Transonic potential flow calculations by two artificial density methods

Abstract

A steady transonic flow over an airfoil is computed by solving the full potential equation discretized over a contour-fitting grid in full conservation form. Near shock waves, density is corrected to account for the rise in entropy in the region. A multigrid alternating direction method is used to drive the iteration. In supersonic flow regions, artificial dissipation is introduced by retarding the density in the upstream direction. In a new formulation for this artificial density, the amount by which the density is biased is made proportional to the local flux gradients. This new formulation is compared with the standard formulation that is based on density gradients. The new scheme, as the old one, is second-order accurate throughout the flow field except for a small region near shock waves. Results of calculations with the two schemes show that, when the shock itself is weak, the scheme based on flux gradients gives a sharper resolution of the shock than the scheme based on density gradients. As shock strength increases, the shock-capturing abilities of the two schemes become equal. Throughout the range of cases tested, the two schemes exhibited comparable speed and robustness.