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An immersed boundary method for incompressible flows in complex domains. (English) Zbl 1454.76058

Summary: This paper presents an immersed boundary method (IBM) to model the behaviour of solid-fluid interfaces in incompressible flows on non-conforming, unstructured meshes. Based on a smooth-interface direct forcing formulation, the proposed forcing method directly and implicitly uses the discretised momentum equations to evaluate the source terms required to enforce a no-slip condition on the boundary. The IBM is derived for a finite-volume framework with an implicit pressure-velocity coupling and a colocated variable arrangement, to enable application in complex domains. The novel framework is applied to flows with stationary and moving IBs on both Cartesian and tetrahedral meshes, and the results are compared to and validated with findings reported in the literature. The results demonstrate that the proposed formulation results in an accurate enforcement of the no-slip condition on the IB at every time-step, even for flows with strong transient behaviour and high velocity and pressure gradients. The results are similar to or better than those obtained with other methods that can only be applied on Cartesian meshes. The current method is shown to accurately preserve local continuity in the vicinity of the IB, ensuring local and global mass conservation in addition to satisfying the local no-slip condition. Moreover, the proposed forcing framework shows good results for unstructured meshes, with a similar accuracy as obtained on Cartesian meshes.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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