High order sub-cell finite volume schemes for solving hyperbolic conservation laws I: basic formulation and one-dimensional analysis

作     者：JianHua Pan YuXin Ren 

作者机构：School of Aerospace Engineering Tsinghua University 

出 版 物：《Science China(Physics,Mechanics & Astronomy)》 (中国科学：物理学、力学、天文学（英文版）)

年 卷 期：2017年第60卷第8期

页      面：60-75页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.U1430235 and 11672160) 

主　　题：compact high order method sub-cell finite volume method unstructured grid 

摘      要：In this paper, a family of sub-cell finite volume schemes for solving the hyperbolic conservation laws is proposed and analyzed in one-dimensional cases. The basic idea of this method is to subdivide a control volume(main cell) into several sub-cells and the finite volume discretization is applied to each of the sub-cells. The averaged values on the sub-cells of current and face neighboring main cells are used to reconstruct the polynomial distributions of the dependent variables. This method can achieve arbitrarily high order of accuracy using a compact stencil. It is similar to the spectral volume method incorporating with PNPM technique but with fundamental differences. An elaborate utilization of these differences overcomes some shortcomings of the spectral volume method and results in a family of accurate and robust schemes for solving the hyperbolic conservation laws. In this paper, the basic formulation of the proposed method is presented. The Fourier analysis is performed to study the properties of the one-dimensional schemes. A WENO limiter based on the secondary reconstruction is constructed.