Date of Award

Spring 1988

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Mechanical Engineering

Committee Director

Osama A. Kandil

Committee Member

E. C. Yates

Committee Member

R. L. Ash

Committee Member

O. Baysal

Committee Member

J. H. Heinbockel


An integral equation method for solving the full potential equation has been developed for three dimensional transonic vortex-wing flows. This method is capable of capturing shocks using the Murman-Cole type of finite difference scheme and is capable of predicting accurate and force-free wake shape as well.

Reading the full potential equation as Poisson's equation, the solution for the velocity field has been expressed in terms of an integral equation using Green's theorem. The solution consists of a surface integral of vorticity distribution on the wing and its free-vortex sheets and a volume integral of source distribution within a computational region around the flow domain under consideration. The solution is obtained through two iteration loops: the outer loop iterates the vorticity distribution and wake shape, while the inner loop iterates the field compressibility.

A computer program has been constructed for implementation of this methodology and has been used to solve a flow around a rectangular flat wing with a trailing wake. The program can be modified without difficulties to solve flow problems with complex configurations. The wing and its free-vortex sheets are modeled using a bilinear vortex panel distribution, while the field compressibility of the flow domain under consideration is modeled using a constant, distributed, source strength over each of the discretized rectangular-parallelopiped volume cells.

The technique of pre-calculated and stored induced velocity for field compressibility calculations has greatly reduced the computational time. The successive grid refinement has also effectively and reliably reduced the computational domain and greatly improved the accuracy as well.

The numerical results show that this method is computationally stable and efficient and also show its great potential in solving unsteady transonic flow problems.

The study conducted in this dissertation also sheds some light in the vectorization of an integral equation method which is crucial in achieving better computational efficiency when running on a modern vector computer.