Coupled nodal integral-immersed boundary method (NI-IBM) for simulating convection-diffusion physics

Abstract

The Nodal Integral Method (NIM), which is a coarse grid numerical method, works quite efficiently on orthogonal grids. However, there are many challenges to the implementation of this method in the complex shaped domains due to its intricate discretization process. In contrast, the Immersed Boundary Method (IBM) offers the advantage of implementing boundary conditions in an arbitrarily shaped domain using rectilinear, non-conformal body grids. This work presents the NIM, coupled with the IBM methodology, to solve convection-diffusion physics in complex shaped domains. IBM is utilized to enforce the boundary effect on the non-body-conformal Cartesian grid, while the NIM serves as a numerical technique to discretize the governing equations. The study describes the detailed implementation of coupled NI-IBM (Nodal Integral-Immersed Boundary Method) for convection-diffusion physics. The validation and verification of the NI-IBM methodology is done through the comparison of the numerical results with analytical solutions of the diffusion and convection-diffusion test cases. Results demonstrate that the scheme maintains its accuracy in the coarse grid structure as well as second-order accurate. Furthermore, the numerical results produced by NI-IBM are at par or more accurate with respect to the NIM based schemes for arbitrarily shaped domains and the FV-IBM (Finite Volume-Immersed Boundary Method) method for the convection-diffusion physics. The results also indicate that even with coarse grids and higher convection, the NI-IBM method preserves its nature to produce reasonably accurate numerical results.