Computational modeling for multiphase flows with spacecraft application

Many engineering applications involve interactions between solid, gas and liquid phases under normal or micro-gravity conditions. Numerical simulations of such fluid flows need to track the location and the shape of the fluid interface as part of the solution. The merits and basic characteristics of various approaches for numerical computations of interfacial fluid dynamics are reviewed. The computational challenges include: (i) the algorithmic complexity for handling irregularly shaped moving boundaries that can experience merger and break-up; (ii) resolution refinement techniques to maintain desirable resolution of length scales, in accordance with the evolving fluid dynamics; (iii) data structure needed to support identification of the interface and satisfaction of the physical laws in the bulk fluids as well as around the phase boundaries; and (iv) efficient parallel processing techniques required for practical engineering analysis. The present review focuses on these issues related to the Lagrangian–Eulerian approach, utilizing the immersed boundary method with marker-based tracking, as the main framework for interfacial flow computations on Cartesian grids. Specifically, we offer in-depth discussion of the organization and layout of the mesh systems for both fluid and interface representations, local adaptive refinement on two-dimensional/three-dimensional (2D/3D) Cartesian grids, and multi-level domain decomposition method that utilizes Hilbert space filling curves for parallel processing strategy. The effectiveness of individual components and overall algorithm are presented using various tests such as, binary drop-collision computations to highlight grid adaptation and interface tracking algorithms to handle complex interface behavior, and bubble/droplet placed in a vortex field with various density/viscosity ratios across interfaces to address load balancing and scalability aspects of parallel computing. A time-dependent draining flow problem motivated by spacecraft applications is presented to aid spacecraft design efforts.