Dr.-Ing. Tomislav Maric

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

Working area(s)

Lagrangian / Eulerian numerical methods for multiphase flows


work +49 6151 16-21469

Work L2|06 410
Peter-Grünberg-Straße 10
64287 Darmstadt

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.


[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.

A numerically consistent unstructured geometrical Volume‐of‐Fluid discretization of the single‐field two‐phase momentum convection term with high‐density ratios. Liu, J.; Scheufler, H.; Zuzio, D.; Estivalesez, J. L. & Marić, T. (2023).
A locally signed‐distance preserving level set method (SDPLS) for moving interfaces. Fricke, M.; Marić, T.; Vuckovic, A.; Roisman, I. & Bothe, D. (2023).
A second‐order accurate geometrical phase indicator for the Level Set method on unstructured meshes. Marić, T.; Reitzel, J.; Fricke, M.; Bothe, D.; Juric, D.; Chergui, J. & Shin, S. (2023).
Numerical wetting benchmarks–advancing the plicRDFisoAdvector unstructured Volume‐of‐Fluid (VOF) method. Asghar, M. H.; Fricke, M.; Bothe, D. & Marić, T. (2023).
Stabilizing the unstructured Volume‐of‐Fluid method for capillary flows in microstructures using artificial viscosity. Nagel, L.; Lippert, A.; Tolle, T.; Leonhardt, R.; Zhang, H. & Marić, T. (2023).
An unstructured finite‐volume Level Set / Front Tracking method for two‐phase flows with large density‐ratios. Liu, J.; Tolle, T.; Bothe, D. & Marić, T. (2023), Journal of Computational Physics 493, 112426.
Asymmetry During Fast Stretching of a Liquid Bridge. Asghar, H. M.; Brockmann, P.; Dong, X.; Niethammer, M.; Marić, T.; Roisman, I. & Bothe, D. (2023), Chemical Engineering & Technology, Vol. 46, Issue 9, 1800-1807.
A benchmark for surface‐tension‐driven incompressible twophase flows. Lippert, A.; Tolle, T.; Dörr, A. & Marić, T. (2022),
A Research Software Engineering Workflow for Computational Science and Engineering. Marić, T.; Gläser, D.; Lehr, J.-P.; Papagiannidis, I.; Lambie, B.; Bischof, C. & Bothe, D. (2022),
Lagrangian / Eulerian Interface Advection (LEIA) methods for two‐phase flows ‐ lecture materials. Marić, T. (2022), Zenodo.
Computing hydrodynamic eigenmodes of channel flow with slip — A highly accurate algorithm. Raju, S.; Gründing, D.; Marić, T.; & Bothe, D. (2022), The Canadian Journal of Chemical Engineering, Volume 100, Issue 12, 3531-3547.
triSurfaceImmersion: Computing volume fractions and signed distances from triangulated surfaces immersed in unstructured meshes, Tolle, T.; Gründing, D.; Bothe, D. & Marić, T. (2022), Computer Physics Communications, Volume 273, 108249.
The OpenFOAM® Technology Primer. Marić, T.; Höpken, J. & Mooney, K. G. (2021).
Iterative volume‐of‐fluid interface positioning in general polyhedrons with Consecutive Cubic Spline interpolation. Marić, T. (2021), Journal of Computational Physics X, Volume 11, 100093.
Breakup dynamics of capillary bridges on hydrophobic stripes. Hartmann, M.; Fricke, M.; Weimar, L.; Gründing, D.; Marić, T.; Bothe, D. & Hardt, S. (2021), International Journal of Multiphase Flow, Volume 140, 103582.
Unstructured un-split geometrical Volume-of-Fluid methods – A review. Marić, Tomislav & Bothe, Dieter (2020), Journal of Computational Physics 420, 109695.
SAAMPLE: A Segregated Accuracy-driven Algorithm for Multiphase Pressure-Linked Equations. Tolle, T.; Bothe, D. & Marić, T. (2020), Computers & Fluids 200, 104450.
Contact line advection using the geometrical volume-of-fluid method: Data and FORTRAN-implementations. Fricke, M.; Marić, T. & Bothe, D. (2020), Journal of Computational Physics, Volume 407, 109221.
Contact Line Advection using the Level Set Method. Fricke, M.; Marić, T. & Bothe, D. (2019), Proceedings in Applied Mathematics and Mechanics.
Contact Line Advection using the Level Set Method: Data and C++ Implementations. Fricke, Mathis; Marić, Tomislav & Bothe, Dieter; Vucković, Aleksandar (2019).
An enhanced un-split face-vertex flux-based VoF method. Marić, T.; Marschall, H. & Bothe, D. (2018), Journal of Computational Physics 371, 967-993.
Langarian/Eulerian numerical methods for fluid interface advection on unstructured meshes. Marić, Tomislav (2017), Technische Universität Darmstadt.
lentFoam – A hybrid Level Set/Front Tracking method on unstructured meshes. Marić, Tomislav; Marschall, Holger & Bothe, Dieter (2015), Computers & Fluids 113, 20-31.
The OpenFOAM technology primer. Marić, Tomislav; Hopken, Jens & Mooney, Kyle (2014).