True transient vorticity-velocity method using preconditioned Bi-CGSTAB

A fully implicit method for the solution of time-dependent Navier-Stokes equations written in terms of vorticity and velocity is presented. The field equations are discretized using second-order finite-difference technique and cast into a large sparse linear system. The numerical solution of the algebraic problem generated is obtained using a preconditioned Bi-CGSTAB method. The numerical method, developed mainly for the solution of true transient problems, also shows good stability behavior at high Rayleigh numbers. Sample results are presented for the window cavity at 10(4) less than or equal to Ra less than or equal to 10(8) and art oscillatory flow in liquid metal.