Direct Solution Methodologies for the Unsteady Dynamics of an Incompressible Fluid

Abstract

A unified mathematical formulation of the unsteady two- and three- dimensional incompressible Navier-Stokes (NS) equations is presented. It contains the theoretical development from which efficient direct inversion methodologies are then developed. The numerical analysis leads to a single-pass direct inversion of the nonlinear partial differential operator (PDO) governing the unsteady motion of an incompressible viscous fluid within arbitrarily shaped boundaries. The method is uniformly second-order accurate both spatially and temporally. It is possible to extend this formulation to include the effect of compressibility.