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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
##### Keywords:
second-order interpolation
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##### References:
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