TY - JOUR
T1 - A New Exponential Compact Scheme for the Two-Dimensional Unsteady Nonlinear Burgers' and Navier-Stokes Equations in Polar Cylindrical Coordinates
AU - Mohanty , R.K.
AU - Yuan , Li
AU - Sharma , Divya
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 488
EP - 507
PY - 2021
DA - 2021/01
SN - 14
DO - http://doi.org/10.4208/nmtma.OA-2020-0053
UR - https://global-sci.org/intro/article_detail/nmtma/18608.html
KW - Half-step discretization, compact scheme in exponential form, two-level implicit
scheme, Burgers' equation, Navier-Stokes equations of motion, Taylor-vortex problem.
AB - <p style="text-align: justify;">In this article, a new compact difference scheme is proposed in exponential form to solve two-dimensional unsteady nonlinear Burgers&#39; and Navier-Stokes
equations of motion in polar cylindrical coordinates by using half-step discretization. At each time level by using only nine grid points in space, the proposed scheme
gives accuracy of order four in space and two in time. The method is directly applicable to the equations having singularities at boundary points. Stability analysis
is explained in detail and many benchmark problems like Burgers&#39;, Navier-Stokes
and Taylor-vortex problems in polar cylindrical coordinates are solved to verify the
accuracy and efficiency of the scheme.</p>