A finite element immersed boundary method for fluid flow around rigid objects

Abstract

This paper proposes a new immersed boundary (IB) method for solving fluid flow problems in the presence of rigid objects which are not represented by the mesh. Solving the flow around objects with complex shapes may involve extensive meshing work that has to be repeated each time a change in the geometry is needed. Important benefit would be reached if we are able to solve the flow without the need of generating a mesh that fits the shape of the immersed objects. This work presents a finite element IB method using a discretization covering the entire domain of interest, including the volume occupied by immersed objects, and which produces solutions of the flow satisfying accurately the boundary conditions at the surface of immersed bodies. In other words the finite element solution represents accurately the presence of immersed bodies while the mesh does not. This is done by including additional degrees of freedom on interface cut elements which are then eliminated at element level. The boundary of immersed objects is defined using a level set function. Solutions are shown for various flow problems and the accuracy of the present approach is measured with respect to solutions obtained on body‐fitted meshes. Copyright © 2010 Crown in the right of Canada.

A finite element immersed boundary method for fluid flow around moving objects

“…The algorithm used to treat the immersed boundary surface is the same as for the static IB method [11]. However, the change in position of the fluid/solid interface from one time step to another commands a special integration of time derivative terms.…”

“…Our recently proposed approach [11] demonstrated on fixed immersed objects achieves the level of accuracy of cut cell dynamic node addition techniques with none of their drawbacks (increased CPU time and costly dynamic data structures). This approach is extended to moving fluid/solid interfaces in the present contribution.…”

Thermal conduction in particle packs via finite elements

“…This property implies that the CDFEM accuracy is no less than that afforded by XFEM with Heaviside enrichment [12]. When applied to problems with Dirichlet boundary conditions, CDFEM is very similar to the recently proposed immersed finite element method [20,21]. Both methods decompose the background mesh into conformal elements.…”

Three-dimensional Finite Element Solution of the Flow in Single and Twin-Screw Extruders

“…Most of these developments were made using a finite difference framework. IB methods using finite elements were developed more recently (Glowinski et al, 1994) and an overview can be found in (Ilinca and Hétu, 2010a). In most IB methods, boundary conditions on immersed surfaces are handled either accurately by using dynamic data structures to add/remove grid points as needed or in an approximate way by imposing the boundary conditions to the grid point closest to the surface or through least-squares.…”

“…In most IB methods, boundary conditions on immersed surfaces are handled either accurately by using dynamic data structures to add/remove grid points as needed or in an approximate way by imposing the boundary conditions to the grid point closest to the surface or through least-squares. Our recently proposed approach (Ilinca and Hétu, 2010a) achieves the level of accuracy of cut cell dynamic node addition techniques with none of their drawbacks (increased CPU time and costly dynamic data structures). This approach was extended to moving fluid/solid interfaces in (Ilinca and Hétu, 2010b).…”