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Volume 10, Issue 3
A New Compact Scheme in Exponential Form for Two-Dimensional Time-Dependent Burgers' and Navier-Stokes Equations

R.K. Mohanty, Li Yuan & Divya Sharma

DOI: 10.4208/eajam.141119.110220

East Asian J. Appl. Math., 10 (2020), pp. 437-454.

Published online: 2020-06

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  • Abstract

A new compact implicit exponential scheme for Burgers' and Navier-Stokes equation is developed. The method has fourth order accuracy in space and second order accuracy in time. It uses only two time levels for computation and requires nine grid points at each time level. The stability of the method is proven for linearised Burgers' equation. It is applied to a modified Taylor vortex problem. Numerical examples confirm the theoretical results and show the accuracy of the method.

  • Keywords

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{EAJAM-10-437, author = {Mohanty , R.K.Yuan , Li and Sharma , Divya}, title = {A New Compact Scheme in Exponential Form for Two-Dimensional Time-Dependent Burgers' and Navier-Stokes Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {3}, pages = {437--454}, abstract = {

A new compact implicit exponential scheme for Burgers' and Navier-Stokes equation is developed. The method has fourth order accuracy in space and second order accuracy in time. It uses only two time levels for computation and requires nine grid points at each time level. The stability of the method is proven for linearised Burgers' equation. It is applied to a modified Taylor vortex problem. Numerical examples confirm the theoretical results and show the accuracy of the method.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.141119.110220}, url = {http://global-sci.org/intro/article_detail/eajam/16976.html} }
TY - JOUR T1 - A New Compact Scheme in Exponential Form for Two-Dimensional Time-Dependent Burgers' and Navier-Stokes Equations AU - Mohanty , R.K. AU - Yuan , Li AU - Sharma , Divya JO - East Asian Journal on Applied Mathematics VL - 3 SP - 437 EP - 454 PY - 2020 DA - 2020/06 SN - 10 DO - http://doi.org/10.4208/eajam.141119.110220 UR - https://global-sci.org/intro/article_detail/eajam/16976.html KW - Compact scheme in exponential form, two-level implicit scheme, Burgers’ equation, Navier-Stokes equations of motion, Taylor-vortex problem. AB -

A new compact implicit exponential scheme for Burgers' and Navier-Stokes equation is developed. The method has fourth order accuracy in space and second order accuracy in time. It uses only two time levels for computation and requires nine grid points at each time level. The stability of the method is proven for linearised Burgers' equation. It is applied to a modified Taylor vortex problem. Numerical examples confirm the theoretical results and show the accuracy of the method.

Mohanty , R.K.Yuan , Li and Sharma , Divya. (2020). A New Compact Scheme in Exponential Form for Two-Dimensional Time-Dependent Burgers' and Navier-Stokes Equations. East Asian Journal on Applied Mathematics. 10 (3). 437-454. doi:10.4208/eajam.141119.110220
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