A high-order finite volume method on unstructured grids using RBF reconstruction
A high-order finite volume method on unstructured grids using RBF reconstruction
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DOI：
10.1016/j.camwa.2016.06.024
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发表时间：
2016-08
期刊：
影响因子：
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通讯作者：
Yilang Liu;Weiwei Zhang;Yuewen Jiang;Zhengyin Ye
中科院分区：
文献类型：
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作者：
Yilang Liu;Weiwei Zhang;Yuewen Jiang;Zhengyin Ye
本文提出了一种基于径向基函数重构的高阶有限体积法，在非结构网格上求解Euler和Navier-Stokes方程。与传统的多项式K-精确方法相比，RBF方法对不同重建尺度的适应性更强，插值点的选择更灵活。详细阐述了在非结构三角形网格上采用多二次基函数对二阶和三阶格式进行流场重构的具体过程。随后，通过数值算例验证了径向基函数方法的精度阶.并将该方法应用于几种典型流场的求解。与传统的K-精确高阶格式相比，径向基函数方法具有更高的精度和更低的数值耗散，可以得到更精细、更精确的结果。
This paper proposes a high-order finite volume method based on radial basis function (RBF) reconstruction for the solution of Euler and Navier–Stokes equations on unstructured grids. Unlike traditional polynomial K-exact method, RBF method has stronger adaptability for different reconstruction stencils and more flexibility in choosing interpolating points. We expatiate on the detailed process of flow-field reconstruction by using multiquadric (MQ) basis function for the second-order and third-order schemes on unstructured triangular grids. Subsequently, we validate the accuracy order of RBF method through the numerical test case. Furthermore, the method is used to solve several typical flow fields. Compared with traditional K-exact high-order scheme, RBF method is more accurate and has lower numerical dissipation, which can obtain more elaborate and precise results.