Effects of Accuracy of Transformation From Physical to Computational Coordinate on Flow Prediction based on WENO Scheme

Capturing shock and separation flow accurately is of great importance in the design of cascade/airfoil. Weighted essentially non-oscillatory (WENO) scheme has attracted attention owing to its capability to achieve arbitrarily high order formal accuracy in smooth regions while maintaining stable, non-oscillatory, and sharp discontinuity transitions. The schemes are usually constructed on a uniform grid, in which local grid refinement is required to reduce computational cost, which means a non-uniform grid should always be generated in engineering. Coordinate transformation is one of the most efficient methods for applying the scheme on a non-uniform grid. However, the effect of coordinate transformation accuracy on WENO scheme has yet to be known. In this paper, the influence of coordinate transformation accuracy on the dissipative and precision of WENO scheme is studied. Furthermore, along with the practical engineering problems, the influence on shock resolution and separation flow capturing are also studied. Finally, we give the engineering application recommendations, so as to provide the basis for the computational fluid mechanics and improve the accuracy of the finite difference WENO scheme on a non-uniform grid.