An analysis of the fractional step method
The fractional step method for solving the incompressible Navier-Stokes equations in primitive variables is analyzed as a block LU decomposition. In this formulation the issues involving boundary conditions for the intermediate velocity variables and the pressure are clearly resolved. In addition, it is shown that poor temporal accuracy (first-order) is not due to boundary conditions, but due to the method itself. A generalized block LU decomposition that overcomes this difficulty is presented, allowing arbitrarily high temporal order of accuracy.
scientific article; zbMATH DE number 425471