A High-Order Hybrid Compact-WENO Finite-Difference Immersed Boundary Method for Computing Two-Dimensional Inviscid Compressible Flows

Abstract

In the present study, a high-order hybrid compact-weighted essentially non-oscillatory (WENO) scheme is applied in conjunction with the immersed boundary method for efficiently computing compressible inviscid flows around two-dimensional solid bodies. For this aim, the two-dimensional unsteady compressible Euler equations written in the conservative form are considered and they are discretized in the space by using the hybrid fifth-order compact-WENO (CW) finite-difference scheme and the third-order explicit TVD Runge–Kutta scheme in the time. The solid bodies are appropriately imposed to the computational domain by using the immersed boundary method as an effective procedure in modeling the complex configurations without the difficulties usually encountered in generating the computational grid over such problems. Different test cases are simulated by applying the hybrid CW immersed boundary method and the present results are compared with those of available finite-difference immersed boundary methods. To further assess the solution method applied, the present results are also obtained by the high-order WENO immersed boundary scheme, and these two high-order accurate solution procedures are thoroughly compared with each other. The main advantage of using the hybrid CW finite-difference immersed boundary method applied here is that it provides a more accurate solution with lower computational cost in comparison with the traditional and high-order WENO finite-difference immersed boundary methods. It is shown that the solution procedure based on the hybrid CW scheme implemented via the immersed boundary method has still reasonable shock-capturing features and it can effectively be applied for accurately computing the compressible inviscid flows with the complicated flow structures and the embedded discontinuities such as the shocks over the complicated geometries.