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 $$2\le p_{\ell }^{(x)}\le 16$$ (space) and $$2\le p^{(t)}\le 16$$ (time) respectively. $$\ell $$ 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 $$\ell $$. 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.

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