Numer. Math. Theor. Meth. Appl., 14 (2021), pp. 488-507.
Published online: 2021-01
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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.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2020-0053}, url = {http://global-sci.org/intro/article_detail/nmtma/18608.html} }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.