Motion of a solid particle in a bounded viscous flow using the Sparse Cardinal Sine Decomposition

This work investigates the Sparse Cardinal Sine Decomposition (SCSD) method ability to efficiently deal with a Stokes flow about a solid particle immersed in a liquid. In contrat to Alouges and Aussal (Numer Algorithms 70:1–22, 2015), the liquid domain is bounded by a solid and motionless wall. The advocated procedure inverts on the particle and truncated wall boundaries the boundary-integral equation governing the stress there. This is numerically achieved by implementing a Galerkin method. The resulting linear system, with fully-populated and non-symmetric influence matrix, is both compressed and solved by the new SCSD method which allows to accurately deal with a large number of unknowns. Both analytical and numerical comparisons are reported for a spherical particle and several bounded liquid domains. Moreover, the rigid-body motion of spheroidal particles settling in a cylindrical tube is examined.