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This master thesis presents the development and application of a Finite Volume Level Set Method for simulating two-phase flows on unstructured meshes within the OpenFOAM Computational Fluid Dynamics (CFD) framework. The proposed method focuses on incompressible, immiscible, non-reactive, isothermal, two-phase Newtonian fluid flows, considering surface tension forces and gravity. A main objective is to implement and evaluate the Signed Distance Preserving Level Set (SDPLS) method, as proposed by Fricke et al. [17]. Furthermore, the developed Level Set (LS) method is tested with various advection schemes on various mesh types, including hexahedral, perturbed hexahedral, and polyhedral meshes. Lastly, the LS method is coupled to the Navier-Stokes (NS) equations with the Continuum Surface Force (CSF) model proposed by Brackbill et al. [4] and the use of the geometrical phase indicator proposed by us [40], which does not rely on a signed distance property of the LS field. A segregated solver is implemented and validated through numerical studies of the 3D stationary droplet test case.

[4] J. U. Brackbill, D. B. Kothe, and C. Zemach. “A continuum method for modeling surface tension”. In: Journal of Computational Physics 100.2 (June 1, 1992), pp. 335– 354. doi: 10.1016/0021-9991(92)90240-Y. (Visited on 04/03/2023).

[17] M. Fricke et al. A locally signed-distance preserving level set method (SDPLS) for moving interfaces. Aug. 2, 2022. doi: 10.48550/arXiv.2208.01269. (Visited on 04/03/2023).

[40] T. Marić et al. An second-order accurate geometrical phase indicator for the Level Set method on unstructured meshes. in preparation.

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