The J-lay method is regarded as one of the most feasible methods to lay a pipeline in deep water and ultra-deep water. A numerical model that accounts for the nonlinear soil stiffness is developed in this study to eva...The J-lay method is regarded as one of the most feasible methods to lay a pipeline in deep water and ultra-deep water. A numerical model that accounts for the nonlinear soil stiffness is developed in this study to evaluate a J-lay pipeline. The pipeline considered in this model is divided into two parts： the part one is suspended in water, and the part two is laid on the seabed. In addition to the boundary conditions at the two end points of the pipeline, a special set of the boundary conditions is required at the touchdown point that connects the two parts of the pipeline. The two parts of the pipeline are solved by a numerical iterative method and the finite difference method, respectively. The proposed numerical model is validated for a special case using a catenary model and a numerical model with linear soil stiffness. A good agreement in the pipeline configuration, the tension force and the bending moment is obtained among these three models. Furthermore, the present model is used to study the importance of the nonlinear soil stiffness. Finally, the parametric study is performed to study the effect of the mudline shear strength, the gradient of the soil shear strength, and the outer diameter of the pipeline on the pipelaying solution.展开更多
Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying.For one such process as liquid-metal dealloying(LMD),phase field models have been developed to understand the mechanisms l...Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying.For one such process as liquid-metal dealloying(LMD),phase field models have been developed to understand the mechanisms leading to complex morphologies.However,the LMD governing equations in these models often involve coupled non-linear partial differential equations(PDE),which are challenging to solve numerically.In particular,numerical stiffness in the PDEs requires an extremely refined time step size(on the order of 10−12s or smaller).This computational bottleneck is especially problematic when running LMD simulation until a late time horizon is required.This motivates the development of surrogate models capable of leaping forward in time,by skipping several consecutive time steps at-once.In this paper,we propose a U-shaped adaptive Fourier neural operator(U-AFNO),a machine learning(ML)based model inspired by recent advances in neural operator learning.U-AFNO employs U-Nets for extracting and reconstructing local features within the physical fields,and passes the latent space through a vision transformer(ViT)implemented in the Fourier space(AFNO).We use U-AFNOs to learn the dynamics of mapping the field at a current time step into a later time step.We also identify global quantities of interest(QoI)describing the corrosion process(e.g.,the deformation of the liquid-metal interface,lost metal,etc.)and show that our proposed U-AFNO model is able to accurately predict the field dynamics,in spite of the chaotic nature of LMD.Most notably,our model reproduces the key microstructure statistics and QoIs with a level of accuracy on par with the high-fidelity numerical solver,while achieving a significant 11,200×speed-up on a high-resolution grid when comparing the computational expense per time step.Finally,we also investigate the opportunity of using hybrid simulations,in which we alternate forward leaps in time using the U-AFNO with high-fidelity time stepping.We demonstrate that while advantageous for some surrogate model design choices,our proposed U-AFNO model in fully auto-regressive settings consistently outperforms hybrid schemes.展开更多
基金supported by the China Scholarship Council,the Technology Major Project of China(Grant No.2011ZX05027-002)the National Natural Science Foundation of China(Grant No.51409128)the University Natural Science Research Project of Jiangsu Province(Grant No.14KJB570001)
文摘The J-lay method is regarded as one of the most feasible methods to lay a pipeline in deep water and ultra-deep water. A numerical model that accounts for the nonlinear soil stiffness is developed in this study to evaluate a J-lay pipeline. The pipeline considered in this model is divided into two parts： the part one is suspended in water, and the part two is laid on the seabed. In addition to the boundary conditions at the two end points of the pipeline, a special set of the boundary conditions is required at the touchdown point that connects the two parts of the pipeline. The two parts of the pipeline are solved by a numerical iterative method and the finite difference method, respectively. The proposed numerical model is validated for a special case using a catenary model and a numerical model with linear soil stiffness. A good agreement in the pipeline configuration, the tension force and the bending moment is obtained among these three models. Furthermore, the present model is used to study the importance of the nonlinear soil stiffness. Finally, the parametric study is performed to study the effect of the mudline shear strength, the gradient of the soil shear strength, and the outer diameter of the pipeline on the pipelaying solution.
文摘Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying.For one such process as liquid-metal dealloying(LMD),phase field models have been developed to understand the mechanisms leading to complex morphologies.However,the LMD governing equations in these models often involve coupled non-linear partial differential equations(PDE),which are challenging to solve numerically.In particular,numerical stiffness in the PDEs requires an extremely refined time step size(on the order of 10−12s or smaller).This computational bottleneck is especially problematic when running LMD simulation until a late time horizon is required.This motivates the development of surrogate models capable of leaping forward in time,by skipping several consecutive time steps at-once.In this paper,we propose a U-shaped adaptive Fourier neural operator(U-AFNO),a machine learning(ML)based model inspired by recent advances in neural operator learning.U-AFNO employs U-Nets for extracting and reconstructing local features within the physical fields,and passes the latent space through a vision transformer(ViT)implemented in the Fourier space(AFNO).We use U-AFNOs to learn the dynamics of mapping the field at a current time step into a later time step.We also identify global quantities of interest(QoI)describing the corrosion process(e.g.,the deformation of the liquid-metal interface,lost metal,etc.)and show that our proposed U-AFNO model is able to accurately predict the field dynamics,in spite of the chaotic nature of LMD.Most notably,our model reproduces the key microstructure statistics and QoIs with a level of accuracy on par with the high-fidelity numerical solver,while achieving a significant 11,200×speed-up on a high-resolution grid when comparing the computational expense per time step.Finally,we also investigate the opportunity of using hybrid simulations,in which we alternate forward leaps in time using the U-AFNO with high-fidelity time stepping.We demonstrate that while advantageous for some surrogate model design choices,our proposed U-AFNO model in fully auto-regressive settings consistently outperforms hybrid schemes.
