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An analysis of the fractional step method. (English) Zbl 0778.76064
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.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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