L. Yuan et al., NUMERICAL-SIMULATION OF AXISYMMETRICAL UNSTEADY INCOMPRESSIBLE-FLOW BY A VORTICITY-VELOCITY METHOD, International journal for numerical methods in fluids, 21(5), 1995, pp. 401-411
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.