A new alternating bi-diagonal compact scheme for non-uniform grids

A new compact scheme has been developed for any non-uniform grid. The compact scheme has been developed for spatial discretization and is analyzed here in conjunction with four-stage, fourth order Runge-Kutta (RK4) scheme for time integration while solving the one-dimensional convection equation. The space-time discretization combination is calibrated by subjecting the system to global spectral analysis (GSA) which was developed by the authors' group. Here, the compact scheme has been obtained by using a combination of two bi-diagonal schemes. The novel aspect of this scheme is its application in the physical plane directly without the necessity of mapping or transformations. Some typical cases for problems in acoustics, as well as fluid mechanics, have been studied here and potential use in large eddy simulations (LES) has been demonstrated by solving Navier-Stokes equation for lid driven cavity.