Point-matching method for examining time-dependent Stokesian flow around a stationary axisymmetric body

We recast the time-dependent Stokesian flow about an axisymmetric body as a scattering problem, and solve the resulting boundary value problem using the point-matching method (PMM). The fluid is modeled to be viscous and incompressible. The velocity and pressure fields from the resulting linearized equations are cast as phasors in the frequency domain, and are broken up into incident and scattered components which are expressed in terms of spherical harmonic functions. For the numerical results presented, the incident velocity phasor is assumed to be a transverse plane wave progressing parallel to the symmetry axis of the body, and the PMM is applied to determine the scattered pressure and velocity phasors. Numerical results are shown for spheroids whose aspect ratios vary between 2/3 and 3/2. Two different boundary condition cases are tackled: pure stick (i.e., no-slip) and pure slip. The extinction efficiency, a measure of the change in energy due to the presence of the scattering body, is also computed.