A novel level-set FEM with Zienkiewicz elements for microdroplets in the strong capillary regime

Roberto F. Ausas

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 246, issue C, 257-289

Abstract: This paper introduces a novel finite element-level set framework for simulating incompressible, immiscible two-phase flows dominated by strong capillary forces. At the core of our method is the use of the Zienkiewicz element for the level set function, a key innovation which we demonstrate provides superior interface representation compared to the standard linear element, while still using only nodal unknowns. The flow solution employs a stabilized equal-order formulation with linear velocity elements and a modified discontinuous pressure space. We detail several critical implementation aspects, including robust implicit and semi-implicit time-stepping schemes, a new redistancing algorithm, and a global mass correction procedure. The capabilities of our approach are rigorously assessed through challenging 2D axisymmetric benchmarks. The results reveal an excellent balance of computational efficiency and accuracy in capturing the interfacial dynamics of microdroplets.

Keywords: Level set method; Two-phase flow; Surface tension; Interface; Spurious velocities; Boussinesq–Scriven law (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:246:y:2026:i:c:p:257-289

DOI: 10.1016/j.matcom.2026.02.002

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