THESIS
2014
xvii, 73 pages : illustrations (some color) ; 30 cm
Abstract
We propose several modifications to the grid based particle method (GBPM)
1
for moving interface modeling. There are several nice features of the proposed algorithm.
The new method can significantly improve the distribution of sampling
particles on the evolving interface. Unlike the original GBPM where footpoints
(sampling points) tend to cluster to each other, the sampling points in the new
method tend to be better separated on the interface. Moreover, by replacing
the grid-based discretization using the cell-based discretization, we naturally decompose
the interface into segments so that we can easily approximate surface
integrals. As a possible alternative to the local polynomial least square approximation,
we also study a geometric basis for local reconstruction in the resa...[
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We propose several modifications to the grid based particle method (GBPM)
1
for moving interface modeling. There are several nice features of the proposed algorithm.
The new method can significantly improve the distribution of sampling
particles on the evolving interface. Unlike the original GBPM where footpoints
(sampling points) tend to cluster to each other, the sampling points in the new
method tend to be better separated on the interface. Moreover, by replacing
the grid-based discretization using the cell-based discretization, we naturally decompose
the interface into segments so that we can easily approximate surface
integrals. As a possible alternative to the local polynomial least square approximation,
we also study a geometric basis for local reconstruction in the resampling
step. We will show that such modification can simplify the overall implementations.
Numerical examples in two- and three-dimensions will show that the
algorithm is computationally efficient and accurate.
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