空气动力学学报2023，Vol.41Issue(11)：103-115,13.DOI:10.7638/kqdlxxb-2022.0128
一种分裂形式CPR格式在欠解析流动中的稳定性研究
On the stability of a split form CPR scheme in under-resolved flows
摘要
Abstract
The correction procedure via reconstruction(CPR)method is a compact and efficient high-order method suitable for unstructured grids.However,when discretizing the nonlinear convection term,it is easy to cause numerical instability due to the accumulation of aliasing errors.In the present work,we study the stability of the split form CPR method based on LG(Legendre-Gauss)points in under-resolved flows,and combine the method with the subcell limiting technique to solve under-resolved flows with shock waves.First,numerical tests are carried out to verify that the split form CPR method based on LG points with the boundary flux correction can satisfy the discrete conservation law,and such conservation is still preserved under subcell limiting.In the simulation of under-resolved flows without shock waves,compared to the divergence form CPR method,the split form significantly improves the stability of the calculation,and has smaller numerical errors than the split form CPR method using LGL(Legendre-Gauss-Lobatto)points.When solving under-resolved flows with shock waves,compared to the subcell limiting strategy of discontinuous Galerkin spectral element method based on LGL points,the subcell limiting strategy of split form CPR scheme based on LG points developed in this paper has higher resolution and less oscillation.关键词
CPR格式/分裂形式/非线性稳定性/混淆误差/欠解析流动Key words
CPR scheme/split form/nonlinear stability/aliasing errors/under-resolved flow分类
航空航天引用本文复制引用
贾斐然,朱华君,严红,燕振国,石京昶..一种分裂形式CPR格式在欠解析流动中的稳定性研究[J].空气动力学学报,2023,41(11):103-115,13.基金项目
国家数值风洞工程(NNW) （NNW）
国家自然科学基金(12172375,11902344) （12172375,11902344）
空气动力学国家重点实验室基金(SKLA2019010101) （SKLA2019010101）
