With powerful computer and newer methods, it is routine to solve the governing Navier Stokes equation resolving all scales of turbulent flows of DNS for moderate Reynolds number. In this context, the compact and other higher order schemes are finding more and more applications. Similarly, in wave propagation problems, one solves hyperbolic partial differential equations and such solutions are required to be accurate in the far field and for long time periods. These requirements demand that the adopted numerical method be highly accurate and dispersion error free. The compact schemes, based on Pade approximation, offer high accuracy, higher order approximations to differential and integral operators using compact implicit stencils.
For DNS of incompresible flows, it is important to compute flows with large directional convection of vortical structures. Thus, DNS requires capturing high amplitude signals without suffering numerical instabilities. This instability may be caused due to linear instability, error accumulation due to aliasing or non-linear instabilities. While using compact schemes, it is thus quite common to add numerical dissipation via upwinding, or filtering the solution after some time interval.
In this area our aim is two-folds. Firstly, we would like to find out the eigen-spectrum of jets. Secondly, we would use these information to calibrate the DNS of the jet. Our eventual aim is to calculate the emitted noise from the jet. We have obtained spectrum of plane Bickley jet with respect to symmetric and anti-symmetric disturbance fields. We have also calculated the spectrum for the round Bickley jet for symmetric disturbance field. These have been obtained using Compound Matrix Method (CMM). The information of the spectrum is necessary for DNS of jets at relevant Reynolds numbers.