A Multilevel Adaptive Projection Method for Unsteady Incompressible Flow

There are two main requirements for practical simulation of unsteady ow at high Reynolds number: the algorithm must accurately propagate discontinuous ow elds without excessive artiicial viscosity, and it must have some adaptive capability to concentrate computational eeort where it is most needed. We satisfy the rst of these requirements with a second-order Godunov method similar to those used for high-speed ows with shocks, and the second with a grid-based reenement scheme which avoids some of the drawbacks associated with unstructured meshes. These two features of our algorithm place certain constraints on the projection method used to enforce incompressibility. Velocities are cell-based, leading to a Lapla-cian stencil for the projection which decouples adjacent grid points. We discuss features of the multigrid and multilevel iteration schemes required for solution of the resulting decoupled problem. Variable-density ows require use of a modiied projection operator|we have found a multigrid method for this modiied projection that successfully handles density jumps of thousands to one. Numerical results are shown for the 2D adaptive and 3D variable-density algorithms.