We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations ...We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations of nonlinear hyperbolic problems with properties that greatly simplify the design of invariant domain-preserving high-resolution schemes.Compared to many other continuous and discontinuous Galerkin method variants,a particular advantage of the LGL spectral operator is the availability of a natural decomposition into a compatible subcellflux discretization.Representing a highorder spatial semi-discretization in terms of intermediate states,we performflux limiting in a manner that keeps these states and the results of Runge-Kutta stages in convex invariant domains.In addition,local bounds may be imposed on scalar quantities of interest.In contrast to limiting approaches based on predictor-corrector algorithms,our MCL procedure for LGL-DGSEM yields nonlinearflux approximations that are independent of the time-step size and can be further modified to enforce entropy stability.To demonstrate the robustness of MCL/DGSEM schemes for the compressible Euler equations,we run simulations for challenging setups featuring strong shocks,steep density gradients,and vortex dominatedflows.展开更多
The airborne electromagnetic （AEM） method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, e...The airborne electromagnetic （AEM） method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element （SE） method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell＇s equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic geology.展开更多
We apply the spectral-element method（SEM）,a high-order finite-element method（FEM） to simulate seismic wave propagation in complex media for exploration and geotechnical problems. The SEM accurately treats geometri...We apply the spectral-element method（SEM）,a high-order finite-element method（FEM） to simulate seismic wave propagation in complex media for exploration and geotechnical problems. The SEM accurately treats geometrical complexities through its flexible FEM mesh and accurately interpolates wavefields through high-order Lagrange polynomials. It has been a numerical solver used extensively in earthquake seismology. We demonstrate the applicability of SEM for selected 2D exploration and geotechnical velocity models with an open-source SEM software package SPECFEM2D. The first scenario involves a marine survey for a salt dome with the presence of major internal discontinuities,and the second example simulates seismic wave propagation for an open-pit mine with complex surface topography. Wavefield snapshots,synthetic seismograms,and peak particle velocity maps are presented to illustrate the promising use of SEM for industrial problems.展开更多
The investigation was performed on 4 Mullets (27～49 cm long and weighing 225～1 500 g each) of both sexes from the waters off Tianjin. Small pieces of the gills were sliced and immersionfixed in a buffer mixture of 1...The investigation was performed on 4 Mullets (27～49 cm long and weighing 225～1 500 g each) of both sexes from the waters off Tianjin. Small pieces of the gills were sliced and immersionfixed in a buffer mixture of 1.5% glutaraldehyde, 1.5% paraformaldehyde and 0.1 mol/dm~3 phosphate for at least 24 h. After fixation in phosphate buffered 1% OOat 4 ℃ for 1 h, the tissues were展开更多
膨润土作为缓冲或回填材料,具有吸水性极强、膨胀性较大、渗透性极低等特性。膨润土在饱和状态与非饱和状态之间转换时,因其湿胀干缩产生的裂缝会导致工程屏障受到破坏。因此,对具有高膨胀性的膨润土的持水特性及微观结构特征进行试验...膨润土作为缓冲或回填材料,具有吸水性极强、膨胀性较大、渗透性极低等特性。膨润土在饱和状态与非饱和状态之间转换时,因其湿胀干缩产生的裂缝会导致工程屏障受到破坏。因此,对具有高膨胀性的膨润土的持水特性及微观结构特征进行试验研究显得非常必要。分别运用滤纸法和饱和盐溶液蒸汽平衡法对膨润土进行了持水特性试验研究,得到了不同吸力范围内膨润土的土-水特征曲线;联合用蒸汽平衡法和扫描电子显微镜(SEM)对特定吸力点(367.54、149.51、71.12、38.00 MPa)的膨润土试样进行扫描电镜试验研究。膨润土的持水特性试验结果表明,滤纸法和饱和盐溶液蒸汽平衡法测得的土-水特征曲线均随吸力的增大而减小。根据滤纸法量测的试验数据,运用origin软件获得了Fredlund and Xing(1994)提出的模型参数,通过建立模型参数与干密度之间的关系,给出了膨润土的土-水特征曲线的预测公式。膨润土的微观定性分析表明:随着吸力的增大,膨润土集聚体逐渐增大,膨润土颗粒之间也越紧密;孔隙数量随着吸力的增大而减少、孔径也随吸力的增大而减小。展开更多
员工满意度的高低直接影响着企业经营活动的效率。本文首先介绍了结构方程模型(SEM 模型)的基本原理,然后从轨道交通企业的特点出发,建立了轨道交通企业员工满意度评价的 SEM 模型及指标体系,最后以深圳地铁运营分公司员工满意度评价为...员工满意度的高低直接影响着企业经营活动的效率。本文首先介绍了结构方程模型(SEM 模型)的基本原理,然后从轨道交通企业的特点出发,建立了轨道交通企业员工满意度评价的 SEM 模型及指标体系,最后以深圳地铁运营分公司员工满意度评价为例,对 SEM 模型进行了实证性研究。展开更多
文摘We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations of nonlinear hyperbolic problems with properties that greatly simplify the design of invariant domain-preserving high-resolution schemes.Compared to many other continuous and discontinuous Galerkin method variants,a particular advantage of the LGL spectral operator is the availability of a natural decomposition into a compatible subcellflux discretization.Representing a highorder spatial semi-discretization in terms of intermediate states,we performflux limiting in a manner that keeps these states and the results of Runge-Kutta stages in convex invariant domains.In addition,local bounds may be imposed on scalar quantities of interest.In contrast to limiting approaches based on predictor-corrector algorithms,our MCL procedure for LGL-DGSEM yields nonlinearflux approximations that are independent of the time-step size and can be further modified to enforce entropy stability.To demonstrate the robustness of MCL/DGSEM schemes for the compressible Euler equations,we run simulations for challenging setups featuring strong shocks,steep density gradients,and vortex dominatedflows.
基金financially supported by the Key Program of National Natural Science Foundation of China(No.41530320)China Natural Science Foundation for Young Scientists(No.41404093)+1 种基金Key National Research Project of China(Nos2016YFC0303100 and 2017YFC0601900)China Natural Science Foundation(No.41774125)
文摘The airborne electromagnetic （AEM） method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element （SE） method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell＇s equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic geology.
基金supported by the Natural Sciences and Engineering Research Council of Canada (NSERC)Center for Excellence in Mining Innovations (CEMI,through SUMIT project)+2 种基金Computations for this study were performed on hardwares purchased through the combined funding of Canada Foundation for Innovation (CFI)Ontario Research Fund (ORF)University of Toronto Startup Fund
文摘We apply the spectral-element method（SEM）,a high-order finite-element method（FEM） to simulate seismic wave propagation in complex media for exploration and geotechnical problems. The SEM accurately treats geometrical complexities through its flexible FEM mesh and accurately interpolates wavefields through high-order Lagrange polynomials. It has been a numerical solver used extensively in earthquake seismology. We demonstrate the applicability of SEM for selected 2D exploration and geotechnical velocity models with an open-source SEM software package SPECFEM2D. The first scenario involves a marine survey for a salt dome with the presence of major internal discontinuities,and the second example simulates seismic wave propagation for an open-pit mine with complex surface topography. Wavefield snapshots,synthetic seismograms,and peak particle velocity maps are presented to illustrate the promising use of SEM for industrial problems.
文摘The investigation was performed on 4 Mullets (27～49 cm long and weighing 225～1 500 g each) of both sexes from the waters off Tianjin. Small pieces of the gills were sliced and immersionfixed in a buffer mixture of 1.5% glutaraldehyde, 1.5% paraformaldehyde and 0.1 mol/dm~3 phosphate for at least 24 h. After fixation in phosphate buffered 1% OOat 4 ℃ for 1 h, the tissues were
文摘膨润土作为缓冲或回填材料,具有吸水性极强、膨胀性较大、渗透性极低等特性。膨润土在饱和状态与非饱和状态之间转换时,因其湿胀干缩产生的裂缝会导致工程屏障受到破坏。因此,对具有高膨胀性的膨润土的持水特性及微观结构特征进行试验研究显得非常必要。分别运用滤纸法和饱和盐溶液蒸汽平衡法对膨润土进行了持水特性试验研究,得到了不同吸力范围内膨润土的土-水特征曲线;联合用蒸汽平衡法和扫描电子显微镜(SEM)对特定吸力点(367.54、149.51、71.12、38.00 MPa)的膨润土试样进行扫描电镜试验研究。膨润土的持水特性试验结果表明,滤纸法和饱和盐溶液蒸汽平衡法测得的土-水特征曲线均随吸力的增大而减小。根据滤纸法量测的试验数据,运用origin软件获得了Fredlund and Xing(1994)提出的模型参数,通过建立模型参数与干密度之间的关系,给出了膨润土的土-水特征曲线的预测公式。膨润土的微观定性分析表明:随着吸力的增大,膨润土集聚体逐渐增大,膨润土颗粒之间也越紧密;孔隙数量随着吸力的增大而减少、孔径也随吸力的增大而减小。
