加权梯度限制器在节点DG格式中的应用  

Application of Linear-weighted Gradient Limiter for Nodal Discontinuous Galerkin Method

作　　者：刘逸鸥[1] 杨永[1] 张强[1] 

机构地区：[1]西北工业大学翼型叶栅空气动力学国防科技重点实验室,陕西西安710072

出　　处：《航空计算技术》2013年第3期9-12,16,共5页Aeronautical Computing Technique

基　　金：国家自然科学基金项目资助(11002117)

摘　　要：在使用节点间断Galerkin(DG)方法求解存在激波的流动问题时,为抑制Gibbs效应导致的非物理振荡,对一种加权梯度限制器进行研究,在二维非结构网格上对定常欧拉方程求解。限制器以原始变量作为限制对象,对其梯度进行限制,以加权形式进行重构。对翼型的跨音速流场、超燃冲压发动机内流场和前台阶模型流场进行模拟,结果表明限制器能很好抑制间断解附近的非物理振荡,有效避免计算中断,体现了DG格式精度高、对间断捕捉敏感的特点。When applying the nodal discontinuous Galerkin（DG） method for the simulation of flow problems with discontinuities,a linear-weighted gradient limiter has been studied in order to damp the unphysical oscillations caused by the Gibbs effects,in solving the conservative Euler equations on unstructured grids.This limiter regards the primitive variables as limiting object,of which the gradients are limited.A weighting strategy has been applied for the reconstruction of flow field solutions.The limiting effects have been tested on examples of the transonic flow over airfoils,a scramjet inlet flow model,and a supersonic uniform flow encountering a forward facing step.The simulation results illustrate that the limiter can successfully damp the unphysical oscillations around the discontinuities,while the advantages of DG method as the accurate detection for discontinuities are demonstrated.

关 键 词：节点间断Galerkin有限元方法 加权梯度限制器 间断捕捉 Gibbs效应 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]