Computations of drop dynamics with the immersed boundary method, part 1: Numerical algorithm and buoyancy-induced effect

A computational capability based on the combined projection method for unsteady transport equations and the immersed boundary technique for interface tracking is presented for simulating multiphase flows with heat transfer. The approach employs a fixed Cartesian grid computation while tracking the moving interface between phases with Lagrangian particles. Special attention is paid to treat the physical situation that the transport properties such as density between liquid and vapor phases changes substantially, around O(1,000) under the atmospheric condition. Furthermore, the multigrid method is incorporated to help reduce the computational cost incurred in such flow computations. In the first of the two-part article, the basic elements of the computational technique are presented for general axisymmetric two-phase flow problems. To demonstrate the performance as well as validate the correctness of the technique, a single bubble under either a static equilibrium condition or influenced by buoyancy is investigated for different grid size, transport properties, and flow parameters.