POINT-MATCHING METHOD FOR EXAMINING TIME-DEPENDENT STOKESIAN FLOW AROUND A STATIONARY AXISYMMETRICAL BODY

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