Problems in fluid dynamics

Abstract

A scheme was developed for the parametric differentiation and integration of gas dynamics equations. A numerical integration of the gas dynamics equations is necessarily performed for a specific set of parameter values. The linear variational equations are obtained by differentiating the exact equations with respect to each of the relevant parameters. The resulting matrix of flow quantities is referred to as the Jacobi matrix. The subsequent procedure is then straightforward. The method was tested for two dimensional supersonic flow past an airfoil, with airfoil thickness, camber, and angle of attack varied. This approach has great potential value for rapidly assessing the effect of design changes. The other focus of the work was on problems in fluid stability, bifurcations, and turbulence