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An immersed-boundary finite volume method for simulations of flow in complex geometries. (English) Zbl 1057.76039
Summary: A new immersed-boundary method for simulating flows over or inside complex geometries is developed by introducing a mass source/sink as well as a momentum forcing. The method is based on a finite volume approach on a staggered mesh together with a fractional-step method. Both momentum forcing and mass source are applied on the body surface or inside the body to satisfy the no-slip boundary condition on the immersed boundary, and also to satisfy the continuity for the cell containing the immersed boundary. In the immersed-boundary method, the choice of an accurate interpolation scheme satisfying the no-slip condition on the immersed boundary is important because the grid lines generally do not coincide with the immersed boundary. Therefore, we propose a stable second-order interpolation scheme for evaluating the momentum forcing on the body surface or inside the body. Three different flow problems (decaying vortices and flows over a cylinder and a sphere) are simulated using the immersed-boundary method, and the results agree well with previous numerical and experimental results.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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[1] Peskin, C.S., The fluid dynamics of heart valves: experimental, theoretical, and computational methods, Annu. rev. fluid mech., 14, 235, (1982)
[2] Goldstein, D.; Handler, R.; Sirovich, L., Modeling a no-slip flow boundary with an external force field, J. comput. phys., 105, 354, (1993) · Zbl 0768.76049
[3] Saiki, E.M.; Biringen, S., Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method, J. comput. phys., 123, 450, (1996) · Zbl 0848.76052
[4] J. Mohd-Yusof, Combined Immersed-Boundary/B-Spline Methods for Simulations of Flow in Complex Geometries, Annual Research Briefs (Center for Turbulence Research, NASA Ames and Stanford University, 1997, p, 317.
[5] Fadlun, E.A.; Verzicco, R.; Orlandi, P.; Mohd-Yusof, J., Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations, J. comput. phys., 161, 35, (2000) · Zbl 0972.76073
[6] Ye, T.; Mittal, R.; Udaykumar, H.S.; Shyy, W., An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries, J. comput. phys., 156, 209, (1999) · Zbl 0957.76043
[7] Akselvoll, K.; Moin, P., Large eddy simulation of turbulent confined coannular jets and turbulent flow over a backward facing step, (1995)
[8] Kim, J.; Moin, P., Application of a fractional-step method to incompressible navier – stokes equations, J. comput. phys., 59, 308, (1985) · Zbl 0582.76038
[9] Park, J.; Kwon, K.; Choi, H., Numerical solutions of flow past a circular cylinder at Reynolds numbers up to 160, KSME int. J., 12, 1200, (1998)
[10] Lai, M.-C.; Peskin, C.S., An immersed-boundary method with formal second-order accuracy and reduced numerical viscosity, J. comput. phys., 160, 705, (2000) · Zbl 0954.76066
[11] Williamson, C.H.K., Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers, J. fluid mech., 206, 579, (1989)
[12] Fornberg, B., Steady viscous flow past a sphere at high Reynolds numbers, J. fluid mech., 190, 471, (1988)
[13] Johnson, T.A.; Patel, V.C., Flow past a sphere up to a Reynolds number of 300, J. fluid mech., 378, 19, (1999)
[14] Constantinescu, G.S.; Squires, K.D., LES and DES investigations of turbulent flow over a sphere, (2000) · Zbl 1113.76354
[15] Sakamoto, H.; Haniu, H., A study on vortex shedding from spheres in a uniform flow, J. fluid eng., 112, 386, (1990)
[16] Johnson, T.A., Numerical and experimental investigation of flow past a sphere up to a Reynolds number of 300, (1996), University of Iowa
[17] Jeong, J.; Hussain, F., On the identification of a vortex, J. fluid mech., 285, 69, (1995) · Zbl 0847.76007
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