Nodal Integral Immersed Boundary Method for convection-diffusion physics in complex domain
In this work, Nodal Integral Immersed Boundary Method (NIIBM) is proposed. In NIIBM, a non-conformal body grid method named Immersed Boundary Method (IBM) is coupled with the Nodal Integral Method (NIM). This method enables to achieve the accurate results at significantly lower grid sizes. The accuracy of developed numerical framework is presented through simulating convection-diffusion problem in 2D cylindrical wedge shape geometry for wide range of convection strength (i.e. at different Peclet numbers: Pe). The achieved results are compared with the analytical solution and also found to be in good agreement at much coarser grid. Further, the L2 norm error is also plotted which shows that the proposed scheme preserves nearly second order accuracy. Overall, a novel, simple, effective, computationally efficient and nearly second order accurate coupled NIIBM numerical framework has been presented for solving thermo-fluid problems involving complex geometry.