Exponential Compact Higher Order Scheme for Steady Incompressible Navier-Stokes Equations

An Exponential Compact Higher Order (ECHO) scheme is developed for the stream function voracity form of steady viscous incompressible Navier-Stokes equations. The coupled equations are solved using an iterative procedure. The developed scheme has been validated initially using two model problems with known analytic solutions and demonstrated the fourth order rate of convergence and about fifth order for highly convection dominated problems. Thus the developed scheme requires smaller number of grid points for the computation. Finally the tested code is used to simulate the lid-driven square cavity flow up to Reynolds number 10,000.