Finite difference modified WENO schemes for hyperbolic conservation laws with non-convex flux,International Journal for Numerical Methods in Fluids

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Finite difference modified WENO schemes for hyperbolic conservation laws with non-convex flux
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-06-01 , DOI: 10.1002/fld.5020
Asha K. Dond ₁ , Rakesh Kumar ₂

Affiliation

The Weighted Essentially Non-Oscillatory (WENO) reconstruction provides higher-order accurate solutions to hyperbolic conservation laws for convex flux. But it fails to capture composite structure in the case of non-convex flux and converges to the wrong solution (Qiu & Shu SIAM J Sci Comput. 2008;31:584-607). In this article, we have developed a Modified WENO (MWENO) scheme in the finite difference framework, which can resolve the composite structure and ensures the entropic convergence. The MWENO reconstruction procedure involves the identification of the troubled-cells, followed by the use of first-order monotone modification in the troubled-cells and employ the fifth-order WENO reconstruction in the non-troubled cells. A new troubled-cell indicator is developed using the information of the smoothness indicator of the WENO reconstruction. Numerical experiments are performed for 1D and 2D test cases, which ensure the entropic convergence of the proposed schemes.

中文翻译：

非凸通量双曲守恒定律的有限差分修正 WENO 方案

加权基本非振荡 (WENO) 重建为凸通量的双曲守恒定律提供了更高阶的准确解。但它无法在非凸通量的情况下捕获复合结构并收敛到错误的解决方案 (Qiu & Shu SIAM J Sci Comput. 2008;31:584-607)。在本文中，我们在有限差分框架中开发了一种改进的 WENO (MWENO) 方案，该方案可以解决复合结构并确保熵收敛。MWENO 重建过程涉及识别问题细胞，然后在问题细胞中使用一阶单调修改，并在非问题细胞中使用五阶 WENO 重建。利用WENO重建的平滑度指标信息，开发了一种新的故障细胞指标。

更新日期：2021-06-01

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