The Effect of Aliased and De-aliased Formulation for DNS Analysis in Plane Poiseuille Flow

Abstract

In this research, the performance of various aliased and de-aliased schemes was studied in pseudo-spectral (PS) simulation. The PS method was used to perform aliased and de-aliased direct numerical simulation of a turbulent plane Poiseuille channel flow. The effects of aliasing errors in Navier–Stokes equations were examined for both common skew-symmetric and rotational forms. Due to boundary conditions, Fourier series in periodic directions and Chebyshev expansion in normal direction were considered. A third-order backward difference scheme was used for temporal approximation method, and different types of “2/3 rule” de-aliasing procedures in various directions were examined. The results for aliased and de-aliased formulation showed that generally, the skew-symmetric form gives the most accurate results. But de-aliased rotational form was more robust and presented fewer errors. The amount of aliasing errors for the ordinary rotation form is about two times larger than for De-aliased XYZ rotational scheme and common skew-symmetric form. From a practical point of view, the choice between the skew-symmetric form and de-aliased rotational method with the same accuracy reduces to the last one if final decision rests on the amount of computational time.