RECENT PROGRESS IN THE CALCULATION 

 OF POTENTIAL FLOWS 



A. M. O. Smith 

 Douglas Aircraft Division, McDonnell Douglas Corp. 

 Long Beach, Calif. 



" ABSTRACT 



Since about 1954, work has been underway at Douglas Aircraft on the 

 problem of calculating flow about arbitrary bodies by means of a surface 

 source -sink treatment that leads to solution of a Fredholm integral equa- 

 tion of the second kind. The method has been quite successful, and a 

 general review of this work was published in 1966. The present paper 

 describes work done since about 1965, the latest year reported in the pub- 

 lished review, and begins with a review of the basic method. 'Then at- 

 tention is directed to the principal topics dealt with since 1965. They are: 



1. Nonlinear, unsteady airfoil and hydrofoil theory, including two- 

 body problems. 



Z. Compilation of a report containing extensive flow-field charts 

 for a variety of two-dimensional and axisymmetric bodies. 



3. Numerical integration of oscillating functions having nonlinear 

 arguments. This problem arises in wave resistance theory. 



4. The dynamics of a three-dimensional floating body subject to 

 simple harmonic motion in any of the six modes (heave, roll, etc.) but 

 otherwise at rest. 



5. Some remarks about Laplace problems that do not necessarily 

 deal with fluid flows. 



Several interesting results from work on these topics are available and 

 are presented as supporting material. 



INTRODUCTION 



The subject of this paper is a very general method of flow calculation about 

 arbitrary bodies. A broad review of the work up to 1965 can be found in Ref. 1, 

 which was issued late in 1966. This work has continued to be active, and it is 

 timely to report on the developments that have occurred since 1965. As many 

 readers are not familiar with the work, we shall begin by presenting a short 

 description of the basic method, as well as some examples. We will follow with 

 descriptions of the new work, which includes unsteady-airfoil theory, flow fields, 



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