An implicit finite-volume method for solving the Euler equations

Although the explicit methods which have been developed for the solution of steady or unsteady transonic flow Euler equations allow the prediction of supercritical flows around airfoils without restriction on shock wave strength and motion, they are computing time-intensive due to the limitation on the time step required for numerical stability. This limitation is removed through the application of the present, second-order and noniterative implicit method for the solution of Euler equations. An important feature of the present method is that the implicit terms are of the order of the truncation error, allowing simpler and easier treatment of boundary conditions. The method is expressed in the finite volume formulation and applied to both steady and unsteady transonic flows. The computing time reduction achieved while obtaining accurate results is noted.