Abstract

An implicit fractional-step method for the numerical solution of the time-dependent incompressible Naiver-Stokes equations in primitive variables is developed and studied in this paper. The method, which is first order accurate in the time-step, is shown to convergence to an exact solution of the equations. By adequately splitting the viscous term, it allows to enforce full Dirichlet boundary conditions on the velocity in all substeps of the scheme, while needing no boundary condition at all for the pressure. It is also shown to be related to an iterative predictor-multicorrector algorithm for evolution equations, when this is applied to the incompressible Naiver-Stokes system. A new derivation of the algorithm in a general setting is provided. Two different finite element interpolations are considered for the implementation of the algorithm; numerical results obtained with them for standard benchmark cases are presented.

Abstract

An implicit fractional-step method for the numerical solution of the time-dependent incompressible Naiver-Stokes equations in primitive variables is developed and studied in this paper. The method, which is first order accurate in the time-step, is shown to convergence to an exact solution of the equations. By adequately splitting the viscous term, it allows to enforce full Dirichlet boundary conditions on the velocity in all substeps of the scheme, while needing no boundary condition at all for the pressure. It is also shown to be related to an iterative predictor-multicorrector algorithm for evolution equations, when this is applied to the incompressible Naiver-Stokes system. A new derivation of the algorithm in a general setting is provided. Two different finite element interpolations are considered for the implementation of the algorithm; numerical results obtained with them for standard benchmark cases are presented.