Adaptation of Structured Grid for Supersonic and Transonic Flows

Two distinct redistribution grids - adaptation techniques, spring analogy and elliptic grid generator are applied to two-dimensional steady, inviscid, shocked flows, and the ability of each technique is examined and compared. Euler equations are solved base on Roe's Reimann solver approach to simulate supersonic flow around a sphere, transonic flow about an airfoil and supersonic flow in a symmetric diffuser. In redistribution method using spring analogy, the movement of grid points was controlled by forces analogous to tensional and torsional spring forces set between grid points. In elliptic grid generation, the body fitted coordinate were used based on arc length of the grid lines. It is shown that the use of arc length in grid lines instead of the length of straight lines between grids which were used by other, produces better results in one-direction, but introduces some skew ness problem in the generated grids for in both directions. The results show that when expansion or shock waves are only along one direction of the curvilinear coordinate, the use of elliptic equations to produce adapted grid base on the arc length of the grid lines is suitable and produces good results. Specially, it is most suitable when the elliptic equations and flow equations are solved simultaneously. The ability of the adapted grid technique depends upon the flow configurations. For example for flow over a sphere, both techniques provide good results, but for flow over an airfoil, the spring adaptive technique introduces better results. Also, the elliptic grid generator is more suitable for complex flows.