Efficient numerical method for simulation of supersonic viscous flow past a blunted body at a small angle of attack

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For solving the three-dimensional (3-D) full viscous shock-layer (FVSL) equations in a body-oriented coordinate system, an asymptotic method is used with the angle of attack as a small parameter. In using a small parameter method, the (3-D) FVSL system is separated into an axisymmetric set and a linear 2-D set of equations. The method of global iterations was used to solve both the axisymmetric and linearized sets of equations. Global iterations were carried out on the pressure gradient tangential component and on the shock wave tangle. The method is used uniformly for both the blunted and conic parts of the body. The shock wave angle was found by using the Rankine-Hugoniot boundary condition for the normal component of the velocity. A computational grid adapted to the solution was used in solving both systems of equations. The comparison of this approach with 3-D implicit time-marching methods shows that the time neccessary for the calculation in the 3-D case is about 100 times less, while the accuracy of the calculations is essentially the same. Also, the small parameter method enables one to find a one-parameter family of solutions; the parameter in question is the angle of attack.