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A Fast, Efficient Multi-Direct Forcing of Immersed Boundary
Method for Flow in Complex Geometry
Anyang Wei, Hui Zhao, Jin Jun and Jianren Fan
State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou, P.R. China
Keywords: Immersed Boundary Method, Efficient, Fast, Multi-Direct Forcing.
Abstract: The Immersed Boundary method (IBM) has received wide attention from last decade, due to its promising
application to solve the fluid-solid interaction problems in large quantities of practical engineering areas.
This paper implemented IBM with Multi-Direct-Forcing (MDF), presenting the evaluation of momentum
forces on the body surface - interaction forces between fluid-solid. Grounded on the Multi-Direct-Forcing
method, we constructed a new system that could be efficiently and fast solved. Meanwhile, this proposed
algorithm is easy to code and implement parallelization. Besides, it can be extended to three-dimensional
simulation without much more extra efforts. Accuracy of the proposed MDF immersed boundary method
has been investigated, as well as some applications such as flow past the cylinder at a set of low Reynolds
numbers.
1 INTRODUCTION
The incompressible fluid flows involving complex
boundaries, which may be stationary or in motion,
are of practical and academic importance. These
problems can be solved by the traditional body-fitted
numerical methods, in which governing equations
are discretized in a curvilinear coordinate system
that conforms to the boundaries, with re-meshing at
each time step. This procedure is not trivial and the
re-mesh computation is heavily cost. To solve the
complex geometrical fluid-interaction problem,
Peskin (Peskin 1972) proposed the Immersed
Boundary method in 1972, when he studied the flow
in heart valves based on the Cartesian grid. With
many structure grid properties retained, this method
gave the complex geometrical fluid-interaction prob-
lems an effective solution direction.
In the past two decades, we have seen the boom of
the Immersed Boundary Method. Several variants of
Immersed Boundary Method have appeared, like
Immersed Interface Method (Peskin 1972; Leveque
and Li 1994), Direct-Forcing Method (Uhlmann
2005) et al.. But all these methods, as the original
method proposed by Peskin, need an interpolation
between the immersed boundary Lagrangian and
Eulerian grid points. When this process is applied to
simple geometries or multiphase flows with a small
amount of particles, it is quantified. However, when
it comes to large quantities of particles or practical
geometries, it also costs a lot, though it is much
easier to implement than body-fitted numerical
method. These days, Ceniceros and Fisher
(Ceniceros and Fisher 2011) have applied the
treecode combined with FMM (Fast March Method)
to simulate large systems, but this method is not
trivial to implement. Wu and Shu et al.(Wu and Shu
2010) directly performed the fluid-interaction force,
deriving a linear system with the immersed bounda-
ry force density as variables. They deemed it was
easy to implement, but they only test two-
dimensional problems, however when it comes
across the three-dimensional systems or large quan-
tities of particles in multiphase flow simulation, that
linear system would be very huge, and the above
metioned FMM and treecode can be a good candi-
date.
Grounded on the work of Luo et al. (Luo, Wang
et al. 2007), Wu and Shu (Wu and Shu 2010), we
proposed another efficient fast immersed boundary
method based on the multi-direct-forcing immersed
boundary method. This paper is organized as fol-
lows. In section 2, firstly the governing equations for
the incompressible Navier–Stokes equations are
presented. Then immersed boundary method imple-
mented with multi-direct-forcing will be briefly
described. At the end of this section, we will propose
309
Wei A., Zhao H., Jun J. and Fan J..
A Fast, Efficient Multi-Direct Forcing of Immersed Boundary Method for Flow in Complex Geometry.
DOI: 10.5220/0004049303090314
In Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH-2012),
pages 309-314
ISBN: 978-989-8565-20-4
Copyright
c
2012 SCITEPRESS (Science and Technology Publications, Lda.)