Fictitious Domain and Immersed Boundary methods in OpenFOAM: Application to Complex Geometries

Building high quality meshes can be a difficult task when dealing with complex geometries. Furthermore, many industrial applications require topological optimization procedures in order to, for example, minimize the drag force exerted on an immersed body. In other situations, it may be necessary to simulate a complex moving object, like a stirrer. The most straightforward (but sub-optimal) approach consists in defining moving patches in OpenFOAM and to perform a re-meshing procedure that results in a drastic change of the mesh topology. Furthermore, a subsequent mapping of previous fields into the new mesh is required. Both procedures are time consuming, since the meshing algorithm has to ensure a minimum mesh quality, and the overall quality of the resulting solution tends to decrease.

In our present contribution we show how to address these problems using two alternative strategies: a Fictitious Domain (FD) and Immersed Boundary (IB) methodology. Both methods rely on a suitable representation of immersed objects by means of additional terms in the governing equations rather than imposing complex boundary conditions. This allows us (i) to use structured, fixed grids, and (ii) to avoid remeshing operations. Clearly, this results in major savings in computational time, improved stability of the calculation, and increased accuracy due to the fixed, high-quality meshes, and the lack of the field mapping step.

We will show how the method can be implemented in OpenFOAM in a conservative and numerically stable way. We do this in the frame if a projection method for pressure-based solvers. Finally, we will show examples of applications, as well as present results of a verification study.