A boundary condition-enforced immersed boundary method for compressible viscous flows

A boundary condition-enforced immersed boundary method (IBM) for simulating compressible viscous flows is presented in this paper. It is developed from the implicit velocity correction-based IBM proposed by Wu and Shu (Journal of Computational Physics 228, 1963-1979 (2009)) for simulation of incompressible viscous flows. In their work, the velocity field is corrected by implementing the no-slip boundary condition. However, their method cannot be directly applied to simulate compressible flows. This is because the immersed boundary has a great effect on velocity, temperature, density and pressure fields in compressible flows, but their method has no mechanism to correct the density and pressure fields. To overcome this difficulty, in this work, the momentum field is firstly corrected by converting the no-slip velocity condition to the momentum condition. After that, from the continuity equation, the density correction can be made from the momentum correction. Then, the corrected velocity field can be given from the corrected momentum field and corrected density. Similar to the correction of momentum field, the temperature field can be corrected from the given temperature condition. Finally, the pressure can be obtained from the equation of state by using the corrected density and temperature. In this way, all the flow variables are corrected and the given physical boundary conditions are accurately implemented. To validate the proposed method, the flows over a stationary cylinder and one or two airfoils at different Mach and Reynolds numbers are simulated. Compared to the results in the literature, good agreement is achieved. (C) 2016 Elsevier Ltd. All rights reserved.