An immersed boundary solver for inviscid compressible flows

In this paper, a simple and efficient immersed boundary (IB) method is developed for the numerical simulation of inviscid compressible Euler equations. We propose a method based on coordinate transformation to calculate the unknowns of ghost points. In the present study, the body-grid intercept points are used to build a complete bilinear (2-D)/trilinear (3-D) interpolation. A third-order weighted essentially nonoscillation scheme with a new reference smoothness indicator is proposed to improve the accuracy at the extrema and discontinuity region. The dynamic blocked structured adaptive mesh is used to enhance the computational efficiency. The parallel computation with loading balance is applied to save the computational cost for 3-D problems. Numerical tests show that the present method has second-order overall spatial accuracy. The double Mach reflection test indicates that the present IB method gives almost identical solution as that of the boundary-fitted method. The accuracy of the solver is further validated by subsonic and transonic flow past NACA2012 airfoil. Finally, the present IB method with adaptive mesh is validated by simulation of transonic flow past 3-D ONERA M6 Wing. Global agreement with experimental and other numerical results are obtained.