A Numerical Method of Solving Inverse Problem in 2-Dimensional Viscous Flow Field

Abstract

This paper presents a numerical method solving inverse problem in 2-dimensional viscous flow past a body. The sensitivity coefficients for unit change of the design variables in the shape function are formulated by using the variation of Navier-Stokes equation and a prescribed body-shape function. The inverse problem for obtaining body shape with specified flow variables, such as pressure and/or wake velocity, in the fluid domain, is converted to an iterative optimization problem for minimizing errors of the specified variables. The optimization procedure also includes the sensitivity coefficients and appropriate constraints to find a feasible direction at each iterative step.The authors applied the method to problems for specifying pressure distribution on the body boundary, wake distribution, and both of them. The results of the computation show fairly good agreements with the target body profiles in case when they are prescribed. It is also found that the order of magnitude of the sensitivity coefficients should be of same order and that the specified pressure points should cover the whole body boundary for getting reasonable results.