A high-order finite volume method on unstructured grids using RBF reconstruction. (August 2016)

• Record Type: Journal Article
• Authors: Liu, Yilang; Zhang, Weiwei; Jiang, Yuewen; Ye, Zhengyin
• Is Part Of: Computers & mathematics with applications. Volume 72:issue 4(2016)
• Page Start: 1096
• Page End: 1117
• Publication Date: 2016-08
• Subjects: Finite volume method -- Unstructured grids -- High order scheme -- RBF reconstruction method -- Navier–Stokes equations; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.06.024
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: 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.