Investigation of the one-Dimensional Numerical Filters Effects on the Fourier Pseudo-Spectral Embedded Boundary Solution of the Incompressible Navier-Stocks Equations

The purpose of this study is to review the necessity of applying a family of smoothers in processing of pseudo-spectral of immersed boundary of incompressible, two-dimentional navier-stokes equations, and also to destroy the effects of Gibbs phenomenon all around the domain, and reaching to a exponential accuracy. Thus, firstly approximation functions were reviewed by Fourier series. Then, Gibbs phenomenon, its appearance reason, and how computational processing are affected by this phenomenon, are analyzed. In the following, how to apply different computational boundaries to complicated geometries and also advantages and disadvantages of method of applying immersed boundary method to these geometries, are reviewed. It is indicated that in such processing, we should expect the creation of Gibbs phenomenon and subsequently undershoot in rate of convergence to answer. Then, different computational filters were reviewed for confronting Gibbs phenomenon, and two most important of them that is; high-order implicit filtering and one-dimentional smoothers have been explained. In final section, these methods are described in details by reviewing several periodic processing fields. Beside accuracy, efficiency of using smoothers and comparing them with other filtering methods have been reviewed in this article.