On the use of polyhedral unstructured grids with a moving immersed boundary method

Abstract A moving immersed boundary method for unstructured grids is presented which offers several advantages over the standard ones with Cartesian grids. The flexibility provided by the unstructured grids allows for smaller grid sizes and meshing of complex flow configurations. The method features a conservative fluid domain characterization together with a flexible least-squares flow reconstruction to emulate the immersed body. The method is validated with several test cases and different grid types: polyhedral, triangular and Cartesian. A static problem is first simulated in order to demonstrate the expected second order accuracy. Then, a benchmark moving body problem is studied, where the method is shown to compute the correct velocity and pressure fields independently of the grid type. The effects of the cell topology in the spurious force oscillations (SFO) are also studied and the polyhedral grids are proven to be superior to their Cartesian and triangular counterparts. Finally, some examples of moving bodies in a computational domain with complex static boundaries are provided. The new method allows the use of unstructured grids for the outer fixed boundary, which allows good geometry conformance and therefore a better flow resolution. These grids can include a region with a reduced grid size and smooth transition, located at the body’s path.

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