Accurate finite-volume high-order compact interpolation with non-orthogonal and non-uniform grids for computational aeroacoustics

In recent years, with the development of supercomputers, the need for engineering applications of computational aeroacoustics is increasing. For industrial applications, the finite-volume compact interpolation is often applied as a discretization method. However, the original finite-volume compact interpolation can be applied only for calculation grids which are orthogonal and uniform, because the original finite-volume compact scheme is formulated assuming that calculation grids are orthogonal and uniform. Indeed, calculation grids for the computational aeroacoustics cannot be limited to orthogonal and uniform. Therefore, the finite-volume compact scheme for arbitrary calculation grids is required. In this paper, the finite-volume NOGS compact scheme is established in three dimensions to be suited for calculations using arbitrary grids. The interpolation error tests were conducted using a number of non-orthogonal and non-uniform grids to verify the NOGS compact scheme. From these interpolation tests, it is revealed that the NOGS compact scheme can reduce the interpolation error compared to the original compact scheme. Therefore, it is predicted that the reduction of the interpolation error leads to accurate evaluation of the numerical flux and that the calculation results are improved. Also, the large eddy simulations around a circular cylinder were conducted to verify the influence of the interpolation error reduction on the flow field and on the sound field.