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Space-Time Discontinuous Galerkin Finite Element Method for Two-Fluid Flows.

Summary: Space-Time Discontinuous Galerkin Finite Element
Method for Two-Fluid Flows.
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 offers
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 con-
servative as long as the numerical fluxes are conservative. The numerical


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering