Abstract
We develop a third-order accurate finite volume weighted essentially non-oscillatory (WENO) scheme for numerical solution of hyperbolic conservation laws on unstructured quadrilateral meshes. The high-order non-oscillatory discretization methodology combines third- and second-order accurate reconstructions through linear weights that are positive and adds up to unity. The reconstruction procedure is based on a constrained least-squares approach that leads to a significant reduction in discretization errors. Results from a range of test cases are provided to assess the convergence attributes and test the shock capturing capability of the proposed scheme.
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Acknowledgements
The implementation of the current WENO scheme on unstructured grids was performed in the open-source framework deal.II [13].
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Sunder, D., Vaghani, D., Shukla, R. (2021). Third-Order WENO Schemes on Unstructured Meshes. In: Venkatakrishnan, L., Majumdar, S., Subramanian, G., Bhat, G.S., Dasgupta, R., Arakeri, J. (eds) Proceedings of 16th Asian Congress of Fluid Mechanics. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-5183-3_23
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DOI: https://doi.org/10.1007/978-981-15-5183-3_23
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