İstanbul Technical University Mathematical Engineering Department Seminars
An ALE Formulation for Moving Boundary Problems
Mehmet Şahin
İTÜ, Turkey
Özet :
An Arbitrary Lagrangian-Eulerian (ALE) formulation based on the
unstructured finite volume method is proposed for solving large moving boundary
The numerical method is based on the side-centered arrangement of the primitive
variables that does not require any ad-hoc modifications in order to enhance pressure
coupling. The continuity equation is satisfied within each element at machine precision
and the summation of the continuity equations can be exactly reduced to the domain
boundary, which is important for the global mass conservation. A special attention is
given to construct an ALE algorithm obeying the discrete geometric conservation law
(DGCL) at both local and global levels. The mesh deformation algorithm for the
interior fluid nodes is based on the indirect Radial Basis Function (RBF) algorithm
which allows significantly large boundary motions and deformations. For the parallel
solution of resulting large-scale algebraic equations in a fully coupled form, a matrix
factorization is introduced similar to that of the projection method for the whole
system and the parallel algebraic multigrid solver BoomerAMG is used for the scaled
discrete Laplacian provided by the HYPRE library which we access through the PETSc
library. Then the numerical method is extended for the large-scale numerical
simulation of fluid structure interaction problems in a fully coupled (monolithic) form.
Finally the numerical method is also modified for for multi phase flows with large
viscosity and density ratios. The accuracy and performance of the proposed algorithm
are verified for the several classical benchmark problems in the literature and then
the numerical method is applied to rather challenging problems.
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Tarih |
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04.12.2015 |
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Saat |
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15:00 |
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Yer |
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Fen-Edebiyat Fakültesi B1-226, 2. Kat |
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Dil |
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English |