WLS-ENO: Weighted-least-squares based essentially non-oscillatory schemes for finite volume methods on unstructured meshes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:314

Article

Liu, Hongxu¹  Jiao, Xiangmin¹ 

[1] SUNY Stony Brook, Dept Appl Math & Stat, Stony Brook, NY 11794 USA

关键词: Essentially non-oscillatory scheme;    Weighted least squares;    Finite volume method;    Hyperbolic conservation law;    Unstructured mesh;   

DOI  :  10.1016/j.jcp.2016.03.039

来源: Elsevier

【 摘 要 】

ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes are widely used high-order schemes for solving partial differential equations (PDEs), especially hyperbolic conservation laws with piecewise smooth solutions. For structured meshes, these techniques can achieve high order accuracy for smooth functions while being non-oscillatory near discontinuities. For unstructured meshes, which are needed for complex geometries, similar schemes are required but they are much more challenging. We propose a new family of non-oscillatory schemes, called WLS-ENO, in the context of solving hyperbolic conservation laws using finite-volume methods over unstructured meshes. WLS-ENO is derived based on Taylor series expansion and solved using a weighted least squares formulation. Unlike other non-oscillatory schemes, the WLS-ENO does not require constructing sub-stencils, and hence it provides a more flexible framework and is less sensitive to mesh quality. We present rigorous analysis of the accuracy and stability of WLS-ENO, and present numerical results in 1-D, 2-D, and 3-D for a number of benchmark problems, and also report some comparisons against WENO. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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