| Abstract: | We propose and analyze spectral direction splitting schemes for the incompressibleNavier-Stokes equations. The schemes combine a Legendre-spectral methodfor the spatial discretization and a pressure-stabilization/direction splitting scheme forthe temporal discretization, leading to a sequence of one-dimensional elliptic equationsat each time step while preserving the same order of accuracy as the usual pressure-stabilizationschemes. We prove that these schemes are unconditionally stable, andpresent numerical results which demonstrate the stability, accuracy, and efficiency ofthe proposed methods. |
