A transient higher order compact scheme for incompressible viscous flows on geometries beyond rectangular

In this paper, we propose an implicit high-order compact (HOC) finite-difference scheme for solving the two-dimensional (2D) unsteady Navier–Stokes (N–S) equations on irregular geometries on orthogonal grids. Our scheme is second order accurate in time and fourth order accurate in space. It is used to solve three pertinent fluid flow problems, namely, the flow decayed by viscosity, the lid-driven square cavity and the flow in a constricted channel. It is seen to efficiently capture both transient and steady-state solutions of the N–S equations with Dirichlet as well as Neumann boundary conditions. Apart from including the good features of HOC schemes, our formulation has the added advantage of capturing transient viscous flows involving free and wall bounded shear layers which invariably contain spatial scale variations. Detailed comparison data produced by the scheme for all the three test cases are provided and compared with analytical as well as established numerical results. Excellent comparison is obtained in all the cases.