| Abstract: | In this article, a new compact difference scheme is proposed in exponential form to solve two-dimensional unsteady nonlinear Burgers' 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', Navier-Stokes
and Taylor-vortex problems in polar cylindrical coordinates are solved to verify the
accuracy and efficiency of the scheme. |
