### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 2aSA10. Point-matching technique for scattering of Stokesian flows around
axisymmetric bodies.

**Scott A. Wymer
**

**
Renata S. Engel
**

**
Akhlesh Lakhtakia
**

**
**
*Dept. Eng. Sci. and Mech., The Pennsylvania State Univ., 227 Hammond
Bldg., University Park, PA 16802-1401
*

*
*
In solving for velocity and pressure fields in a slow, viscous,
incompressible fluid, frequency-domain scattering techniques can be brought
into action by taking the Fourier transform of the equations describing
Stokesian flows. This is exemplified by considering the scattering of a
transverse plane wave by an impenetrable axisymmetric body immersed in a fluid
modeled by the unsteady Stoke's equation, the wave number in the ambient
Stoke's fluid being necessarily complex. The pressure and velocity phasors
satisfy the Laplace and the Helmholtz equations, respectively, and are written
as sums of incident and scattered components. These components are then
expanded in terms of spherical harmonic functions. The point-matching technique
is used to satisfy boundary conditions on a discrete set of points on the
surface of the scattering body. Convergence of the resulting series solutions
is studied for spheroids of different aspect ratios and for varying wave
numbers.