并行间断有限元算法求解Navier-Stokes方程

《并行间断有限元算法求解Navier-Stokes方程》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。

1、并行间断有限元算法求解Navier-Stokes方程马欣荣段治健谢公南刘三阳咸阳师范学院数学与信息科学学院西北工业大学航海学院西安电子科技大学数学与统计学院摘要：间断Galerkin有限元方法非常适合在非结构网格上高精度求解Navier-Stokes方程，然而其十分耗费计算资源•为了提高计算效率，提出了高效的MIMD并行算法•采用隐式吋间离散GMRES+LU-SGS格式，结合多重网格方法，当地吋间步长加速算法收敛•为了保证各处理器间负载平衡，采用区域分解二级图方法划分网格，实现内存合理分配，数据只在

2、相邻处理器间传递•数值模拟了RAE2822翼型和M6黏性绕流，加速比基本呈线性变化且接近理想值•结果表明了该算法能有效减少计算时间、合理分配内存，具有较高的加速比和并行效率，适合于MTMD粗粒度科学计算.关键词：间断Galerkin有限元方法;Navier-Stokes方程；并行算法;区域分解算法;作者简介：马欣荣(1980—),女,者.E-mail:mxryxl021@163.com);作者简介：段治健(1980—)，男,(E-mail:zhijianduan@126.com);作者简介：谢公南(

3、1980—),男,作者简介：刘三阳(1959—),男,收稿日期:2017-04-05博士(通讯作副教授，博士教授，博士(E-mai1:xgn@nwpu.edu.cn)教授(E-ma订：liusanyang@126.com).基金：国家自然科学基金(61401383)AParallelDiscontinuousGalerkinFEMforSolvingCompressibleNavier-StokesEquationsMAXin-rongDUANZhi-jianXIEGong-nanLIUSan-ya

4、ngCollegeofMathematicsandInformationScience,XianyangNormalUniversity;SchoolofMarineScienceandTechnology,NorthwesternPolytechnicalUniversity;SchoolofMathematicsandStatistics,XidianUniversity;Abstract：Basedonunstructuredgrids,discontinuousGalerkinfinitee

5、lementmethods(DGFEM)areverysuitedtorealizehigh-orderapproximationsofNavier-Stokesequations,butareratherdemandingincomputingresources.InordertoimprovethecomputationalefficiencyoftheDGFEM,anefficientparallelalgorithmondistributcd-mcniorymulticomputcrscou

6、pledwiththemultigridstrategybasedontheGMRES+LU-SGSprocedurewaspresentedhere.Thedomaindecompositionmethodwasemployedtohandlemeshesproperlyandmakeeachprocessormaintainloadbalancing.Moreover,theLU-SGSandthelocaltimesteppingtechniqueswereusedtoaccelereitet

7、heconvergenceofthesolutionofNavier-Stokesequations.NumcricdltestswereconductedforviscidturbulenceflowproblemsaroundtheRAE2822airfoilandovertheM6wing.Theparallelaccelerationisneartoa1inearconvergeneeanduptotheidealsolutions.Theresultsindicatethattheprop

8、osedparallelalgorithmreducescomputationtimesignificantlyandallocatesmemoryreasonablywithadvantagesofhighaccelerationandefficiency,andisverysuitedforcoarsegrainedscientificcomputationofMIMDmodels.Keyword：discontinuousGalerkinFEM;Navier-S