NUMERICAL-SIMULATION OF AXISYMMETRICAL UNSTEADY INCOMPRESSIBLE-FLOW BY A VORTICITY-VELOCITY METHOD

A new numerical method for solving the axisymmetric unsteady incompres sible Navier-Stokes equations using vorticity-velocity variables and a staggered grid is presented. The solution is advanced in time with an explicit two-stage Runge-Kutta method. At each stage a vector Poisson equation for velocity is solved. Some important aspects of staggering of the variable location, divergence-free correction to the velocity held by means of a suitably chosen scalar potential and numerical trea tment of the vorticity boundary condition are examined. The axisymmetr ic spherical Couette flow between two concentric differentially rotati ng spheres is computed as an initial value problem. Comparison of the computational results using a staggered grid with those using a non-st aggered grid shows that the staggered grid is superior to the non-stag gered grid. The computed scenario of the transition from zero-vortex t o two-vortex flow at moderate Reynolds number agrees with that simulat ed using a pseudospectral method, thus validating the temporal accurac y of our method.