In this study we use a fast Fourier spectral technique to simulate the Navier-Stokes equations with no-slip boundary conditions. This is enforced by an immersed boundary technique called volume-penalization. The approach has been justified by analytical proofs of the convergence with respect to the penalization parameter. However, the solution of the penalized Navier-Stokes equations is not smooth on the surface of the penalized volume. Therefore, it is not a priori known whether it is possible to actually perform accurate fast Fourier spectral computations. Convergence checks are reported using a recently revived, and unexpectedly difficult dipole-wall collision as a test case. It is found that Gibbs oscillations have a negligible effect on the flow evolution. This allows higher-order recovery of the accuracy on a Fourier basis by means of a post-processing procedure.
|Title of host publication||Computational Science - ICCS 2007|
|Place of Publication||Berlin|
|Number of pages||10|
|Publication status||Published - 13 Jul 2007|
|Name||Lecture Notes in Computer Science|
Keetels, G. H., Clercx, H. J. H., & van Heijst, G. J. F. (2007). Fourier Spectral Solver for the Incompressible Navier-Stokes Equations with Volume-Penalization. In Computational Science - ICCS 2007 (pp. 898-905). [10.1007/978-3-540-72584-8_118] (Lecture Notes in Computer Science; Vol. 4487, No. 4487). Berlin: Springer. https://doi.org/10.1007/978-3-540-72584-8_118