Numerical Simulation of Axisymmetric Supersonic Viscous Flow Over Blunt Cone by Using Implicit Fourth Order Finite Difference Method

Document Type : Research Article

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Abstract

In this paper, by using implicit fourth order central difference method and TLNS equations, the numerical solution of the steady axisymmetric viscous supersonic flow is implemented over blunt cone with shock-fitting method. Because of using high order terms of Taylor series in discretization of derivatives, this method has high accuracy and low numerical error (dispersion error) compared with low order method. The boundary-closure scheme has an important role in stability of this method. By 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 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 of this method can be adjusted to accommodate the computational hardware capabilities. 

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