Numerical simulation of axisymmetric supersonic viscous flow over a blunt cone with a diagonal fourth-order finite difference method

作者：Rashidi M M; Bastani M Moradi; Beg O Anwar^*

来源：Proceedings of the Institution of Mechanical Engineers - Part G: Journal of Aerospace Engineering , 2012, 226(G3): 310-326.

DOI：10.1177/0954410011408303

• TLNS equations
• diagonal fourth-order method
• supersonic viscous flow
• shock-fitting

The numerical solution of steady viscous supersonic axisymmetric flowfield modelled by thin-layer Navier-Stokes equations is computed over a blunt cone with the shock-fitting method and the diagonal fourth-order central difference scheme implemented. Owing to the presence of high-order terms of the Taylor series in the discretization of derivatives, this method has high accuracy and low numerical error (dispersion error) compared with low-order methods. The boundary-closure scheme plays an important role in the numerical stability of this method. Using a coarse grid in this method, the results of numerical solution are found to be very close to those obtained with a fine grid employing the implicit second-order (Beam-Warming) method. Higher accuracy of this method is identified relative to the second-order method when the grid is being refined. The convergence rate of this method is also higher than the second-order method. Furthermore, the convergence of the method can be adjusted to accommodate the computational hardware capabilities.

• 出版日期2012-3