A unified adaptive cartesian grid method for solid-multiphase fluid dynamics with moving boundaries

Numerical simulations of flows involving moving boundaries are challenging as they need to address the location and the conditions of the interface that interacts with the flow field. We have developed a unified, marker-based approach, which can treat moving solid and multiphase fluid dynamics using adaptively refined Cartesian grids. The interfaces separating the fluid phases are modeled using a continuous interface method, while the noslip condition on solid interfaces is imposed by a sharp interface method. A smoothly varying Heaviside-like function is used for handling discontinuous material properties between fluids and for identifying the solid-fluid interface location. Furthermore, a distance-based formulation is adopted to treat solid-fluid interface intersections. A domain decomposition method via Hilbert space filling curves and preconditioned multigrid solvers are incorporated into the staggered grid arrangement for scalar and velocity variables. To highlight the performance of the present approach, case studies are conducted for (i) interface shapes, residual volumes, formation of sloshes and corresponding wave periods in draining tank with different control parameters and flow regimes, (ii) fluid dynamics around a flapping airfoil, and (iii) fluid flow around complex solid geometries.