Oscillatory flow in a symmetric sinusoidal wavy-walled channel at intermediate strouhal numbers

Efficient Pseudospectral Flow Simulations in Moderately Complex Geometries

“…Finally, the flowrate depends on time through the relationship Q(t) = Q max sin(2π f t). With these definitions, our values for St and Re coincide with those in [34].…”

“…In this way we can validate the method in problems where there exists a transient driving force, leading to a stationary rather than a steady state. Our benchmark problem was taken from a paper by Nishimura et al [34]. The geometry of the undulating channel is the same as in the steady flow problem examined previously.…”

“…The implication of this change is that within the preconditioner, where the influence matrix technique is applied, the equation for the pressure is formed directly from the preconditioner velocity equations. The equations for the velocity are the same as (34), whereas the pressure equation becomes…”

“…First, the residuals of Eqs. (34) and (35) are constructed spectrally and are solved iteratively within the preconditioner in the form…”

“…Nishimura et al investigated the flow characteristics in a channel with a symmetric, wavy wall for steady and oscillatory flows through numerical calculations and experiments. The equations expressed in terms of the vorticity and the stream function were solved by the Galerkin finite element method [30][31][32][33][34].…”