This article describes the development of a high order finite volume method for the solution of transonic flows. The high order of accuracy is achieved by a reconstruction procedure similar to the weighted essentially non-oscillatory schemes (WENO). On the contrary to the WENO schemes, the weighted least square (WLSQR) scheme is easily extensible to the case of complex geometry.

A NEW multigrid relaxation scheme is developed for the steady-state solution of the Euler and Navier-Stokes equations. The lower-upper Symmetric-Gauss-Seidel method (LUSGS) does not require flux splitting for approximate Newton iteration. The present method, which is vectorizable and unconditionally stable, needs only scalar diagonal inversions. Application to transonic flow shows that the new ...

A practical three-dimensional shape optimization for aerodynamic design of a transonic wing has been performed using Evolutionary Algorithms (EAs). Because EAs coupled with aerodynamic function evaluations require enormous computational time, Numerical Wind Tunnel (NWT) located at National Aerospace Laboratory in Japan has been utilized based on the simple master-slave concept. Parallel process...

Some recent developments in numerical methods for calcuting solutions to the transonic potential flow equation are reviewed, including (1) the construction of stable coordinate independent difference schemes; (2) the use of conservatiation form to insure proper shock jump conditions; (3) analysis of the relaxation method by the time dependent analogy; (4) accelerated iterative schemes.