With the improved moving least-squares (IMLS) approximation, an orthogonal function system with a weight function is used as the basis function. The combination of the element-free Galerkin (EFG) method and the IMLS a...With the improved moving least-squares (IMLS) approximation, an orthogonal function system with a weight function is used as the basis function. The combination of the element-free Galerkin (EFG) method and the IMLS approximation leads to the development of the improved element-free Galerkin (IEFG) method. In this paper, the IEFG method is applied to study the partial differential equations that control the heat flow in three-dimensional space. With the IEFG technique, the Galerkin weak form is employed to develop the discretized system equations, and the penalty method is applied to impose the essential boundary conditions. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the transient heat conduction equations and the boundary and initial conditions are time dependent, the scaling parameter, number of nodes and time step length are considered in a convergence study.展开更多
This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zer...This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zero norm solution. The inversion approach mainly employs forward modeling; a depth weight function is introduced into the objective function of the zero norms. Sparse inversion results are obtained by the corresponding optimal mathematical method. To achieve the practical geophysical and geological significance of the results, penalty function is applied to constrain the density values. Results obtained by proposed provide clear boundary depth and density contrast distribution information. The method's accuracy, validity, and reliability are verified by comparing its results with those of synthetic models. To further explain its reliability, a practical gravity data is obtained for a region in Texas, USA is applied. Inversion results for this region are compared with those of previous studies, including a research of logging data in the same area. The depth of salt dome obtained by the inversion method is 4.2 km, which is in good agreement with the 4.4 km value from the logging data. From this, the practicality of the inversion method is also validated.展开更多
We study continuous data assimilation(CDA)applied to projection and penalty methods for the Navier-Stokes(NS)equations.Penalty and projection methods are more efficient than consistent Ns discretizations,however are l...We study continuous data assimilation(CDA)applied to projection and penalty methods for the Navier-Stokes(NS)equations.Penalty and projection methods are more efficient than consistent Ns discretizations,however are less accurate due to modeling error(penalty)and splitting error(projection).We show analytically and numerically that with measurement data and properly chosen parameters,CDA can effectively remove these splitting and modeling errors and provide long time optimally accurate solutions.展开更多
The safety of risers in hang-off states is a vital challenge in offshore oil and gas engineering.A new hang-off system installed on top of risers is proposed for improving the security of risers.This approach leads to...The safety of risers in hang-off states is a vital challenge in offshore oil and gas engineering.A new hang-off system installed on top of risers is proposed for improving the security of risers.This approach leads to a challenging problem:coupling the dynamics of risers with a new hang-off system combined with multiple structures and complex constraints.To accurately analyze the dynamic responses of the coupled system,a coupled dynamic model is established based on the Euler-Bernoulli beam-column theory and penalty function method.A comprehensive analysis method is proposed for coupled dynamic analysis by combining the finite element method and the Newmarkβmethod.An analysis program is also developed in MATLAB for dynamic simulation.The simulation results show that the dynamic performances of the risers at the top part are significantly improved by the new hang-off system,especially the novel design,which includes the centralizer and articulation joint.The bending moment and lateral deformation of the risers at the top part decrease,while the hang-off joint experiences a great bending moment at the bottom of the lateral restraint area which requires particular attention in design and application.The platform navigation speed range under the safety limits of risers expands with the new hang-off system in use.展开更多
We investigate the numerical approximation for stabilizing the semidiscrete linearized Boussinesq system around an unstable stationary state.Stabilization is attained through internal feedback controls applied to the ...We investigate the numerical approximation for stabilizing the semidiscrete linearized Boussinesq system around an unstable stationary state.Stabilization is attained through internal feedback controls applied to the velocity and temperature equations,localized within an arbitrary open subset.This study follows the framework presented in[14],considering the continuous linearized Boussinesq system.The primary objective is to explore the penalizationbased approximation of the free divergence condition in the semidiscrete case and provide a numerical validation of these results in a two-dimensional setting.展开更多
基金the National Natural Science Foundation of China (Grant No. 11171208)Shanghai Leading Academic Discipline Project (Grant No. S30106)
文摘With the improved moving least-squares (IMLS) approximation, an orthogonal function system with a weight function is used as the basis function. The combination of the element-free Galerkin (EFG) method and the IMLS approximation leads to the development of the improved element-free Galerkin (IEFG) method. In this paper, the IEFG method is applied to study the partial differential equations that control the heat flow in three-dimensional space. With the IEFG technique, the Galerkin weak form is employed to develop the discretized system equations, and the penalty method is applied to impose the essential boundary conditions. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the transient heat conduction equations and the boundary and initial conditions are time dependent, the scaling parameter, number of nodes and time step length are considered in a convergence study.
基金supported by the Development of airborne gravity gradiometer(No.2017YFC0601601)open subject of Key Laboratory of Petroleum Resources Research,Institute of Geology and Geophysics,Chinese Academy of Sciences(No.KLOR2018-8)
文摘This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zero norm solution. The inversion approach mainly employs forward modeling; a depth weight function is introduced into the objective function of the zero norms. Sparse inversion results are obtained by the corresponding optimal mathematical method. To achieve the practical geophysical and geological significance of the results, penalty function is applied to constrain the density values. Results obtained by proposed provide clear boundary depth and density contrast distribution information. The method's accuracy, validity, and reliability are verified by comparing its results with those of synthetic models. To further explain its reliability, a practical gravity data is obtained for a region in Texas, USA is applied. Inversion results for this region are compared with those of previous studies, including a research of logging data in the same area. The depth of salt dome obtained by the inversion method is 4.2 km, which is in good agreement with the 4.4 km value from the logging data. From this, the practicality of the inversion method is also validated.
文摘We study continuous data assimilation(CDA)applied to projection and penalty methods for the Navier-Stokes(NS)equations.Penalty and projection methods are more efficient than consistent Ns discretizations,however are less accurate due to modeling error(penalty)and splitting error(projection).We show analytically and numerically that with measurement data and properly chosen parameters,CDA can effectively remove these splitting and modeling errors and provide long time optimally accurate solutions.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.52271300,52071337,and 51809279)the National Key Research and Development Program of China(Grant No.2022YFC2806501)the High-tech Ship Research Projects Sponsored by MIIT(Grant No.CBG2N21-4-2-5).
文摘The safety of risers in hang-off states is a vital challenge in offshore oil and gas engineering.A new hang-off system installed on top of risers is proposed for improving the security of risers.This approach leads to a challenging problem:coupling the dynamics of risers with a new hang-off system combined with multiple structures and complex constraints.To accurately analyze the dynamic responses of the coupled system,a coupled dynamic model is established based on the Euler-Bernoulli beam-column theory and penalty function method.A comprehensive analysis method is proposed for coupled dynamic analysis by combining the finite element method and the Newmarkβmethod.An analysis program is also developed in MATLAB for dynamic simulation.The simulation results show that the dynamic performances of the risers at the top part are significantly improved by the new hang-off system,especially the novel design,which includes the centralizer and articulation joint.The bending moment and lateral deformation of the risers at the top part decrease,while the hang-off joint experiences a great bending moment at the bottom of the lateral restraint area which requires particular attention in design and application.The platform navigation speed range under the safety limits of risers expands with the new hang-off system in use.
基金supported by the French National Research Agency ANR-22-CE46-0005(NumOpTES)supported by the grant"Numerical simulation and optimal control in view of temperature regulation in smart buildings"of the Nouvelle Aquitaine Regionpartially supported by the Project TRECOS ANR-20-CE40-0009 funded by the ANR(2021-2024).
文摘We investigate the numerical approximation for stabilizing the semidiscrete linearized Boussinesq system around an unstable stationary state.Stabilization is attained through internal feedback controls applied to the velocity and temperature equations,localized within an arbitrary open subset.This study follows the framework presented in[14],considering the continuous linearized Boussinesq system.The primary objective is to explore the penalizationbased approximation of the free divergence condition in the semidiscrete case and provide a numerical validation of these results in a two-dimensional setting.
