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A coupled immersed interface and level set method for simulation of interfacial flows steered by surface tension

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A Correction to this article was published on 05 February 2022

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Abstract

This work presents a methodology to address the problems of bubbles and drops evolving in incompressible, viscous flows due to the effect of surface tension. It is based on the combination of a recently developed immersed interface method to resolve discontinuities, with the level set (LS) method to reproduce the evolving interfaces. The paramount feature of this immersed interface method is the use of Lagrange interpolation enclosing grid points positioned in the vicinity of the interface and few exceptional grid points positioned on the interface. Different problems are considered to assert the accurateness of the proposed methodology, involving both simple and complex interface geometries. Precisely, the following problems are addressed: circular flow with a fixed interface, the dispersion of capillary waves, initially circular, ellipse, star shaped bubbles oscillating to an equilibrium state, and circular drops deforming in shear flows. The transient evolution of bubbles/drops in terms of their shapes, pressure profiles, velocity vectors, deformation ratios of major and minor axis is analyzed to observe the effect of surface tension. The proposed methodology is seen to recover the exact numerical equilibrium between the surface tension and pressure gradient in the vicinity of complex interface geometries as well, while recreating the flow physics with an adequate level of accuracy with well representation of overall trends. Moreover, the numerical results yield a good level of agreement with the reference data.

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Authors and Affiliations

  1. School of Basic Sciences, Indian Institute of Technology Mandi, P.O. Box 175005, Kamand, Mandi, India

    H. V. R. Mittal & Rajendra K. Ray

  2. Faculty of Engineering, University of Bristol, Clifton, BS8 1UB, UK

    Hermes Gadêlha

  3. Department of Mechanical Engineering, Indian Institute of Technology Dharwad, Dharwad, Karnataka, 580011, India

    Dhiraj V. Patil

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  1. H. V. R. Mittal
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  2. Rajendra K. Ray
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  3. Hermes Gadêlha
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  4. Dhiraj V. Patil
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Correspondence to H. V. R. Mittal.

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Mittal, H.V.R., Ray, R.K., Gadêlha, H. et al. A coupled immersed interface and level set method for simulation of interfacial flows steered by surface tension. Exp. Comput. Multiph. Flow 3, 21–37 (2021). https://doi.org/10.1007/s42757-019-0050-x

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  • DOI: https://doi.org/10.1007/s42757-019-0050-x

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