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Simulation of Incompressible Viscous Flows by Local DFD-Immersed Boundary Method

  • Y. L. Wu (a1), C. Shu (a1) and H. Ding (a2)

Abstract

A local domain-free discretization-immersed boundary method (DFD-IBM) is presented in this paper to solve incompressible Navier-Stokes equations in the primitive variable form. Like the conventional immersed boundary method (IBM), the local DFD-IBM solves the governing equations in the whole domain including exterior and interior of the immersed object. The effect of immersed boundary to the surrounding fluids is through the evaluation of velocity at interior and exterior dependent points. To be specific, the velocity at interior dependent points is computed by approximate forms of solution and the velocity at exterior dependent points is set to the wall velocity. As compared to the conventional IBM, the present approach accurately implements the non-slip boundary condition. As a result, there is no flow penetration, which is often appeared in the conventional IBM results. The present approach is validated by its application to simulate incompressible viscous flows around a circular cylinder. The obtained numerical results agree very well with the data in the literature.

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Corresponding author

Corresponding author. URL: http://serve.me.nus.edu.sg/shuchang/, Email: mpeshuc@nus.edu.sg

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[1]Peskin, C. S., Numerical analysis of blood flow in the heart, J. Comput. Phys., 25 (1977), pp. 220252.
[2]Goldstein, D., Hadler, R. and Sirovich, L., Modeling a no-slip flow boundary with an external force field, J. Comput. Phys., 105 (1993), pp. 354366.
[3]Lai, M. and Peskin, C. S., An immersed boundary method with formal second-order accuracy and reduced numerical viscosity, J. Comput. Phys., 160 (2000), pp. 705719.
[4]Linnick, M. N. and Fasel, H. F., A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains, J. Comput. Phys., 204 (2005), pp. 157192.
[5]Lima, E., Silva, A. L. F., Silverira-Neto, A. and Damasceno, J. J. R., Numerical simulation of two-dimensional flows over a circular cylinder using the immersed boundary method, J. Comput. Phys., 189 (2003), pp. 351370.
[6]Feng, Z. G. and Michaelides, E. E., Proteus: a direct forcing method in the simulations of particulate flow, J. Comput. Phys., 202 (2005), pp. 2051.
[7]Chen, S. and Doolen, G. D., Lattice Boltzmann method for fluid flows, Ann. Rev. Fluid. Mech., 30 (1996), pp. 329364.
[8]Niu, X. D., Shu, C., Chew, Y. T. and Peng, Y., A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows, Phys. Lett. A., 354 (2006), pp. 173182.
[9]Peng, Y., Shu, C., Chew, Y. T., Niu, X. D. and Lu, X. Y., Application of multi-block approach in the immersed boundary-lattice Boltzmann method for viscous fluid flows, J. Comput. Phys., 218 (2006), pp. 460478.
[10]Shu, C., Liu, N. Y. and Chew, Y. T., A novel immersed boundary velocity correction-lattice Boltzmann method and its application to simulate flow past a circular cylinder, J. Comput. Phys., 226 (2007), pp. 16071622.
[11]Wu, J. and Shu, C., Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications, J. Comput. Phys., 228 (2009), pp. 19631979.
[12]Shu, C. and Wu, W. L., Adaptive mesh refinement-enhanced local DFD method and its application to solve Navier-Stokes equations, Int. J. Numer. Meth. Fluids., 51 (2006), pp. 897912.
[13]Shu, C. and Fan, L. F., A new discretization method and its application to solve incompressible Navier-Stokes equation, Comput. Mech., 27 (2001), pp. 292301.
[14]Shu, C. and Wu, Y. L., Domain-free discretization method for doubly connected domain and its application to simulate natural convection in eccentric annuli, Comput. Methods. Appl. Mech. Eng., 191 (2002), pp. 18271841.
[15]Wu, Y. L. and Shu, C., Application of local DFD method to simulate unsteady flows around an oscillating circular cylinder, Int. J. Numer. Meth. Fluids., 58 (11) (2008), pp. 12231236.
[16]Kim, J. and Moin, P., Application of fractional-step method to incompressible Navier-Stokes equations, J. Comput. Phys., 59 (1985), pp. 308323.
[17]Ding, H. and Shu, C., A stencil adaptive algorithm for finite difference solution of incompressible viscous flows, J. Comput. Phys., 214 (2006), pp. 397420.
[18]Wu, J. and Shu, C., Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications, J. Comput. Phys., 228 (2009), pp. 19631979.
[19]Dennis, S. C. R. and Chang, G. Z., Numerical solutions for steady flow past a circular cylinder at Reynolds number up to 100, J. Fluid. Mech., 42 (1970), pp. 471489.
[20]He, X. Y. and Doolen, G. D., Lattice Boltzmann method on a curvilinear coordinate system: vortex shedding behind a circular cylinder, Phys. Rev., 56 (1997), pp. 434440.
[21]Calhoun, D., A Cartesian grid method for solving the two-dimensional stream function-vorticity equatins in irregular regions, J. Comput. Phys., 176 (2002), pp. 231275.
[22]Tuann, S. Y. and Olson, M. D., Numerical studies of the flow around a circular cylinder by a finite element method, Comput. Fluid., 6 (1978), pp. 219240.
[23]Ding, H., Shu, C. and Cai, Q. D., Applications of stencil-adaptive finite difference method to incompressible viscous flows with curved boundary, Comput. Fluids., 36 (2007), pp. 786793.
[24]Braza, M., Chassaing, P. and Ha Minh, H., Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder, Fluid. Mech., 165 (1986), pp. 79130.
[25]Liu, C., Zheng, X. and Sung, C. H., Preconditioned multigrid metrhods for unsteady incompressible flows, J. Comput. Phys., 139 (1998), pp. 3957.
[26]Ding, H., Shu, C., Yeo, K. S. and Xu, D., Simulation of incompressible viscous flows past circular cylinder by hybrid FD scheme and meshless least square-based finite difference method, Comput. Methods. Appl. Mech. Eng., 193 (2004), pp. 727744.

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Simulation of Incompressible Viscous Flows by Local DFD-Immersed Boundary Method

  • Y. L. Wu (a1), C. Shu (a1) and H. Ding (a2)

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