Inverse shape design via a new physical-based iterative solution strategy

Abstract

Inverse shape design in the context of fluid flow problems is commonly referred to the determination of the boundary shape corresponding to a given target surface pressure. Designers naturally turn to this class of problems whenever there are concerns regarding pressure-related phenomena such as cavitation, separation, shock waves, surface loading, etc. Numerical solution is often unavoidable and, therefore, three computational tools, i.e. a grid generator, a flow field solver and a shape updater, are required in an iterative solution procedure. In all existing iterative inverse design methods, the shape updater comes from separate mathematical or physical considerations that are not derived solely from the equations governing the flow field. In this paper, the currently used strategies to solve inverse shape design problems are categorized and reviewed, and then a truly physical-based iterative inverse shape design method is introduced in which the governing equations are not only used in the flow solver, but are also employed to update the shape. To explore the features of the proposed method, it is used to solve a number of shape design problems. The previously developed direct shape design method and a typical iterative solution approach are also explained and used for the solution of the same problems for the purpose of comparison. Computational results reveal that the proposed algorithm has a two to three times faster convergence rate as compared to the iterative algorithm. The convergence rate of the proposed algorithm usually stalls after three or two orders of magnitude reduction of the residual. For the test cases in this study, the direct design method is the fastest and most accurate method as compared to other algorithms. Both in-house developed computer codes and commercial software are used as a field solver to show the general applicability of the proposed method in its current state of development.