The solution of the transonic equation by optimal control and finite element methods
Abstract
It is noted that the transonic equation for compressible potential flow has previously been solved using the finite element method in conjunction with an optimal control algorithm. The method, however, is complex and the computation time is high. It is shown that by using a different performance index in the optimal control algorithm, the computation time can be significantly reduced. A numerical example is presented in which the computation time is four times shorter than that using the previous method. It is noted that whereas the algorithm proposed here (minimization in Euclidean space) is simpler and about ten times faster than Bristeau's algorithm for each iteration, it does need a good initial control.
 Publication:

Computer Methods in Applied Mechanics and Engineering
 Pub Date:
 July 1982
 DOI:
 10.1016/00457825(82)900470
 Bibcode:
 1982CMAME..31...69Y
 Keywords:

 Compressible Flow;
 Finite Element Method;
 Flow Equations;
 Optimal Control;
 Potential Flow;
 Transonic Flow;
 Algorithms;
 Computational Fluid Dynamics;
 Differential Equations;
 Euclidean Geometry;
 Nonlinear Equations;
 Run Time (Computers);
 Fluid Mechanics and Heat Transfer