Summary: Two Fluid Space-Time Discontinuous Galerkin Finite
Element Method. Part I: Numerical Algorithm
W.E.H. Sollie, O. Bokhove, J.J.W. van der Vegt
Department of Applied Mathematics, Institute of Mechanics, Processes and Control
Twente, University of Twente, P.O.Box 217, 7500 AE, Enschede, The Netherlands
A novel numerical method for two fluid flow computations is presented,
which combines the space-time discontinuous Galerkin finite element dis-
cretization with the level set method and cut-cell based interface tracking.
The space-time discontinuous Galerkin (STDG) finite element method of-
fers high accuracy, an inherent ability to handle discontinuities and a very
local stencil, making it relatively easy to combine with local hp-refinement.
The front tracking is incorporated via cut-cell mesh refinement to ensure a
sharp interface between the fluids. To compute the interface dynamics the
level set method (LSM) is used because of its ability to deal with merging
and breakup. Also, the LSM is easy to extend to higher dimensions. Small
cells arising from the cut-cell refinement are merged to improve the stability
and performance. The interface conditions are incorporated in the numerical
flux at the interface and the STDG discretization ensures that the scheme is
conservative as long as the numerical fluxes are conservative.