Symmetrized compact scheme for receptivity study of 2D transitional channel flow

In many physical problems, one must maintain symmetry of numerical schemes – the symmetry arising due to geometry and/or physical conditions defining the flow. The direct simulation of transitional plane Poiseuille flow presents one such case, that motivated the present study. It has been shown here, using the method of analyzing non-periodic problems in Sengupta et al. (2003), that compact and other high accuracy schemes display strong directionality of the algorithm and such methods cannot be used for direct simulation of the physical flow. This prevalent, but unacceptable situation for DNS is rectified in the present work and a new scheme is introduced that prevents this asymmetry from contaminating results. The simulated transitional flow past 2D channel here, using the new scheme, are in agreement with experimental results and other recent views of sub-critical instabilities.