A higher-order accurate surface tension modelling volume-of-fluid scheme for 2D curvilinear meshes

• Published in: Journal of computational physics 2020-11, Vol.420, p.109717, Article 109717
• Main Authors: Ilangakoon, Niran A., Malan, Arnaud G., Jones, Bevan W.S.
• Format: Article
• Language: English
• Subjects: Accuracy; Algorithms; Computation; Computational physics; Curvature; Curvilinear meshes; Density ratio; Free surfaces; Gas density; Higher order; Interface reconstruction; Mathematical analysis; Polynomials; Pressure jump; Surface tension; Two dimensional models; Volume of fluid; Weightlessness
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2020.109717

•Second- or fourth-order polynomials are fitted through a local PLIC representation of the interface.•Second- and fourth-order accuracy is demonstrated for the curvature calculation.•The scheme is implemented into a balanced-force continuum-surface-force surface tension model.•Spurious currents are significantly reduced when simulating a static bubble.•Second-order accuracy is achieved for the oscillation frequency of an inviscid droplet in zero gravity. This paper proposes a higher-order accurate curvature calculation method for volume-of-fluid (VOF) based surface tension modelling on 2D curvilinear meshes. The scheme extends the interface reconstruction component of the height function (HF) method to curvilinear meshes in 2D. Linear reconstructions are computed in each column overlapping the interface, which results in a piecewise-linear (PLIC) representation of the free-surface. This is done in a volume conservative manner by employing a novel sweep-line algorithm. The interface curvature is then computed analytically by fitting either second- or fourth-order polynomials to local stencils of PLIC facets. Formal second- and fourth-order accuracy of interface curvature is demonstrated by comparing numerical results with a variety of analytical interface definitions. The curvature algorithm is implemented into a balanced-force continuum-surface-force surface tension scheme for variable-density flows. Second- and fourth-order accuracy are again demonstrated for the Laplace pressure jump in the simulation of a stationary bubble with a high liquid-gas density ratio. Lastly, second-order accuracy is demonstrated in computing the frequency of an inviscid oscillating droplet in zero gravity.