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Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. (English) Zbl 0972.76073
Summary: A second-order accurate, highly efficient method is developed for simulating unsteady three-dimensional incompressible flows in complex geometries. This is achieved by using boundary body forces that allow the imposition of the boundary conditions on a given surface not coinciding with the computational grid. The governing equations, therefore, can be discretized and solved on a regular mesh thus retaining the advantages and the efficiency of the standard solution procedures. Two different forcings are tested showing that while the quality of the results is essentially the same in both cases, the efficiency of the calculation strongly depends on the particular expression. A major issue is the interpolation of the forcing over the grid that determines the accuracy of the scheme; this ranges from zeroth-order for the most commonly used interpolations up to second-order for an ad hoc velocity interpolation.
The present scheme has been used to simulate several flows whose results have been validated by experiments and by other results available in the literature. Finally, in the last example we study the flow inside an IC piston/cylinder assembly at high Reynolds number; to our knowledge this is the first example in which the immersed boundary technique is applied to a full three-dimensional complex flow with moving boundaries and with a Reynolds number high enough to require a subgrid-scale turbulence model.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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[1] Peskin, C.S., Flow patterns around heart valves: A numerical method, J. comput. phys., 10, 252, (1972) · Zbl 0244.92002
[2] Peskin, C.S., Numerical analysis of blood flow in the heart, J. comput. phys., 25, 220, (1977) · Zbl 0403.76100
[3] McQueen, D.M.; Peskin, C.S., Shared-memory parallel vector implementation of the immersed boundary method for the computation of blood flow in the beating Mammalian heart, J. supercomp., 11, 213, (1997)
[4] McQueen, D.M.; Peskin, C.S., A three-dimensional computational method for blood flow in the heart. II. contractile fibers, J. comput. phys., 82, 289, (1989) · Zbl 0701.76130
[5] Briscolini, M.; Santangelo, P., Development of the mask method for incompressible unsteady flows, J. comput. phys., 84, 57, (1989) · Zbl 0678.76021
[6] 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
[7] 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
[8] Goldstein, D.; Handler, R.; Sirovich, L., Direct numerical simulation of the turbulent flow over a modelled riblet covered surface, J. fluid mech., 302, 333, (1995) · Zbl 0885.76074
[9] Goldstein, D.; Tuan, T.-C., Secondary flow induced by riblets, J. fluid mech., 363, 115, (1998) · Zbl 0924.76038
[10] Saiki, E.M.; Biringen, S., Spatial numerical simulation of boundary layer transition: effects of a spherical particle, J. fluid mech., 345, 133, (1997) · Zbl 0902.76067
[11] Arthurs, K.M.; Moore, L.C.; Peskin, C.S.; Pitman, F.B., Modeling arteriolar flow and mass transport using the immersed boundary method, J. comput. phys., 147, 402, (1998) · Zbl 0936.76062
[12] Mohd-Yusof, J., Combined immersed boundaries/B-splines methods for simulations of flows in complex geometries, (1997)
[13] Verzicco, R.; Orlandi, P., Wall/vortex ring interactions, App. mech. rev. ASME, 49, 447, (1996)
[14] Shariff, K.; Moser, R.D., Two-dimensional mesh embedding for B-spline methods, J. comput. phys., 145, 471, (1998) · Zbl 0910.65083
[15] Kravchenko, A.P.; Moin, P.; Moser, R.D., Zonal embedded grids for numerical simulations of wall-bounded turbulent flows, J. comput. phys., 127, 412, (1996) · Zbl 0862.76062
[16] Fornberg, B., Steady viscous flow past a sphere a high Reynolds number, J. fluid mech., 190, 471, (1988)
[17] Mittal, R., Planar symmetry in the unsteady wake of a sphere, Aiaa j., 37, 388, (1999)
[18] Batchelor, G.K., An introduction to fluid mechanics, (1967) · Zbl 0152.44402
[19] Morse, A.P.; Whitelaw, J.H.; Yanneskis, M., Turbulent flow measurement by laser Doppler anemometry in a motored reciprocating engine, (1978)
[20] R. Verzicco, J. Mohd-Yusof, P. Orlandi, and, D. C. Haworth, LES in complex geometries using boundary body forces, in, Proc. of the 1998 CTR Summer Program, VII, 1999, p, 171.
[21] Germano, M.; Piomelli, U.; Moin, P.; Cabot, W.H., A dynamic subgrid-scale eddy viscosity model, Phys. fluids A, 3, 1760, (1991) · Zbl 0825.76334
[22] Lilly, D.K., A proposed modification of the Germano subgrid-scale closure method, Phys. fluids A, 4, 633, (1992)
[23] Haworth, D.C., Large-eddy-simulation of in-cylinder flows, Multidimensional simulation of engine internal flows, (1998)
[24] D. C. Haworth, and, K. Jansen, Large-eddy-simulation on unstructured deforming meshes: Towards reciprocating IC engines, Comput. & Fluids, in press.
[25] Roma, A.M.; Peskin, C.S.; Berger, M.J., An adaptive version of the immersed boundary method, J. comput. phys., 153, 509, (1999) · Zbl 0953.76069
[26] Verzicco, R.; Orlandi, P., A finite-difference scheme for three dimensional incompressible flows in cylindrical coordinates, J. comput. phys., 123, 403, (1996) · Zbl 0849.76055
[27] Ferziger, J.H.; Peric, M., Computational methods for fluid dynamics, (1996) · Zbl 0869.76003
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