Numerical simulation of ﬂuid–solid interaction using an immersed boundary ﬁnite element method
NRC Industrial Materials Institute; National Research Council Canada
Computers & Fluids
Immersed boundary method; Fluid-solid interaction; Finite elements; Non-body-conformal mesh; Body conformal enrichment
This paper presents applications of a recently proposed immersed boundary method to the solution of ﬂuid–solid interaction. Solid objects immersed into the ﬂuid are considered rigid and their movement is determined from the interaction forces with the ﬂuid. The use of body-conformal meshes to solve such problems may involve extensive mesh adaptation work that has to be repeated each time a change in the shape of the domain or in the position of immersed solids is needed. Mesh generation and solution interpolation between successive grids may be costly and introduce errors if the geometry changes signiﬁ- cantly during the course of the computation. These drawbacks are avoided when the solution algorithm can tackle grids that do not ﬁt the shape of immersed objects. We present here an extension of our recently developed immersed boundary (IB) ﬁnite element method to the computation of interaction forces between the ﬂuid and immersed solid bodies. A ﬁxed mesh is used covering both the ﬂuid and solid regions, and the boundary of immersed objects is deﬁned using a time dependent level-set function. Boundary conditions on the immersed solid surfaces are imposed accurately by using a Body Conformal Enrichment (BCE) method. In this approach, the ﬁnite element discretization of interface elements is enriched by including additional degrees of freedom which are latter eliminated at element level. The forces acting on the solid surfaces are computed from the enriched ﬁnite element solution and the solid movement is determined from the rigid solid momentum equations. Solutions are shown for various ﬂuid–solid interaction problems and the accuracy of the present approach is measured with respect to solutions on body-conformal meshes.