二维非结构网格上的高精度有限体积WENO格式  

High order finite volume weighted essentially non-oscillatory schemes on two dimensional unstructured meshes

作　　者：郑华盛[1] 赵宁[2] 朱君[3] 

机构地区：[1]南昌航空大学数学与信息科学学院,江西南昌330063 [2]南京航空航天大学航空宇航学院,江苏南京210016 [3]南京航空航天大学理学院,江苏南京210016

出　　处：《空气动力学学报》2010年第4期446-451,共6页Acta Aerodynamica Sinica

基　　金：江西省自然科学基金(0611096);江西省教育厅2008年度科技项目(GJJ08224);南昌航空大学博士启动基金(EA200607031)资助

摘　　要：构造了非结构网格上二维双曲型守恒律的一类新的高精度有限体积WENO格式。其主要思想是:根据格式精度的要求,按照谱体积方法对三角形单元网格进行剖分,通过选取适当的子单元组成模板,利用WENO重构方法重构二阶和三阶多项式,利用有限体积公式和高阶Runge-Kutta TVD时间离散方法,构造了非结构网格上二维双曲型守恒律的一致二阶和三阶精度的有限体积WENO格式。然后,推广到二维Euler方程组。最后,给出几个数值算例,验证了格式的稳定性、高阶精度和高分辨捕捉激波等间断的能力。A class of new high-order accurate finite volume WENO schemes for two-dimensional hyperbolic conservation laws on unstructured meshes is presented.The main idea is as follows.According to the reqired accuracy,the partition of triangular cells is implemented by the spectral volume method.The stencil of subcell are property seleceted.And second-and third-order reconstruction polynomial on each subcell is implemented by WENO reconstruction with finite volume formulation and high order Runge-Kutta TVD time discretization method,we obtained uniformly second-and third-order finite volume WENO schemes for two-dimensional nonlinear hyperbolic conservation laws on unstructured grids.Furthermore,the extension to two-dimensional Euler equations is carried out.Finally,several typical numerical examples are given to show the stability and high resolution and robustness of these schemes.

关 键 词：非结构网格 WENO格式 高阶精度 有限体积 

分 类 号：O241.8[理学—计算数学] V211.3[理学—数学]