| A new solution procedure was developed to solve the Euler equations for steady, compressible, rotational, inviscid flows. The approach is aimed to achieve real inviscid solutions in Euler calculations by eliminating the numerical diffusion inherent in conventional approaches. In conventional approaches which solve for the time-dependent conservation equations, the numerical diffusion is either built-in through finite truncations or added externally for reasons of numerical stability. The resulting solutions are, therefore, not solutions to the Euler equations but to the pseudo Navier-Stokes equations with numerical viscosity instead of physical viscosity. That is, convective quantities in resulting Euler solutions are contaminated by numerical diffusion and false entropy production. This numerical diffusion is also responsible for the solution dependency on the grids used and the solution reliability of the Navier-Stokes solutions with physical viscosity terms.;The present approach is based on splitting the character of the Euler equations into elliptic and convective quantities by using the Clebsch velocity decomposition. In the approach, the continuity equation is solved by a finite volume algorithm in the conservative form and then convective quantities are transported along streamlines without numerical diffusion. An efficient upwind difference scheme is developed to solve the convection equation for streamlines. The physical production of convective quantities, such as entropy across a shock wave, is implemented as a source term in the convection equation. The approach is an extension of the full potential formulation into the rotational Euler physics by allowing the variation of convective quantities. This aspect provides many benefits. Boundary conditions are simple and easy to implement, and there are no wave reflections as in the time dependent approaches. The approximation level of physical modeling is easily controllable and convertible; for example, Euler near-field, full potential mid-field, and Prandtl-Glauert far-field by freezing corresponding convective quantities.;The proposed approach is tested and demonstrated for several transonic cases. Numerical solutions are compared with those from the full potential equation and other Euler approaches, for a channel flow with a bump and the flow around a two-dimensional airfoil. |
