A third-order weighted essentially non-oscillatory-flux limiter scheme for two-dimensional incompressible Navier-Stokes equations

Document Type : Research Paper


School of Engineering Science, College of Engineering, University of Tehran, Iran.


In this paper, the 2D incompressible Navier-Stokes (INS) equations in terms of vorticity and stream function are considered. These equations describe the physics of many phenomena of scientific and engineering. By combining monotone upwind methods and weighted essentially non-oscillatory (WENO) procedures, a new numerical algorithm is proposed to approximate the solution of INS equations. To design this algorithm, after obtaining an optimal polynomial, it is rewritten as a convex combination of second-order modified ENO polynomials. Following the methodology of the traditional WENO procedure, the new non-linear weights are calculated. The performance of the new scheme on a number of numerical examples is illustrated.


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Volume 11, Issue 1
January 2023
Pages 1-11
  • Receive Date: 29 September 2021
  • Revise Date: 05 March 2022
  • Accept Date: 30 March 2022
  • First Publish Date: 01 April 2022