A fundamental problem of simulating multiphase flows lies in determining which part of the space is occupied by which phase. When fluid phases do not mix, a moving fluid interface forms between them. A first example that comes to mind is the interface between water and air. Numerical methods that used for tracking this fluid interface must ensure accurate, computationally efficient, and numerically robust results, even when the interface changes topologically. For example, when a rain droplet breaks up into many satellite droplets.
Research of numerical methods for the fluid interface evolution is very active, and the methods are quite interdisciplinary, often connecting fluid dynamics, high-performance computing, applied numerical mathematics, computational geometry, and computer graphics.
Different methods have been developed so far, improving on volume conservation, numerical boundedness and geometrical accuracy [1,7]. Recent developments [2,3,5,6,8] rely on hybrid approaches that combine sub-algorithms of different methods for their advantages.
The research focus is placed on developing new Lagrangian / Eulerian (LE) methods for multiphase flows using the unstructured Finite Volume Method. Lagrangian / Eulerian methods rely on geometrical approximations of the fluid interface to improve the overall quality of the simulation. Although LE methods are showing promising results, their interdisciplinary nature poses the main challenge in the development of computational software that is applicable to a wide range of multiphase flow problems.
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We gratefully acknowledge the financial support by the German Council of Science and Humanities, in the framework of the Collaborative Research Center 1194, Project Z-INF and the Initiation of International Collaboration “Hybrid Level Set / Front Tracking methods for simulating multiphase flows in geometrically complex systems”, MA 8465/1-1.