LEAST-SQUARES COMPUTATION OF HYPERSONIC FLOWS

The steady Euler equations are written in conservative form for the density and the components of the velocity as unknowns. The pressure is eliminated in the equations of conservation of momentum by using Bernoulli's equation for steady flows. The resulting first-order nonlinear hyperbolic system is solved globally by means of Newton linearization and a least-squares embedding. This method is stable for the subsonic as well as the supersonic regime. It is applied to compute hypersonic flows around a circular cylinder or an ellipse in 2D and a sphere in 3D. Depending on the initialization, an entropy corrector is required to capture the bow shock, then a mesh adaptation procedure is used to fit the mesh to the shock front. The solutions are very close to those available in the literature.