A finite difference solution for steady natural convective flow within the human eye, modelled as a sphere with a specified temperature distribution over its surface, has been obtained. The stream functionvorticity formulation of the equations of motion for the unsteady axisymmetric flow is used interest lying in the final steady solution. Forward differences are used for the time derivatives and secondorder central differences for the space derivatives. The alternating direction implicit method is used for solution of the discretization equations. Local onedimensional grid adaptation is used to resolve the steep gradients in some regions of the flow at large Rayleigh numbers. The breakup into multicellular flow is found at high Rayleigh numbers. Results identify regions of stagnant fluid in locations similar to those of blind spots in the eye.
International Journal of Numerical Methods for Heat & Fluid Flow – Emerald Publishing
Published: Mar 1, 1992