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A discrete droplet method for modelling thin film flows. (English) Zbl 1505.76046


MSC:

76F10 Shear flows and turbulence
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[1] Luo, J.; Wen, S.; Huang, P., Thin film lubrication. part i. study on the transition between ehl and thin film lubrication using a relative optical interference intensity technique, Wear, 194, 1-2, 107-115 (1996)
[2] Overhoff, K.; Johnston, K.; Tam, J.; Engstrom, J.; Williams III, R., Use of thin film freezing to enable drug delivery: a review, J. Drug Deliv. Sci. Technol., 19, 2, 89-98 (2009)
[3] Jiang, R.; Pawliszyn, J., Thin-film microextraction offers another geometry for solid-phase microextraction, TrAC, Trends Anal. Chem., 39, 245-253 (2012)
[4] Lee, D.; Condrate, R., Ftir spectral characterization of thin film coatings of oleic acid on glasses: i. coatings on glasses from ethyl alcohol, J. Mater. Sci., 34, 1, 139-146 (1999)
[5] Tvingstedt, K.; Dal Zilio, S.; Inganäs, O.; Tormen, M., Trapping light with micro lenses in thin film organic photovoltaic cells, Opt. Express, 16, 26, 21608-21615 (2008)
[6] O’Hara, J. F.; Withayachumnankul, W.; Al-Naib, I., A review on thin-film sensing with terahertz waves, J. Infrared Millimeter Terahertz Waves, 33, 3, 245-291 (2012)
[7] Rabiei, E.; Haberlandt, U.; Sester, M.; Fitzner, D., Rainfall estimation using moving cars as rain gauges-laboratory experiments, Hydrol. Earth Syst. Sci., 17, 11, 4701-4712 (2013)
[8] Benney, Long waves on liquid films, J. Math. Phys., 45, 1-4, 150-155 (1966) · Zbl 0148.23003
[9] Ng, C.-O.; Mei, C. C., Roll waves on a shallow layer of mud modelled as a power-law fluid, J. Fluid Mech., 263, 151-184 (1994) · Zbl 0841.76011
[10] Atherton, R.; Homsy, G., On the derivation of evolution equations for interfacial waves, Chem. Eng. Commun., 2, 2, 57-77 (1976)
[11] O’Brien, S. B.; Schwartz, L. W., Thin Film Flows: Theory and Modeling, Encyclopedia of Surface and Colloid Science, Third Edition, 7377-7390 (2015), CRC Press
[12] Myers, T. G., Thin films with high surface tension, SIAM Rev., 40, 3, 441-462 (1998) · Zbl 0908.35057
[13] Danov, K. D.; Alleborn, N.; Raszillier, H.; Durst, F., The stability of evaporating thin liquid films in the presence of surfactant. i. lubrication approximation and linear analysis, Phys. Fluids, 10, 1, 131-143 (1998) · Zbl 1185.76630
[14] Bertozzi, A. L.; Pugh, M., The lubrication approximation for thin viscous films: regularity and long-time behavior of weak solutions, Commun. Pure Appl. Math., 49, 2, 85-123 (1996) · Zbl 0863.76017
[15] Barra, V.; Afkhami, S.; Kondic, L., Interfacial dynamics of thin viscoelastic films and drops, J. Nonnewton Fluid Mech., 237, 26-38 (2016)
[16] Schwartz, L.; Weidner, D., Modeling of coating flows on curved surfaces, J. Eng. Math., 29, 1, 91-103 (1995) · Zbl 0823.76021
[17] Fernández-Nieto, E. D.; Noble, P.; Vila, J.-P., Shallow water equations for non-newtonian fluids, J. Nonnewton Fluid Mech., 165, 13-14, 712-732 (2010) · Zbl 1274.76023
[18] Noble, P.; Vila, J.-P., Thin power-law film flow down an inclined plane: consistent shallow-water models and stability under large-scale perturbations, J. Fluid Mech., 735, 29-60 (2013) · Zbl 1294.76056
[19] Chun, S.; Eskilsson, C., Method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces, J. Comput. Phys., 333, 1-23 (2017) · Zbl 1375.35369
[20] Ren, B.; Yuan, T.; Li, C.; Xu, K.; Hu, S.-M., Real-time high-fidelity surface flow simulation, IEEE Trans. Vis. Comput. Graph, 24, 8, 2411-2423 (2017)
[21] Fang, S., Nash embedding, shape operator and navier-stokes equation on a riemannian manifold, Acta Math. Appl. Sinica English Ser., 36, 2, 237-252 (2020) · Zbl 1437.35533
[22] Samavaki, M.; Tuomela, J., Navier-stokes equations on riemannian manifolds, J. Geom. Phys., 148, 103543 (2020) · Zbl 1434.53082
[23] Chan, C. H.; Czubak, M.; Disconzi, M. M., The formulation of the navier-stokes equations on riemannian manifolds, J. Geom. Phys., 121, 335-346 (2017) · Zbl 1376.58009
[24] Zhao, Y.; Tan, H. H.; Zhang, B., A high-resolution characteristics-based implicit dual time-stepping vof method for free surface flow simulation on unstructured grids, J. Comput. Phys., 183, 1, 233-273 (2002) · Zbl 1021.76033
[25] Nguyen, V.-T.; Park, W.-G., A free surface flow solver for complex three-dimensional water impact problems based on the vof method, Int. J. Numer. Methods Fluids, 82, 1, 3-34 (2016)
[26] Issakhov, A.; Zhandaulet, Y.; Nogaeva, A., Numerical simulation of dam break flow for various forms of the obstacle by vof method, Int. J. Multiphase Flow, 109, 191-206 (2018)
[27] Larmaei, M. M.; Mahdi, T.-F., Simulation of shallow water waves using vof method, J. Hydro-Environ. Res., 3, 4, 208-214 (2010)
[28] Fries, T.-P., Higher-order surface fem for incompressible navier-stokes flows on manifolds, Int. J. Numer. Methods Fluids, 88, 2, 55-78 (2018)
[29] Jankuhn, T.; Olshanskii, M. A.; Reusken, A., Incompressible fluid problems on embedded surfaces: modeling and variational formulations, Interfaces Free Boundaries, 20, 3, 353-377 (2018) · Zbl 1406.35224
[30] Gross, B. J.; Atzberger, P. J., Hydrodynamic flows on curved surfaces: spectral numerical methods for radial manifold shapes, J. Comput. Phys., 371, 663-689 (2018) · Zbl 1415.76489
[31] Xu, X.; Dey, M.; Qiu, M.; Feng, J. J., Modeling of van der waals force with smoothed particle hydrodynamics: application to the rupture of thin liquid films, Appl. Math. Model., 83, 719-735 (2020) · Zbl 1481.76027
[32] Solenthaler, B.; Bucher, P.; Chentanez, N.; Müller, M.; Gross, M., Sph based shallow water, Simulation (2011)
[33] Chang, T.-J.; Kao, H.-M.; Chang, K.-H.; Hsu, M.-H., Numerical simulation of shallow-water dam break flows in open channels using smoothed particle hydrodynamics, J. Hydrol. (Amst.), 408, 1-2, 78-90 (2011)
[34] Wang, M.; Deng, Y.; Kong, X.; Prasad, A. H.; Xiong, S.; Zhu, B., Thin-film smoothed particle hydrodynamics fluid, ACM Trans. Graphic. (TOG), 40, 4, 1-16 (2021)
[35] Kordilla, J.; Tartakovsky, A. M.; Geyer, T., A smoothed particle hydrodynamics model for droplet and film flow on smooth and rough fracture surfaces, Adv. Water Resour., 59, 1-14 (2013)
[36] Härdi, S.; Schreiner, M.; Janoske, U., Enhancing smoothed particle hydrodynamics for shallow water equations on small scales by using the finite particle method, Comput. Methods Appl. Mech. Eng., 344, 360-375 (2019) · Zbl 1440.76109
[37] Härdi, S.; Schreiner, M.; Janoske, U., Simulating thin film flow using the shallow water equations and smoothed particle hydrodynamics, Comput. Methods Appl. Mech. Eng., 358, 112639 (2020) · Zbl 1441.76021
[38] Suchde, P.; Kuhnert, J., A fully lagrangian meshfree framework for pdes on evolving surfaces, J. Comput. Phys., 395, 38-59 (2019) · Zbl 1452.65178
[39] Suchde, P.; Kuhnert, J., A meshfree generalized finite difference method for surface pdes, Comput. Math. Appl., 78, 8, 2789-2805 (2019) · Zbl 1443.65287
[40] Suchde, P., A meshfree lagrangian method for flow on manifolds, Int. J. Numer. Methods Fluids, 93, 6, 1871-1894 (2021)
[41] Lu, L.; Gopalan, B.; Benyahia, S., Assessment of different discrete particle methods ability to predict gas-particle flow in a small-scale fluidized bed, Ind. Eng. Chem. Res., 56, 27, 7865-7876 (2017)
[42] Zahari, N.; Zawawi, M.; Sidek, L.; Mohamad, D.; Itam, Z.; Ramli, M.; Syamsir, A.; Abas, A.; Rashid, M., Introduction of discrete phase model (dpm) in fluid flow: a review, AIP Conference Proceedings, volume 2030, 020234 (2018), AIP Publishing LLC
[43] Longest, P. W.; Xi, J., Evaluation of continuous and discrete phase models for simulating submicrometer aerosol transport and deposition, Comput. Fluid Dyn. Heat Transf.: Emerg. Top., 23, 425 (2011) · Zbl 1452.76256
[44] Liu, G.-R.; Liu, M. B., Smoothed particle hydrodynamics: A meshfree particle method (2003), World scientific · Zbl 1046.76001
[45] Domínguez, J.; Crespo, A.; Gómez-Gesteira, M.; Marongiu, J., Neighbour lists in smoothed particle hydrodynamics, Int. J. Numer. Methods Fluids, 67, 12, 2026-2042 (2011) · Zbl 1426.76595
[46] Drumm, C.; Tiwari, S.; Kuhnert, J.; Bart, H.-J., Finite pointset method for simulation of the liquid-liquid flow field in an extractor, Comput. Chem. Eng., 32, 12, 2946-2957 (2008)
[47] Suchde, P.; Kuhnert, J., Point cloud movement for fully lagrangian meshfree methods, J. Comput. Appl. Math., 340, 89-100 (2018) · Zbl 1432.76197
[48] LeVeque, R. J., Finite volume methods for hyperbolic problems, volume 31 (2002), Cambridge university press · Zbl 1010.65040
[49] Saucedo-Zendejo, F. R.; Reséndiz-Flores, E. O., A new approach for the numerical simulation of free surface incompressible flows using a meshfree method, Comput. Methods Appl. Mech. Eng., 324, 619-639 (2017) · Zbl 1439.76130
[50] Basic, J.; Degiuli, N.; Blagojevic, B.; Ban, D., Lagrangian differencing dynamics for incompressible flows, J. Comput. Phys., 111198 (2022) · Zbl 07536724
[51] Mingham, C.; Causon, D., High-resolution finite-volume method for shallow water flows, J. Hydraul. Eng., 124, 6, 605-614 (1998)
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