Immersed Boundary Method (IBM) with an Irrotational Discrete Delta Function for Simulations of 2D and Axisymmetric Free-Fail Water Droplet

摘要

Stability and conservation of energy are strongly required for long time-scale simulations of free-fall water droplet. However, it is well known that parasitic currents are persistently present in the immersed boundary method, leading to generation of unphysical kinetic energy. It is shown that the irrotational property of delta function must be preserved in discretized form to eliminate those unphysical parasitic currents. As a solution, a new irrotational discrete delta function is proposed in this study. Furthermore, the method of B-spline curve fitting by least squares replaces the Lagrange interpolation polynomial in the interpolation and redistribution of Lagrangian markers for stable computation of curvature. The new immersed boundary method is verified through static droplet and free oscillating droplet test cases. The new method is also successfully applied to the simulations of free-fall water droplet.