三角网格间断有限元法弹性波模拟精度分析  

Analysis of elastic wave simulation accuracy with discontinuous Galerkin finite element method based on triangular meshes

作　　者：韩德超 刘卫华[1,2] 司文朋[1,2] HAN Dechao;LIU Weihua;SI Wenpeng(SINOPEC Geophysical Research Institute,Nanjing,Jiangsu 211103,China;SINOPEC Key Laboratory of Geophysics,Nanjing,Jiangsu 211103,China)

机构地区：[1]中国石化石油物探技术研究院,江苏南京211103 [2]中国石化地球物理重点实验室,江苏南京211103

出　　处：《石油地球物理勘探》2021年第4期758-770,I0010,共14页Oil Geophysical Prospecting

基　　金：国家科技重大专项“页岩气储层岩石物理实验研究”(2017ZX05036-005-001);中石化科技部项目“三维数字岩心岩石物理数值模拟技术研究”(P18075-1)联合资助。

摘　　要：精度分析是地震波数值模拟的基础。针对基于三角形网格的间断Galerkin有限元方法(DGFEM)的稳定性、数值频散及耗散问题,构建了周期性三角形单元网格,可以更灵活地分析不同形态的三角形单元对模拟精度的影响。理论和数值实验的分析结果表明:三角形网格中基于Runge-Kutta时间格式的DGFEM的稳定性条件与三角形的形态有关。模拟的最大时间步长与单元内切圆半径呈线性关系,且正三角形单元的稳定性条件最宽松。同时,基于局部Lax-Friedrichs数值流的DGFEM模拟波场呈弱频散、强耗散的特征,且频散与耗散在周期性网格中均具有方向性。此外,模拟误差与网格尺寸在双对数坐标系呈线性关系。数值实验结果对比了网格形态对波场的影响,直观地验证了理论分析的方向性差异,可为DGFEM中三角形网格的划分、参数的设置和数值流的选择提供理论依据。Accuracy analysis is the foundation for numerical simulation of seismic waves.With regard to the numerical stability,dispersion,and dissipation of the discontinuous Galerkin finite element method(DGFEM)based on triangular meshes,a triangular periodic mesh model is constructed,which can be used to study the effects of different triangular elements on simulation accuracy.The theoretical and numerical results show that the stability condition of the DGFEM based on the Runge-Kutta time scheme is related to the shape of triangle elements.The maximum time step for stable modeling has a linear relationship with the radius of the inscribed circle of the element,and the equilateral triangle element has the least rigorous stability condition.Meanwhile,the wave field from DGFEM simulation based on the local Lax-Friedrichs flux shows weak dispersion but strong dissipation,and both dispersion and dissipation present directivity in the periodic mesh.In addition,the logarithm of the modeling error has a linear relationship with that of the mesh size.The numerical experiments compare the influence of different mesh shapes on the wave field and verify the theoretical directional difference.The results of this paper can provide a theoretical basis for the triangular mesh division,parameter setting,and selection of numerical flow in DGFEM.

关 键 词：间断Galerkin有限元方法 Runge-Kutta时间格式 三角形网格 稳定性分析 数值频散 数值耗散 

分 类 号：P631[天文地球—地质矿产勘探]