Space-time discontinuous Galerkin finite element method for two-fluid flows


Sollie, Warnerius Egbert Hendrikus (2010) Space-time discontinuous Galerkin finite element method for two-fluid flows. thesis.

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Abstract:The aim of this research project was to develop a discontinuous Galerkin
method for two-fluid flows, which is accurate, versatile and can alleviate
some of the problems commonly encountered with existing methods.
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.
A front tracking approach is chosen because these methods ensure a sharp
interface between the fluids are capable of high accuracy. The front tracking
is incorporated by means of cut-cell mesh refinement, because this type of
refinement is very local in nature and hence combines well with the STGD.
To compute the interface dynamics the level set method (LSM) is chosen, because of its ability to deal with merging and breakup, since it was ex-
pected that the LSM combines well with the cut-cell mesh refinement and
also because the LSM is easy to extend to higher dimensions. The small
cell problem caused by the cut-cell refinement is solved by using a merg-
ing procedure involving bounding box elements, which improves stability
and performance of the method. 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 conserva-
tive. All possible cuts the 0-level set can make with square and cube shaped
background elements are identified and for each cut an element refinement
is defined explicitly.
To investigate the numerical properties and performance of the numeri-
cal algorithm it is applied to a number of one and two dimensional single and
two-fluid test problems. Also, the Object Oriented Programming (OOP)
design and implementation of the two-fluid method were discussed.
Item Type:Thesis
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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