Volume 14, Issue 2
A New Exponential Compact Scheme for the Two-Dimensional Unsteady Nonlinear Burgers' and Navier-Stokes Equations in Polar Cylindrical Coordinates

R.K. Mohanty, Li YuanDivya Sharma

Numer. Math. Theor. Meth. Appl., 14 (2021), pp. 488-507.

Published online: 2021-01

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  • 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.

  • Keywords

Half-step discretization, compact scheme in exponential form, two-level implicit scheme, Burgers' equation, Navier-Stokes equations of motion, Taylor-vortex problem.

  • AMS Subject Headings

65M06, 65M10, 65Z05, 65Y99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-14-488, author = {Mohanty , R.K. and Yuan , Li and Sharma , Divya}, title = {A New Exponential Compact Scheme for the Two-Dimensional Unsteady Nonlinear Burgers' and Navier-Stokes Equations in Polar Cylindrical Coordinates}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2021}, volume = {14}, number = {2}, pages = {488--507}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2020-0053}, url = {http://global-sci.org/intro/article_detail/nmtma/18608.html} }
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 -

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.

R.K. Mohanty, Li Yuan & Divya Sharma. (2021). A New Exponential Compact Scheme for the Two-Dimensional Unsteady Nonlinear Burgers' and Navier-Stokes Equations in Polar Cylindrical Coordinates. Numerical Mathematics: Theory, Methods and Applications. 14 (2). 488-507. doi:10.4208/nmtma.OA-2020-0053
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