EXTENSION OF THE FRACTIONAL STEP METHOD TO GENERAL CURVILINEAR COORDINATE SYSTEMS

摘要

The extension of the fractional step method to three-dimensional, time-dependent incompressible flows in non-orthogonal curvilinear coordinate systems is presented. A formulation based on block-LU decomposition is combined with a mired implicit / explicit treatment of the discretized equations. Using local volume flares as dependent variables, the block-LU decomposition enables a unique definition of the sequential operations of the fractional step method for general coordinate systems. in this work a semi-direct scheme is developed for solution of the Poisson equation using series expansion along one coordinate direction that is discretized on a uniform, Cartesian grid Also investigated in this study is solution of a simplified Poisson equation obtained by neglecting cross derivatives in the full Poisson equation. If is shown that for fractional step methods satisfaction of the zero-divergence constraint is still possible using the simplified Poisson equation, but the associated error is larger than theta(Delta t). [References: 13]