A Hierarchical Space-Time Spectral Element and Moment-of-Fluid Method for Improved Capturing of Vortical Structures in Incompressible Multi-phase/Multi-material Flows

A novel block structured adaptive space-time spectral element and moment-of-fluid method is described for computing solutions to incompressible multi-phase/multi-material flows. The new method implements a space-time spectrally accurate method in the bulk regions of a multi-phase/multi-material flow and implements the cell integrated semi-Lagrangian moment-of-fluid method in the vicinity of mixed material computational cells. In the new method, the space-time order can be prescribed to be 2 <= p(l)((x)) <= 16 (space) and 2 <= p((t)) <= 16 (time) respectively. l represents the adaptive mesh refinement level. Regardless of the space-time order, only one ghost layer of cells is communicated between neighboring grid patches that are on different compute nodes or different adaptive levels l. The new method is first tested on incompressible vortical flow benchmark tests, then the new method is tested on the following incompressible multi-phase/multi-material problems: (i) vortex shedding past a tilted cone and (ii) atomization and spray of a liquid jet in a gas cross-flow.