[hal-01096742] A fourth-order accurate curvature computation in a level set framework for two-phase flows subjected to surface tension forces

We propose a fourth-order accurate and robust curvature estimation and extension algorithm in a level set framework for the transport of the interface. The method is used to efficiently calculate surface tension forces for two-phase flows, based on the Continuum Surface Force approach. In this framework, accuracy mostly relies on the precise computation of the surface's curvature that we propose to accomplish in a two-step algorithm. First by computing a reliable fourth-order curvature estimation from the level set function. Secondly by extending rigorously this curvature in the viscinity of the surface, following the Closest Point principle. The algorithm is easy to implement and to integrate to existing solvers, furthermore naturally extensible to 3D. We propose a detailed analyze of the geometrical and numerical criteria that are responsible of the appearance of spurious currents, a phenomenon widely explored in the community in various numerical frameworks. We study the response of the novel numerical method on state-of-the-art test cases showing that it permits to greatly reduce parasitic currents, converging at fourth-order regarding spatial discretization, two orders better than common results from the litterature. We also show the necessity of high-order transport methods for the surface by studying the case of the 2D advection of a column at equilibrium proving the robustness of the proposed approach. The algorithm is validated on more complex test cases such as a rising bubble.



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