ナビエ・ストークス方程式の数値解を用いた非線形計画法による物体形状の最適化 (第2報) : 数値解の挙動に関する考察

抄録

Numerical experiments are carried out to examine the accuracy and convergency of numerical solutions by the optimization method developed in the preceding paper for obtaining a body profile with minimum viscous drag. The nonlinear programming technique based on the modified feasible direction method was incorporated into the time-marching procedure for numerical solution of the incompressible Navier-Stokes equation. Some improvements were made on the discretization scheme of the governing equation and boundary conditions and on the implementation of the constraints associated with the optimization problem. The finite-difference solution of the Navier-Stokes equation shows weak but persistent unsteadiness which may give rise to large error in finding the usable feasible direction in the time-marching procedure. Applying the finite-volume formulation with geometric conservation, on the other hand, possibly reduces the error due to the unsteadiness to a satisfactory level. The results of numerical experiments indicate that the gradient of viscous drag with respect to the deformation of body profile dep ends on the computational resolution as well as the deformation increment. It is concluded that the relative accuracy in evaluating the gradient of drag required for finding the feasible direction is one of the most important factors of the successful convergence to the optimum solution. The improved results computed within the relative accuracy of 0.1% suggest again that one of the optimum solutions at the Reynolds number of 100 is an asymmetric profile of the fore and aft parts quite different from those obtained in Stokes and Oseen flows.