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Parallel unstructured multigrid simulation of 3D unsteady flows and fluid structure interaction in

Parallel unstructured multigrid simulation of 3D unsteady flows and fluid structure interaction in.m

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methods includes immersed boundary method and fictitious domain method, etc. Peskin et al. [8,9] proposed the
immersed boundary method to simulate the motion of
the human hearts and heart valves. It treats immersed elastic structure as a part of the fluid domain on which additional forces arising from elastic stresses of immersed
structure are applied. Glowinski et al. [10,11] studied a
Lagrange multiplier based fictitious domain method for
the numerical solutions of three-dimensional elliptic problems with Dirichlet boundary conditions and also for the
Navier–Stokes equations modeling incompressible viscous
flows. This method is based on the imposition of velocity
constraints associated with moving internal boundaries
by means of Lagrange multiplier. Generally, Eulerian
methods are relatively less-complicated techniques in terms
of using fixed fluid mesh, which reduces greatly the computational costs. However, the above Eulerian methods do
not allow for ‘jump’ conditions across both sides o
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