求解多维欧拉方程的二阶非结构网格混合旋转Riemann求解器  

A Second-order Hybrid Rotated Riemann Solver for Multi-dimensional Euler Equations on Unstructured Meshes

作　　者：雷国东[1] 任玉新[1] 

机构地区：[1]清华大学工程力学系,北京100084

出　　处：《计算物理》2009年第6期799-805,共7页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(10572075)项目资助

摘　　要：将基于旋转近似Riemann求解器的二阶精度迎风型有限体积方法推广到非结构网格,采用基于网格中心的有限体积法,梯度的计算采用基于节点的方法引入更多的控制体模板,限制器的构造采用与非结构化网格相适应的形式.在求解Riemann问题时,沿具有一定物理意义的两个迎风方向,即控制体界面两侧速度差矢量方向及与之正交的方向.能够完全消除基于Riemann求解器的通量差分裂格式存在的激波不稳定或"红斑"现象.为减小计算量,采用HLL和Roe FDS混合旋转格式.A second-order rotational upwind transport scheme for multi-dimensional compressible Euler equations on unstructured meshes is presented. Cell-centered FVM is employed in which gradient calculation is node-based with more neighbor cells. Slope limiter schemes are constructed for unstructured meshes. Numerical fluxes are evaluated by solving two Riemann problems in two upwind directions, including velocity-difference vector and perpendicular direction. The scheme eliminate shock instabilities or carbuncle phenomena in flux-difference splitting type schemes completely. A hybrid rotated Riemann solver is employed to form an economical numeric flux function and base Riemann solvers employ HLL and Roe FDS.

关 键 词：非结构网格 旋转Riemann求解器 欧拉方程 Riemann求解器 多维格式 激波捕捉 “红斑”现象 

分 类 号：O35[理学—流体力学]