An Improvement of Third Order WENO Scheme for Convergence Rate at Critical Points with New Non-linear Weights

  • Anurag Kumar
  • Bhavneet KaurEmail author
Original Research


In this paper, we construct and implement a new improvement of third order weighted essentially non-oscillatory (WENO) scheme in the finite difference framework for hyperbolic conservation laws. In our approach, a modification in the global smoothness measurement is reported by applying all three points on global stencil \((i-1,i,i+1)\) which is used for convergence of non-linear weights towards the optimal weights at critical points and achieves the desired order of accuracy for third order WENO scheme. We use the third order accurate total variation diminishing (TVD) Runge-Kutta time stepping method. The major advantage of the proposed scheme is its better numerical accuracy in smooth regions. The computational performance of the proposed WENO scheme with this global smoothness measurement is verified in several benchmark one- and two-dimensional test cases for scalar and vector hyperbolic equations. Extensive computational results confirm that the new proposed scheme achieves better performance as compared with WENO-JS3, WENO-Z3 and WENO-F3 schemes.


Smoothness measurement WENO Critical points Sufficient condition Convergence analysis Accuracy 



The authors are thankful to Center for Fundamental Research in Space Dynamics and Celestial Mechanics (CFRSC), New Delhi, Delhi, India for providing research facilities. We also express gratitude to CSIR, Govt. of India for the grant reference no. 09/045(1438)/2016-EMR-I.


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Copyright information

© Foundation for Scientific Research and Technological Innovation 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of DelhiDelhiIndia
  2. 2.Department of Mathematics, Lady Shri Ram College for WomenUniversity of DelhiDelhiIndia

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