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.

针对二维曲线网格上基于流体体积（VOF）的表面张力建模，本文提出了一种高阶精确曲率计算方法。该方案将高度函数（HF）方法的界面重构组件扩展为2D曲线网格。在与界面重叠的每一列中计算线性重构，这导致自由表面的分段线性（PLIC）表示。这是通过采用新颖的扫掠线算法以体积保守的方式完成的。然后通过将二阶或四阶多项式拟合到PLIC小平面的局部模版来解析计算界面曲率。通过将数值结果与各种分析性界面定义进行比较，可以证明界面曲率的形式二阶和四阶精度。曲率算法被实现为用于变密度流的平衡力连续表面力表面张力方案。在高液气密度比的固定气泡的模拟中，再次证明了拉普拉斯压力跃迁的二阶和四阶精度。最后，在计算零重力下无粘性振荡液滴的频率时，证明了二阶精度。