Department of Mathematics, Florida State University
"A hierarchical space-time spectral element method for simulating multiphase flows"
There are practical applications for the detailed simulation of atomization and spray problems (application: fuel injection systems) and bubbly flow problems (application: boiling in cooling pipes). For these problems, it is not only important to accurately simulate transport processes along fluidic interfaces separating gas and liquid, but it is also important to accurately simulate the complex flow that can emerge away from interfaces.
It is possible that there is 2-way coupling between the interface dynamics and the flow in the bulk regions. So, we have developed a hierarchical spectral element method in which we use the low order moment-of-fluid method on fine dynamic meshes for simulating complex deforming interfaces, and away from interfaces, we have implemented a new space-time spectral element method on coarse meshes.
Our new method is designed so that one can increase the order of accuracy of almost any low order, stable, operator split method for solving PDEs, in order to be a stable and spectrally accurate method in both space and time.
Some sample results are presented for complex incompressible single and multiphase flows.
This work was done in collaboration with Dr. Chaoxu Pei and Professor M. Yousuff Hussaini.