Enriched immersed boundary method for convective conjugate heat transfer with level set-based surface reconstruction

We present an enriched immersed boundary method (EIBM) to simulate convective conjugate heat transfer processes for moving structures with complex geometry. The objective is to address the challenge of handling temperature and flux boundary conditions at the fluid-structure interface. The EIBM duplicates the temperature degree of freedom (DoF) of cut elements and imposes Neumann boundary conditions with property discontinuities through a discontinuous Galerkin approach. Furthermore, we augment the EIBM with a level-set-based surface reconstruction approach for the immersed structure. This method allows exact volumetric integration over the cut elements, remedying the small-cut problem commonly seen in immersed boundary methods. We present a series of numerical examples to demonstrate the efficacy of the proposed method. The results show the proposed method's enhanced predictive accuracy, particularly in capturing the boundary conditions.