Seismic modeling is a useful tool for studying the propagation of seismic waves within complex structures. However, traditional methods of seismic simulation cannot meet the needs for studying seismic wavefields in th...Seismic modeling is a useful tool for studying the propagation of seismic waves within complex structures. However, traditional methods of seismic simulation cannot meet the needs for studying seismic wavefields in the complex geological structures found in seismic exploration of the mountainous area in Northwestern China. More powerful techniques of seismic modeling are demanded for this purpose. In this paper, two methods of finite element-finite difference method （FE-FDM） and arbitrary difference precise integration （ADPI） for seismic forward modeling have been developed and implemented to understand the behavior of seismic waves in complex geological subsurface structures and reservoirs. Two case studies show that the FE-FDM and ADPI techniques are well suited to modeling seismic wave propagation in complex geology.展开更多
This paper discusses conforming mixed finite element approximations for the Stokes eigenvalue problem. Firstly, several mixed finite element identities are proved. Based on these identities, the following new results ...This paper discusses conforming mixed finite element approximations for the Stokes eigenvalue problem. Firstly, several mixed finite element identities are proved. Based on these identities, the following new results are given： （1） It is proved that the numerical eigenvalues obtained by mini-element, P1-P1 element and Q1-Q1 element approximate the exact eigenvalues from above. （2） As for the P1-P1, Q1-Q1 and Q1-Po element eigenvalues, the asymptotically exact a posteriori error indicators are presented. （3） The reliable and efficient a posteriori error estimator proposed by Verfiirth is applied to mini-element eigenfunctions. Finally, numerical experiments are carried out to verify the theoretical analysis.展开更多
In this paper,the discontinuous Galerkin(DG)method combined with localized artificial diffusivity is investigated in the context of numerical simulation of broadband compressible turbulent flows with shocks for under-...In this paper,the discontinuous Galerkin(DG)method combined with localized artificial diffusivity is investigated in the context of numerical simulation of broadband compressible turbulent flows with shocks for under-resolved cases.Firstly,the spectral property of the DG method is analyzed using the approximate dispersion relation(ADR)method and compared with typical finite difference methods,which reveals quantitatively that significantly less grid points can be used with DG for comparable numerical error.Then several typical test cases relevant to problems of compressible turbulence are simulated,including one-dimensional shock/entropy wave interaction,two-dimensional decaying isotropic turbulence,and two-dimensional temporal mixing layers.Numerical results indicate that higher numerical accuracy can be achieved on the same number of degrees of freedom with DG than high order finite difference schemes.Furthermore,shocks are also well captured using the localized artificial diffusivity method.The results in this work can provide useful guidance for further applications of DG to direct and large eddy simulation of compressible turbulent flows.展开更多
This paper is devoted to a new error analysis of nonconforming finite element methods.Compared with the classic error analysis in literature,only weak continuity,the F-E-M-Test for nonconforming finite element spaces,...This paper is devoted to a new error analysis of nonconforming finite element methods.Compared with the classic error analysis in literature,only weak continuity,the F-E-M-Test for nonconforming finite element spaces,and basic Hm regularity for exact solutions of 2m-th order elliptic problems under consideration are assumed.The analysis is motivated by ideas from a posteriori error estimates and projection average operators.One main ingredient is a novel decomposition for some key average terms on(n.1)-dimensional faces by introducing a piecewise constant projection,which defines the generalization to more general nonconforming finite elements of the results in literature.The analysis and results herein are conjectured to apply for all nonconforming finite elements in literature.展开更多
基金supported by the Natural Science Foundation of China(Grant No.40574050,40821062)the National Basic Research Program of China(Grant No.2007CB209602)the Key Research Program of China National Petroleum Corporation(Grant No.06A10101)
文摘Seismic modeling is a useful tool for studying the propagation of seismic waves within complex structures. However, traditional methods of seismic simulation cannot meet the needs for studying seismic wavefields in the complex geological structures found in seismic exploration of the mountainous area in Northwestern China. More powerful techniques of seismic modeling are demanded for this purpose. In this paper, two methods of finite element-finite difference method （FE-FDM） and arbitrary difference precise integration （ADPI） for seismic forward modeling have been developed and implemented to understand the behavior of seismic waves in complex geological subsurface structures and reservoirs. Two case studies show that the FE-FDM and ADPI techniques are well suited to modeling seismic wave propagation in complex geology.
基金supported by National Natural Science Foundation of China (Grant No.10761003)Science and Technology Foundation of Guizhou Province of China (Grant No. [2011] 2111)
文摘This paper discusses conforming mixed finite element approximations for the Stokes eigenvalue problem. Firstly, several mixed finite element identities are proved. Based on these identities, the following new results are given： （1） It is proved that the numerical eigenvalues obtained by mini-element, P1-P1 element and Q1-Q1 element approximate the exact eigenvalues from above. （2） As for the P1-P1, Q1-Q1 and Q1-Po element eigenvalues, the asymptotically exact a posteriori error indicators are presented. （3） The reliable and efficient a posteriori error estimator proposed by Verfiirth is applied to mini-element eigenfunctions. Finally, numerical experiments are carried out to verify the theoretical analysis.
基金supported by the National Basic Research Program of China(Grant No.2009CB724104)
文摘In this paper,the discontinuous Galerkin(DG)method combined with localized artificial diffusivity is investigated in the context of numerical simulation of broadband compressible turbulent flows with shocks for under-resolved cases.Firstly,the spectral property of the DG method is analyzed using the approximate dispersion relation(ADR)method and compared with typical finite difference methods,which reveals quantitatively that significantly less grid points can be used with DG for comparable numerical error.Then several typical test cases relevant to problems of compressible turbulence are simulated,including one-dimensional shock/entropy wave interaction,two-dimensional decaying isotropic turbulence,and two-dimensional temporal mixing layers.Numerical results indicate that higher numerical accuracy can be achieved on the same number of degrees of freedom with DG than high order finite difference schemes.Furthermore,shocks are also well captured using the localized artificial diffusivity method.The results in this work can provide useful guidance for further applications of DG to direct and large eddy simulation of compressible turbulent flows.
基金supported by National Natural Science Foundation of China(Grant Nos.11031006 and 11271035)
文摘This paper is devoted to a new error analysis of nonconforming finite element methods.Compared with the classic error analysis in literature,only weak continuity,the F-E-M-Test for nonconforming finite element spaces,and basic Hm regularity for exact solutions of 2m-th order elliptic problems under consideration are assumed.The analysis is motivated by ideas from a posteriori error estimates and projection average operators.One main ingredient is a novel decomposition for some key average terms on(n.1)-dimensional faces by introducing a piecewise constant projection,which defines the generalization to more general nonconforming finite elements of the results in literature.The analysis and results herein are conjectured to apply for all nonconforming finite elements in literature.
