Immersed Boundary Method Based on the Implementation of Conservation Equations along the Boundary using Control-Volume Finite-Element Scheme

ABSTRACT In this study conservation equations were implemented along the boundaries via ghost control-volume immersed boundary method. The control-volume finite-element method was applied on a cartesian grid to simulate 2-D incompressible flow. In this approach, mass and momentum equations were conserved in the whole domain including boundary control volumes by introducing ghost-control volume concept. The Taylor problem was selected to validate the present method. Four different case studies of Taylor problem encompassing both inviscid and viscous flow conditions in ordinary and 45º rotated grid were used for more investigation. Comparisons were made between the results of the present method and those obtained from the exact solution. Results of the present method indicated accurate predictions of the velocity and pressure fields in midline, diagonal, and all boundaries. The agreement between the results of the present method and the exact solution was very good throughout the whole temporal domain. Furthermore, comparison of the rate of kinetic energy decay in viscous case showed same level of agreement between the results.