Immersed boundary method with irrotational discrete delta vector for droplet simulations of large density ratio

摘要

An accurate estimation of the physical properties of a free-falling raindrop such as its falling speed, shape, and oscillation amplitude are expected to improve the numerical models used for weather forecasting. Developing a numerical tool for Direct Numerical Simulations (DNS) of water droplets by the Immersed Boundary Method (IBM) is one of the efficient ways to obtain empirical formulae for those physical properties. However, it is known that the IBM suffers from two instability problems in capillarity-dominant water droplet simulations. One is the spontaneous generation of unphysical kinetic energy, which is known as parasitic currents, and the other is spurious surface reconstruction. In this work, a new IBM is developed for stable water droplet simulations. A new force spreading scheme, which preserves the irrotational condition, is proposed to remove the spurious currents. Furthermore, B-spline fitting by least squares is adopted to relocate the Lagrangian markers for a smooth surface reconstruction. The conventional scheme and new scheme are implemented in a multigrid finite volume DNS solver and are subjected to standard test cases. It is confirmed that the unphysical parasitic currents are substantially reduced in the new scheme. The new scheme is applied to simulations of an axisymmetric free-falling droplet of low density ratio, a two-dimensional (2D) free-falling water droplet, and a rising bubble to demonstrate its robustness in a wide range of shape deformation and the capability of stable long-time-scale simulations for future application to raindrop simulations. (C) 2019 Elsevier Inc. All rights reserved.