@Article{EAJAM-7-714,
author = {Dongdong He and Kejia Pan},
title = {A Fifth-Order Combined Compact Difference Scheme for Stokes Flow on Polar Geometries},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {7},
number = {4},
pages = {714--727},
abstract = {<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>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.200816.300517a},
url = {http://global-sci.org/intro/article_detail/eajam/10715.html}
}