538 |
| [43] | N. Mujaković, One-dimensional flow of a compressible viscous micropolar fluid: Stabilization of the solution, in ed. by Drmač, Z., Marušić, M., Tutek, Z., Proceedings of the Conference on Applied Mathematics and Scientific Computing (Springer, Dordrecht, 2005). doi:10.1007/1-4020-3197-1_18 · Zbl 1329.76293 |
| [44] | Mujaković, N.; Črnjarić-Žic, N., Convergent finite difference scheme for 1D flow of compressible micropolar fluid, Int. J. Numer. Anal. Model., 12, 1, 94-124, 2015 · Zbl 1329.35251 |
| [45] | Mujaković, N.; Črnjarić Žic, N., Convergence of a finite difference scheme for 3d flow of a compressible viscous micropolar heat-conducting fluid with spherical symmetry, Int. J. Numer. Analy. Model., 13, 705-738, 2016 · Zbl 1358.35126 |
| [46] | N. Mujaković, N. Črnjarić Žic, Finite difference formulation for the model of a compressible viscous and heat-conducting micropolar fluid with spherical symmetry, in ed. by S. Pinelas, Z. Došlá, O. Došlý, P.E. Kloeden, Differential and Difference Equations with Applications, vol. 164 (Springer, Berlin, 2016), pp. 293-301. doi:10.1007/978-3-319-32857-7-27 · Zbl 1398.76154 |
| [47] | Mujaković, N.; Dražić, I., Numerical approximations of the solution for one-dimensional compressible viscous micropolar fluid model, Int. J. Pure Appl. Math., 38, 285-296, 2007 · Zbl 1131.35380 |
| [48] | N. Mujaković, I. Dražić, The cauchy problem for one-dimensional flow of a compressible viscous fluid: stabilization of the solution. Glasnik Matematički. Serija III 46 (2011). doi:10.3336/gm.46.1.16 · Zbl 1219.35194 |
| [49] | Mujaković, N.; Dražić, I., 3-d flow of a compressible viscous micropolar fluid with spherical symmetry: a local existence theorem, Boundary Value Prob., 226, 1-17, 2014 · Zbl 1304.35564 |
| [50] | Mujekaović, N.; Dražić, I.; Simčić, L., 3-d flow of a compressible viscous micropolar fluid with cylindrical symmetry: uniqueness of a generalized solution, Math. Methods Appl. Sci., 40, 7, 2686-2701, 2017 · Zbl 1367.35125 · doi:10.1002/mma.4191 |
| [51] | Nermina, M., One-dimensional flow of a compressible viscous micropolar fluid: the cauchy problem, Math. Commun., 10, 1-14, 2005 · Zbl 1076.35103 |
| [52] | Nermina, M., Uniqueness of a solution of the cauchy problem for one-dimensional compressible viscous micropolar fluid model, Appl. Math. E-Notes, 6, 113-118, 2006 · Zbl 1154.76045 |
| [53] | M. Nermina, One-dimensional compressible viscous micropolar fluid model: stabilization of the solution for the cauchy problem. Boundary Value Prob. 2010 (2010). doi:10.1155/2010/796065 · Zbl 1198.35198 |
| [54] | Papautsky, I.; Brazzle, J.; Ameel, T.; Frazier, A., Laminar fluid behavior in microchannels using micropolar fluid theory, Sensors Actuat. A Phys., 73, 1, 101-108, 1999 · doi:10.1016/S0924-4247(98)00261-1 |
| [55] | Pimputkar, S.; Nakamura, S., Decomposition of supercritical ammonia and modeling of supercritical ammonia-nitrogen-hydrogen solutions with applicability toward ammonothermal conditions, J. Supercrit. Fluids, 107, 17-30, 2016 · doi:10.1016/j.supflu.2015.07.032 |
| [56] | Poland, J.; Kassoy, D., The induction period of a thermal explosion in a gas between infinite parallel plates, Combust. Flame, 50, 259-274, 1983 · doi:10.1016/0010-2180(83)90069-X |
| [57] | Qin, Y.; Huang, L., Global existence and exponential stability for the pth power viscous reactive gas, Nonlinear Analy.-Theory Methods Appl., 73, 2800-2818, 2010 · Zbl 1402.76106 · doi:10.1016/j.na.2010.06.015 |
| [58] | Y. Qin, L. Huang, Regularity and exponential stability of the pth newtonian fluid in one space dimension. Math. Models Methods Appl. Sci. - M3AS 20 (2010). doi:10.1142/S0218202510004350 · Zbl 1191.35208 |
| [59] | Y. Qin, L. Huang, Global Well-posedness of Nonlinear Parabolic-Hyperbolic Coupled Systems. Frontiers in Mathematics, 1st edn. (Birkhäuser, Basel, 2012). doi:10.1007/978-3-0348-0280-2 · Zbl 1273.35008 |
| [60] | Y. Qin, J. Zhang, X. Su, J. Cao, Global existence and exponential stability of spherically symmetric solutions to a compressible combustion radiative and reactive gas. J. Math. Fluid Mech. 18 (2016). doi:10.1007/s00021-015-0242-5 · Zbl 1346.35148 |
| [61] | Simčić, L., A shear flow problem for compressible viscous micropolar fluid: uniqueness of a generalized solution, Math. Methods Appl. Sci., 42, 5, 6358-6368, 2019 · Zbl 1434.35121 · doi:10.1002/mma.5727 |
| [62] | I. Vardoulakis, Cosserat Continuum Mechanics: With Applications to Granular Media. Lecture Notes in Applied and Computational Mechanics, vol. 87 (Springer International Publishing, Cham, 2019) · Zbl 1430.74002 |
| [63] | Wang, T., One dimensional p-th power newtonian fluid with temperature-dependent thermal conductivity, Commun. Pure Appl. Analy., 15, 477-494, 2016 · Zbl 1329.76295 · doi:10.3934/cpaa.2016.15.477 |
| [64] | L. Wan, T. Wang, Asymptotic behavior for the one-dimensional pth power newtonian fluid in unbounded domains. Math. Methods Appl. Sci. 39 (2015). doi:10.1002/mma.3539 · Zbl 1334.76127 |
| [65] | Watson, S.; Lewicka, M.; Watson, J., Temporal asymptotics for the p’th power newtonian fluid in one space dimension, Zeitschrift für angewandte Mathematik und Physik, 54, 633-651, 2003 · Zbl 1026.76039 · doi:10.1007/s00033-003-1149-1 |
| [66] | Yanagi, S., Asymptotic stability of the spherically symmetric solutions for a viscous polytropic gas in a field of external forces, Trans. Theory Statist. Phys., 29, 333-353, 2000 · Zbl 0998.76075 · doi:10.1080/00411450008205878 |
| [67] | Ye, S.; Zhu, K.; Wang, W., Laminar flow of micropolar fluid in rectangular microchannels, Acta Mech. Sinica, 22, 403-408, 2006 · Zbl 1202.76012 · doi:10.1007/s10409-006-0023-8 |
| [68] | P. Zhang, M. Zhu, Global regularity of 3d nonhomogeneous incompressible magneto-micropolar system with the density-dependent viscosity. Comput. Math. Appl. 76 (2018). doi:10.1016/j.camwa.2018.08.041 · Zbl 1442.76158 |
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