Computing interface curvature from volume fractions: a hybrid approach

The Volume of Fluid method is extensively used for the multiphase flows simulations in which the interface between two fluids is represented by a discrete and abruptly-varying volume fractions field. The Heaviside nature of the volume fractions field presents an immense challenge for the accurate computation of the interface curvature and induces the spurious velocities in the flows with surface-tension effects. A 3D hybrid approach is presented combining the Convolution and Generalized Height Function method for the curvature computation. The volumetric surface tension forces are computed using the balanced-force continuum surface force model. It provides a high degree of robustness at lower grid resolutions with first-order convergence and high accuracy at higher grid resolutions with second-order convergence. The present method is validated for several test cases including a stationary droplet, an oscillating droplet and the buoyant rise of gas bubbles over a wide range of Eötvös (Eo) and Morton (Mo) numbers. Our computational results show an excellent agreement with analytical/experimental results with desired convergence behavior.