Tomislav Maric

Dr.-Ing. Tomislav Maric

Research Group Leader on Lagrangian / Eulerian numerical methods for multiphase flows

+49 6151 16-21469
+49 6151 16-21472

Alarich-Weiss-Straße 10
64287 Darmstadt

Office: L2|06 410


Lagrangian/Eulerian Interface Approximation

Research motivation

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.


Marić, Tomislav, Douglas B. Kothe, and Dieter Bothe. “Unstructured un-split geometrical Volume-of-Fluid methods–A review.” Journal of Computational Physics 420 (2020): 109695.

Tolle, Tobias, Bothe, Dieter, and Maric, Tomislav, “SAAMPLE: A Segregated Accuracy-driven Algorithm for Multiphase Pressure-Linked Equations.” Computers & Fluids 200 (2020): 104450.

Fricke, Mathis, Tomislav Maric, and Dieter Bothe, “Contact Line Advection using the Level Set Method, Proceedings in Applied Mathematics and Mechanics (2019).

Maric, Tomislav, Holger Marschall, and Dieter Bothe., “An enhanced un-split face-vertex flux-based VoF method.” Journal of Computational Physics 371 (2018), 967-993.

Maric, Tomislav, Holger Marschall, and Dieter Bothe, “lentFoam – A hybrid Level Set/Front Tracking method on unstructured meshes.” Computers & Fluids 113 (2015), 20-31.

Maric, Tomislav, Jens Hopken, and Kyle Mooney. “The OpenFOAM technology primer.” (2014)


[1] Agbaglah, G.; Delaux, S.; Fuster, D.; Hoepffner, J.; Josserand, C.; Popinet, S.; Ray, P.; Scardovelli, R. & Zaleski, S., “Parallel simulation of multiphase flows using octree adaptivity and the volume-of-fluid method”, Comptes Rendus Mecanique, 2011, 339, 194-207

[2] Basting, Steffen, and Martin Weismann. “A hybrid level set–front tracking finite element approach for fluid–structure interaction and two-phase flow applications.” Journal of Computational Physics, 2013, 255, 228-244.

[3] Ceniceros, Hector D., et al. “A robust, fully adaptive hybrid level-set/front-tracking method for two-phase flows with an accurate surface tension computation.” Communications in Computational Physics, 2010, 8.1, 51-94.

[4] Jemison, M.; Loch, E.; Sussman, M.; Shashkov, M.; Arienti, M.; Ohta, M. & Wang, Y. A, “Coupled Level Set-Moment of Fluid Method for Incompressible Two-Phase Flows”, Journal of Scientific Computing, 2013, 54, 454-491

[5] Shin, S.; Yoon, I. & Juric, D., “The Local Front Reconstruction Method for direct simulation of two- and three-dimensional multiphase flows”, Journal of Computational Physics, 2011, 230, 6605 – 6646

[6] Le Chenadec, Vincent, and Heinz Pitsch. “A 3d unsplit forward/backward volume-of-fluid approach and coupling to the level set method.”, Journal of computational physics 233 (2013): 10-33.

[7] Tryggvason, G; Bunner, B.; Esmaeeli, A.; Juric, D.; Al-Rawahi, N.; Tauber, W.; Han, J.; Nas, S.; Jan, Y-J, “A front-tracking method for the computations of multiphase flow.” Journal of Computational Physics, 2001, 169.2: 708-759.

[8] Wang, Y.; Simakhina S.; Sussman M., “A hybrid level set-volume constraint method for incompressible two-phase flow.”, Journal of Computational Physics, 2012, 231.19: 6438-6471.


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.

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