×
Shao, Changxiao; Yuan, Shian; Chai, Min; Jin, Tai; Luo, Kun

A generalized variational level set method without frequent reinitialization for simulations of gas-liquid flows. (English) Zbl 07766257

J. Comput. Phys. 495, Article ID 112558, 25 p. (2023).
Summary: A generalized variational level set method without frequent reinitialization process is proposed to address the issue of the traditional level set method for detailed numerical simulations of gas-liquid flows. The gas-liquid interface is captured by the level set method and the discontinuity across the interface is discretized by the ghost fluid method. A penalty term is added in the classical level set advection equation to reduce the frequent reinitialization process. The effect of the frequency of the reinitialization step on the performance of the level set method is evaluated and the effect of the penalty factor on the interface evolution is investigated in the present work. Three typical benchmark cases, including rigid body rotation, two-dimensional shear motion, and three-dimensional shear motion, are used to validate the accuracy of the present variational level set method. It is found that the reinitialization process is not necessary for every time step with the penalty term. A spatially averaged parameter near the interface is proposed to quantitatively evaluate the necessity of reinitialization. The present method is also shown to have second-order accuracy. This work provides an accurate and efficient way to simulate the gas-liquid flows.

MSC:

76Mxx Basic methods in fluid mechanics
65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
76Txx Multiphase and multicomponent flows

Keywords:

variational level set method; ghost fluid method; penalty term; without frequent reinitialization; gas-liquid flows
Cite Review PDF
Full Text: DOI

References:

[1] Hirt, C.; Nichols, B., Volume of fluid (vof) method for the dynamics of free boundaries. J. Comput. Phys., 1, 201-225 (1981) · Zbl 0462.76020
[2] Sethian, J. A.; Smereka, P., Level set methods for fluid interfaces. Annu. Rev. Fluid Mech., 1, 341-372 (2003) · Zbl 1041.76057
[3] Osher, S.; Fedkiw, R., The Level Set Methods and Dynamic Implicit Surfaces, 1-273 (2004), Springer-Verlag, Ch. 1
[4] Anderson, D. M.; McFadden, G. B.; Wheeler, A. A., Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech., 1, 139-165 (1998) · Zbl 1398.76051
[5] Sun, Y.; Beckermann, C., Sharp interface tracking using the phase-field equation. J. Comput. Phys., 2, 626-653 (2007) · Zbl 1228.76110
[6] Luo, K.; Shao, C.; Yang, Y.; Fan, J., A mass conserving level set method for detailed numerical simulation of liquid atomization. J. Comput. Phys., 495-519 (2015) · Zbl 1349.76847
[7] Nourgaliev, R.; Wiri, S.; Dinh, N.; Theofanous, T., On improving mass conservation of level set by reducing spatial discretization errors. Int. J. Multiph. Flow, 12, 1329-1336 (2005) · Zbl 1388.76149
[8] Adalsteinsson, D.; Sethian, J., The fast construction of extension velocities in level set methods. J. Comput. Phys., 1, 2-22 (1999) · Zbl 0919.65074
[9] Olsson, E.; Kreiss, G., A conservative level set method for two phase flow. J. Comput. Phys., 1, 225-246 (2005) · Zbl 1154.76368
[10] Olsson, E.; Kreiss, G.; Zahedi, S., A conservative level set method for two phase flow ii. J. Comput. Phys., 1, 785-807 (2007) · Zbl 1256.76052
[11] Sussman, M.; Puckett, E. G., A coupled level set and volume-of-fluid method for computing 3d and axisymmetric incompressible two-phase flows. J. Comput. Phys., 2, 301-337 (2000) · Zbl 0977.76071
[12] Herrmann, M., A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids. J. Comput. Phys., 4, 2674-2706 (2008) · Zbl 1388.76252
[13] Desjardins, O.; Pitsch, H., A spectrally refined interface approach for simulating multiphase flows. J. Comput. Phys., 5, 1658-1677 (2009) · Zbl 1409.76096
[14] Sussman, M.; Smereka, P.; Osher, S., A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys., 1, 146-159 (1994) · Zbl 0808.76077
[15] Chang, Y.-C.; Hou, T. Y.; Merriman, B.; Osher, S., A level set formulation of Eulerian interface capturing methods for incompressible fluid flows. J. Comput. Phys., 449-464 (1996) · Zbl 0847.76048
[16] McCaslin, J. O.; Desjardins, O., A localized re-initialization equation for the conservative level set method. J. Comput. Phys., 408-426 (2014) · Zbl 1349.76506
[17] Sethian, J., Level set methods and fast marching methods: evolving interfaces in computational geometry · Zbl 0973.76003
[18] Gomes, J.; Faugeras, O., Reconciling distance functions and level sets. J. Vis. Commun. Image Represent., 2, 209-223 (2000)
[19] Li, C.; Xu, C.; Gui, C.; Fox, M., Level set evolution without re-initialization: a new variational formulation, 430-436
[20] Li, C.; Xu, C.; Gui, C.; Fox, M. D., Distance regularized level set evolution and its application to image segmentation. IEEE Trans. Image Process., 12, 3243-3254 (2010) · Zbl 1371.94226
[21] Wu, W.; Wu, Y.; Huang, Q., An improved distance regularized level set evolution without re-initialization, 631-636
[22] Zhao, H.-K.; Chan, T.; Merriman, B.; Osher, S., A variational level set approach to multiphase motion. J. Comput. Phys., 1, 179-195 (1996) · Zbl 0860.65050
[23] Boutaous, M.; Otmani, R. E.; Benhadid, H., Conservative level set method without re-initialization process: application to multiphase flows. Int. J. Model. Simul., 3, 162-172 (2013)
[24] Sabelnikov, V.; Ovsyannikov, A. Y.; Gorokhovski, M., Modified level set equation and its numerical assessment. J. Comput. Phys., 1-30 (2014) · Zbl 1349.65331
[25] Touré, M. K.; Soulaïmani, A., Stabilized finite element methods for solving the level set equation without reinitialization. Comput. Math. Appl., 8, 1602-1623 (2016) · Zbl 1443.65223
[26] Brackbill, J.; Kothe, D.; Zemach, C., A continuum method for modeling surface tension. J. Comput. Phys., 2, 335-354 (1992) · Zbl 0775.76110
[27] Zalesak, S. T., Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys., 3, 335-362 (1979) · Zbl 0416.76002
[28] Min, C.; Gibou, F., A second order accurate level set method on non-graded adaptive Cartesian grids. J. Comput. Phys., 1, 300-321 (2007) · Zbl 1122.65077
[29] Bell, J. B.; Colella, P.; Glaz, H. M., A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys., 2, 257-283 (1989) · Zbl 0681.76030
[30] LeVeque, R. J., High-resolution conservative algorithms for advection in incompressible flow. SIAM J. Numer. Anal., 2, 627-665 (1996) · Zbl 0852.76057
[31] Enright, D.; Fedkiw, R.; Ferziger, J.; Mitchell, I., A hybrid particle level set method for improved interface capturing. J. Comput. Phys., 1, 83-116 (2002) · Zbl 1021.76044
[32] Swaters, G. E., Viscous modulation of the Lamb dipole vortex. Phys. Fluids, 10, 2745-2747 (1988) · Zbl 0654.76056
[33] Meleshko, V.; van Heijst, G., On Chaplygin’s investigations of two-dimensional vortex structures in an inviscid fluid. J. Fluid Mech., 157-182 (1994) · Zbl 0819.76018
[34] Avni, O.; Dagan, Y., Dynamics of evaporating respiratory droplets in the vicinity of vortex dipoles. Int. J. Multiph. Flow (2022)
[35] Lamb, H., Hydrodynamics (1993), Dover Publications: Dover Publications New York · Zbl 0828.01012
[36] Shao, C.; Yuan, S.; Luo, K., A generalized coupled level set/volume-of-fluid/ghost fluid method for detailed simulation of gas-liquid flows. J. Comput. Phys. (2023) · Zbl 07690229
[37] Ashgriz, N.; Poo, J., Coalescence and separation in binary collisions of liquid drops. J. Fluid Mech., 183-204 (1990)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.