Combined WENO Schemes for Increasing the Accuracy of the Numerical Solution of Conservation Laws

	Combined WENO Schemes for Increasing the Accuracy of the Numerical Solution of Conservation Laws
مهندسی مکانیک مدرس
Article 6, Volume 25, Issue 5, 1404, Pages 295-306 PDF (1.27 M)
DOI: 10.48311/mme.2025.24033
Author
Hossein Mahmoodi Darian^*
University of Tehran
Abstract
In this article, we introduce a new method which allows utilizing all the available sub-stencils of a WENO scheme to increase the accuracy of the numerical solution of conservation laws while preserving the non-oscillatory property of the scheme. In this method, near a discontinuity, if there is a smooth sub-stencil with higher-order of accuracy, it is used in the reconstruction procedure. Furthermore, in smooth regions, all the sub-stencils of the same order of accuracy form the stencil with the highest order of accuracy as the conventional WENO scheme. The presented method is assessed using several test cases of the linear wave equation and one- and two-dimensional Euler’s equations of gas dynamics. In addition to the original weights of WENO schemes, the WENO-Z approach is used. The results show that the new method increases the accuracy of the results while properly maintaining the ENO property
Keywords
WENO Schemes; Shock-capturing schemes; Nonlinear Weights
References

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