An improved immersed boundary method by coupling of the multi-direct forcing and Fourier pseudo-spectral methods

Abstract

The present paper aims to report an improve on the development of the IMERSPEC methodology, which is a methodology that couples the Fourier pseudo-spectral and immersed boundary methods, which can now solve flows over complex geometries. In the present work, the Lagrangian mesh that represents the immersed body inside the flow does not have to coincide with the Eulerian mesh. Furthermore, a high accuracy for the resultant methodology is achieved. These two important improvements arise from the development of the multi-direct forcing method and used to calculate the force field of the immersed boundary method. In order to verify the IMERSPEC methodology, a manufactured solution technique was used. The results of a refined mesh were employed, and different distribution and interpolation functions were used and analysed. Finally, flows over a backward-facing step geometry were simulated in two dimensions. This type of flow presents several physical features, for example, detachment and reattachment of the boundary layer and vortex generation, which are difficult to capture using numerical solutions. A comparison with the experimental data is presented and shows that the IMERSPEC methodology is promising for computational fluid dynamics applications and its analysis.