Computation of subsonic inviscid flow past a cone using high-order schemes

A wake-dominated unsteady flow of Mach number 0.2 past a cone of vertex angle 60 deg is calculated numerically using high-order finite difference schemes on structured grids. The three-dimensional compressible Euler equations are solved to simulate an inviscid flow that exhibits large fluctuations of pressure and velocity as a result of the shedding of vortices behind the cone. An axisymmetric structured grid system is used. It is generated by rotating a two-dimensional grid plane around a centerline. The grid singularity at the centerline, where the Jacobian and some grid metrics approach infinity, is avoided by changing the form of the flux vectors in the Euler equations without any asymptotic assumption or simplification. Fourth- and sixth-order finite difference schemes are used for the evaluation of spatial derivatives, and a fourth-order Runge-Kutta scheme is used for marching the solution in time. The complex wake structures and motions behind the cone are investigated by visualizing the vorticity field. The mean flow pattern and periodic phenomena are analyzed and compared with experimental data. This demonstrates the accuracy of the present approach to further analyses of wake-dominated flows past axisymmetric blunt-based bodies.