# A Fast, Efficient Multi-Direct Forcing of Immersed Boundary Method for Flow in Complex Geometry

### Anyang Wei, Hui Zhao, Jin Jun, JianRen Fan

#### 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.

#### References

- Calhoun, D. (2002). A Cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions. Journal of Computational Physics 176(2): 231-275.
- Ceniceros, H. D. and J. E. Fisher (2011). A fast, robust, and non-stiff Immersed Boundary Method. Journal of Computational Physics 230(12): 5133-5153.
- Chiu, P. H., R. K. Lin, et al. (2010). A differentially interpolated direct forcing immersed boundary method for predicting incompressible Navier-Stokes equations in time-varying complex geometries. Journal of Computational Physics 229(12): 4476-4500.
- Chiu, P. H., T. W. H. Sheu, et al. (2008). An effective explicit pressure gradient scheme implemented in the two-level non-staggered grids for incompressible Navier-Stokes equations. Journal of Computational Physics 227(8): 4018-4037.
- Clift, R., Grace, J., Weber, M. E. (1978). Bubbles, Drops, and Particles, Academic Press,Inc.London Ltd.
- Leveque, R. J. and Z. L. Li (1994). The Immersed Interface Method For Elliptic-Equations with Discontinuous Coefficients and Singular Sources. Siam Journal on Numerical Analysis 31(4): 1019-1044.
- Lima E Silva, A. L. F., A. Silveira-Neto, et al., 2003. Numerical simulation of two-dimensional flows over a circular cylinder using the immersed boundary method. Journal of Computational Physics 189(2): 351-370.
- Luo, K., Z. Wang, et al. (2007). Full-scale solutions to particle-laden flows: Multidirect forcing and immersed boundary method. Physical Review E 76(6): 066709.
- Peskin, C. S. (1972). Flow patterns around heart valves - numerical method. Journal of Computational Physics 10(2): 252-271.
- StÃ¥lberg, E., A. Bruger, et al. (2006). High order accurate solution of flow past a circular cylinder. Journal of Scientific Computing 27(1-3): 431-441.
- Tritton, D. J. (1959). Experiments On The Flow Past A Circular Cylinder At Low Reynolds Numbers. Journal of Fluid Mechanics 6(4): 547-567.
- Uhlmann, M. (2005). An immersed boundary method with direct forcing for the simulation of particulate flows. Journal of Computational Physics 209(2): 448-476.
- Wang, Z., J. Fan, et al. (2008). Combined multi-direct forcing and immersed boundary method for simulating flows with moving particles. International Journal of Multiphase Flow 34(3): 283-302.
- Williamson, C. H. K. (1996). Vortex dynamics in the cylinder wake. Annual Review Of Fluid Mechanics 28(1): 477-539.
- Williamson, C. H. K. and G. L. Brown (1998). A series in 1/vRe to represent the Strouhal-Reynolds number relationship of the cylinder wake. Journal of Fluids and Structures 12(8): 1073-1085.
- Wu, J. and C. Shu (2010). An improved immersed boundary-lattice Boltzmann method for simulating three-dimensional incompressible flows. Journal Of Computational Physics 229(13): 5022-5042.

#### Paper Citation

#### in Harvard Style

Wei A., Zhao H., Jun J. and Fan J. (2012). **A Fast, Efficient Multi-Direct Forcing of Immersed Boundary Method for Flow in Complex Geometry** . In *Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,* ISBN 978-989-8565-20-4, pages 309-314. DOI: 10.5220/0004049303090314

#### in Bibtex Style

@conference{simultech12,

author={Anyang Wei and Hui Zhao and Jin Jun and JianRen Fan},

title={A Fast, Efficient Multi-Direct Forcing of Immersed Boundary Method for Flow in Complex Geometry},

booktitle={Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},

year={2012},

pages={309-314},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004049303090314},

isbn={978-989-8565-20-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,

TI - A Fast, Efficient Multi-Direct Forcing of Immersed Boundary Method for Flow in Complex Geometry

SN - 978-989-8565-20-4

AU - Wei A.

AU - Zhao H.

AU - Jun J.

AU - Fan J.

PY - 2012

SP - 309

EP - 314

DO - 10.5220/0004049303090314