Visualization of coalescence behavior of two bubbles with smoothness constraint
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R E G UL A R P A P E R
Fangfang Zhang • Hongjun Li
Visualization of coalescence behavior of two bubbles with smoothness constraint
Received: 30 September 2019 / Revised: 20 February 2020 / Accepted: 2 March 2020 Ó The Visualization Society of Japan 2020
Abstract A new method based on 2D contour curve fitting and 3D rotation surface generation to visualize the coalescence phenomenon of two bubbles in static water is presented. First, some contour points are extracted from key frame images in different coalescence stages of two bubbles. Second, those points are fitted using a new approach combining piecewise curve fitting with a smoothing constraint. Third, a family of transition functions is proposed to deal with continuous changes of contour curves in the process of coalescence. Finally, we use those contours to generate dynamical 3D rotation surfaces and achieve the continuous deformation visualization of two-bubble coalescence. Keywords Bubble surface modeling Coalescence visualization Smooth contour fitting Transition function
1 Introduction Underwater bubbles are a common natural phenomenon and often appear in three-dimensional (3D) computer games and animation. How to model the surface of bubbles and visualize their motion and deformation is an interesting and important topic. Accurate modeling and visualization of bubble phenomenon can improve visual effects in scientific researches (Liu et al. 2007) and virtual reality applications (Nielsen et al. 2013). Published researches involving bubbles focus on deformation (Belov and Prokolov 1972), broken bubbles (Belov and Prokolov 1972; Colombo and Fairweather 2016), coalescence (Grace and Clift 2010; Bandara and Yapa 2011), etc. Among these research topics, analysis and simulation of coalescence phenomena have been receiving the most attention over the years. Numerical simulation is the main method to analyze bubbles’ coalescence behavior. Some researches describe this behavior in two-dimensional (2D) vertical flows (Ruetsch and Meiburg 1993), especially for small bubbles, while others demonstrate the coalescence of bubble pairs in three dimensions (Grace and Clift 2010). And there are two typical approaches, the lattice Boltzmann method (Chen et al. 2016) and the level set method (Zhao et al. 2015). A simplified assumption that a new bubble has a volume equal to the total volume of the bubbles before merging (Pe´rez-Mun˜uzuri and Garaboa-Paz 2016) is generally adopted. The surface shape of a bubble has been approximated by a spherical model in some researches (Belov and Prokolov 1972; Ruetsch and Meiburg 1993). The error of representing one bubble with a sphere or Electronic supplementary material The online version of this article (https://doi.org/10.1007/s12650-020-00641-2) contains supplementary material, which is available to authorized users. F. Zhang H. Li (&) College of Science, Beijing Forestry University, Beijing 100083, China E-mail: [email protected]
F. Zhang, H. Li
ellipse (Zelenka 2014) is acceptable for non-interacting bubbles.
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