TY - JOUR
T1 - Spectral Direction Splitting Schemes for the Incompressible Navier-Stokes Equations
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 215
EP - 234
PY - 2018
DA - 2018/02
SN - 1
DO - http://doi.org/10.4208/eajam.190411.240511a
UR - https://global-sci.org/intro/article_detail/eajam/10905.html
KW - Navier-Stokes equations, projection method, direction splitting, spectral methods.
AB - <p style="text-align: justify;">We propose and analyze spectral direction splitting schemes for the incompressible
Navier-Stokes equations. The schemes combine a Legendre-spectral method
for the spatial discretization and a pressure-stabilization/direction splitting scheme for
the temporal discretization, leading to a sequence of one-dimensional elliptic equations
at each time step while preserving the same order of accuracy as the usual pressure-stabilization
schemes. We prove that these schemes are unconditionally stable, and
present numerical results which demonstrate the stability, accuracy, and efficiency of
the proposed methods.</p>