A comparison of fluid-cell and ghost-cell direct forcing immersed boundary method for incompressible flows with heat transfer

In direct-forcing immersed boundary methods, the forcing terms are generally applied to forcing points on either fluid side (fluid-cell forcing approach) or body side (ghost-cell forcing approach) of the immersed boundary. These direct forcing terms are added to the discretized equations over forcing points in order to implicitly enforce proper boundary conditions on the immersed boundary; hence they dictate the development of the computed flow field. Generally, different forcing approaches adapt different reconstruction models with different stencil supports to compute forcing terms. In this article, a general second-order accurate reconstruction model for solving incompressible Navier-Stokes equations with heat transfer is applied to both the fluid-cell forcing approach and the ghost-cell forcing approach. This allows a meaningful comparison of the solution accuracy and convergence between the two forcing approaches under various boundary conditions. In particular, a simple remedy to reduce the spurious oscillations in pressure force calculation over moving bodies for the ghost-cell forcing approach is devised and verified.