TY - JOUR
T1 - A Fifth-Order Combined Compact Difference Scheme for Stokes Flow on Polar Geometries
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 714
EP - 727
PY - 2018
DA - 2018/02
SN - 7
DO - http://doi.org/10.4208/eajam.200816.300517a
UR - https://global-sci.org/intro/article_detail/eajam/10715.html
KW - Stokes flow, combined compact difference (CCD) scheme, truncated Fourier series, shifted grid, coordinate singularity.
AB - <p style="text-align: justify;">Incompressible flows with zero Reynolds number can be modeled by the
Stokes equations. When numerically solving the Stokes flow in stream-vorticity formulation
with high-order accuracy, it will be important to solve both the stream function
and velocity components with the high-order accuracy simultaneously. In this work, we
will develop a fifth-order spectral/combined compact difference (CCD) method for the
Stokes equation in stream-vorticity formulation on the polar geometries, including a unit
disk and an annular domain. We first use the truncated Fourier series to derive a coupled
system of singular ordinary differential equations for the Fourier coefficients, then use
a shifted grid to handle the coordinate singularity without pole condition. More importantly,
a three-point CCD scheme is developed to solve the obtained system of differential
equations. Numerical results are presented to show that the proposed spectral/CCD
method can obtain all physical quantities in the Stokes flow, including the stream function
and vorticity function as well as all velocity components, with fifth-order accuracy,
which is much more accurate and efficient than low-order methods in the literature.</p>