An Adaptive Mesh Projection Method for Viscous Incompressible Flow

Many uid ow problems of practical interest|particularly at high Reynolds num-ber|are characterized by small regions of complex and rapidly-varying uid motion surrounded by larger regions of relatively smooth ow. EEcient solution of such problems requires an adaptive mesh reenement capability to concentrate computational eeort where it is most needed. We present in this paper a fractional-step version of Chorin's projection method for incompressible ow, with adaptive mesh reenement, which is second-order accurate in both space and time. Convection terms are handled by a high-resolution upwind method which provides excellent resolution of small-scale features of the ow, while a multilevel iterative scheme eeciently solves the parabolic and elliptic equations associated with viscosity and the projection. Numerical examples demonstrate the performance of the method on two-dimensional problems involving vortex spindown with viscosity and inviscid vortex merger.