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 -

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.