Accelerated solution of the steady Euler equations

The present paper is concerned with two methods for the accelerated solution of the steady Euler equations. One method makes use of a second-order embedding to facilitate the derivation of the relaxation solution of the steady equations of motion, while the other method employs a multile-gridding concept to accelerate the convergence of a simple, explicit, time-marching scheme applied to the unsteady equations. It is pointed out that the surrogate equation technique provides a means for formulating problems involving the full steady Euler equations in such a way as to allow the use of relaxation solution procedures. It is, therefore, possible to solve either irrotational or rotational flow problems spanning the entire spectrum of subsonic, transonic, and supersonic conditions. The solutions can be obtained without an employement of either derived dependent variables, semidirect methods, or an unsteady formulation.