Abstract
In this chapter, detailed validations are presented to investigate the accuracy and the efficiency of the Gerris-MHD solver in simulating the MHD flows, respectively with complex solid boundaries or free surfaces.
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Almgren AS, Bell JB, Colella P et al (1998) A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations. J Comput Phys 142(1):1–46
Bhaga D, Weber ME (1981) Bubbles in viscous liquids: shapes, wakes and velocities. J Fluid Mech 105:61–85
Chang CC, Lundgren TS (1961) Duct flow in magnetohydrodynamics. Zeitschrift fr Angewandte Mathematik und Physik (ZAMP) 12(2):100–114
Davidson PA (1995) Magnetic damping of jets and vortices. J Fluid Mech 299:153–186
Grigoriadis DGE, Kassinos SC, Votyakov EV (2009) Immersed boundary method for the MHD flows of liquid metals. J Comput Phys 228(3):903–920
Hunt JCR (1965) Magnetohydrodynamic flow in rectangular ducts. J Fluid Mech 21(4):577–590
Levich VG (1962) Physicochemical hydrodynamics. Prentice Hall, Upper Saddle River
Ma C, Bothe D (2011) Direct numerical simulation of thermocapillary flow based on the volume of fluid method. Int J Multiph Flow 37(9):1045–1058
Mendelson HD (1967) The prediction of bubble terminal velocities from wave theory. AIChE J 13(2):250–253
Minion ML (1996) A projection method for locally refined grids. J Comput Phys 127(1):158–178
Miao X, Lucas D, Ren Z et al (2013) Numerical modeling of bubble-driven liquid metal flows with external static magnetic field. Int J Multiph Flow 48:32–45
Mori Y, Hijikata K, Kuriyama I (1977) Experimental study of bubble motion in mercury with and without a magnetic field. J Heat Transf 99(3):404–410
Mück B, Gnther C, Müller U et al (2000) Three-dimensional MHD flows in rectangular ducts with internal obstacles. J Fluid Mech 418:265–295
Mutschke G, Gerbeth G, Shatrov V et al (2001) The scenario of three-dimensional instabilities of the cylinder wake in an external magnetic field: a linear stability analysis. Phys Fluids 13(3):723–734
Nas S, Tryggvason G (2003) Thermocapillary interaction of two bubbles or drops. Int J Multiph Flow 29(7):1117–1135
Popinet S (2003) Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J Comput Phys 190(2):572–600
Popinet S (2009) An accurate adaptive solver for surface-tension-driven interfacial flows. J Comput Phys 228(16):5838–5866
Samad SKA (1981) The flow of conducting fluids through circular pipes having finite conductivity and finite thickness under uniform transverse magnetic fields. Int J Eng Sci 19(9):1221–1232
Shercliff JA (1953) Steady motion of conducting fluids in pipes under transverse magnetic fields. Math Proc Camb Philos Soc 49(1):136–144 (Cambridge University Press)
Shercliff JA (1956) The flow of conducting fluids in circular pipes under transverse magnetic fields. J Fluid Mech 1(6):644–666
Shercilff JA (1962) Magnetohydrodynamic pipe flow. Part 2:513
Tao Z, Ni MJ (2015) Analytical solutions for MHD flow at a rectangular duct with unsymmetrical walls of arbitrary conductivity. Sci China Phys Mech Astron 58(2):1–18
Verlarde MG (2012) Physicochemical hydrodynamics: interfacial phenomena. Springer Science and Business Media, Berlin
Williamson CHK (1996) Vortex dynamics in the cylinder wake. Ann Rev Fluid Mech 28(1):477–539
Young NO, Goldstein JS, Block MJ (1959) The motion of bubbles in a vertical temperature gradient. J Fluid Mech 6(3):350–356
Zenit R, Magnaudet J (2008) Path instability of rising spheroidal air bubbles: a shape-controlled process. Phys Fluids 20(6):061702
Zhang C, Eckert S, Gerbeth G (2006) Determination of the flow structure in bubble-driven liquid metal flows using ultrasound Doppler method. In: 5th international symposium on ultrasonic Doppler methods for fluid mechanics and fluid engineering, Zrich, Switzerland
Zhang C, Eckert S, Gerbeth G (2007) The flow structure of a bubble-driven liquid-metal jet in a horizontal magnetic field. J Fluid Mech 575:57–82
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Zhang, J. (2019). The Validations of the Numerical Methodology. In: The Developments and the Applications of the Numerical Algorithms in Simulating the Incompressible Magnetohydrodynamics with Complex Boundaries and Free Surfaces. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-10-6340-4_4
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DOI: https://doi.org/10.1007/978-981-10-6340-4_4
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