Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations.

*(English)*Zbl 0972.76073Summary: 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.

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 |

##### Keywords:

second-order accurate method; interpolation of forcing; finite difference method; unsteady three-dimensional incompressible flows; complex geometries; IC piston/cylinder; high Reynolds number; immersed boundary technique
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\textit{E. A. Fadlun} et al., J. Comput. Phys. 161, No. 1, 35--60 (2000; Zbl 0972.76073)

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