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

Abstract

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.