Block-structured solution of Euler equations for transonic flows

A block-structured solution scheme is developed for the solution of Euler equations for steady three-dimensional transonic flows*. The Euler equations are expressed in terms of Clebsch variables w = v + Svn. The resulting set of equations for conservation of mass, entropy (5) and the Clebsch variable j\ are solved using a block-based relaxation scheme. The flowfield is divided into a series of individual blocks representing local regions of the flowfield. The employed grid generation scheme provides local refinement of each block yet ensures one-to-one matching of grid points on the surfaces of adjoining blocks. For each of the blocks, either potential or Euler equations can be solved. For every block, the conservation of mass equation is solved to determine . For blocks with rotationality, two additional equations for determining S and T\ are solved. In this paper, the basic steps of the developed solution scheme are presented. The computational considerations involved in utilizing the present scheme are demonstrated for several two-dimensional sample problems.