Direct and inverse problems in gas dynamics
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Three problems in computational fluid dynamics are considered. Steady, inviscid, irrotational flow of a perfect gas in two dimensions is considered in the tangent gas approximation. A fast and accurate method of solution is proposed and solved numerically. Comparison of tangent gas and exact flows are presented. Tangent gas solutions, when used as the first step in the iterative solution of the exact flowfield, are shown to give substantial reduction in computational time. The inverse problem in the tangent gas approximation is considered. An exact method in this approximation for designing airfoils is presented. A simple numerical algorithm which is fast and accurate is presented. Comparison of designed airfoils using the tangent gas method with exact Euler results is found to be excellent for subcritical and slightly supercritical flows. An exact inverse method for designing airfoils is presented. The inverse problem is formulated in terms of a boundary value problem in speed only and the body angle is computed from the boundary estimate of the normal derivative of speed. Closure constraints are not imposed thus allowing the designed airfoil to be an open body.
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