Gridless spectral algorithm for Stokes flow with moving boundaries

A gridless, spectrally-accurate algorithm for the Stokes flow with moving boundaries is presented. The algorithm uses fixed computational domain with boundaries of the flow domain moving inside the computational domain. The spatial discretization is based on the Fourier expansions in the streamwise direction and the Chebyshev expansions in the transverse direction. Temporal discretization uses one- and two-steps implicit formulations. The boundary conditions on the moving boundaries are imposed using the immersed boundary conditions concept. Numerical tests confirm the spectral accuracy in space and theoretically-predicted accuracy in time. Different variants of the solution procedure are presented and their relative advantages are discussed.