Two-Level Defect-CorrectionMethod for Steady Navier-Stokes Problem with Friction Boundary Conditions

In this paper,we present two-level defect-correction finite element method for steady Navier-Stokes equations at high Reynolds number with the friction boundary conditions,which results in a variational inequality problem of the second kind.Based on Taylor-Hood element,we solve a variational inequality problem of Navier-Stokes type on the coarse mesh and solve a variational inequality problem of Navier-Stokes type corresponding to Newton linearization on the fine mesh.The error estimates for the velocity in the H1 norm and the pressure in the L^(2) norm are derived.Finally,the numerical results are provided to confirm our theoretical analysis.

Computational fluid dynamics simulation of friction stir welding:A comparative study on different frictional boundary conditions

Numerical simulation based on computational fluid dynamics （CFD） is a useful approach for quantitatively investigating the underlying thermal-mechanical conditions during FSW, such as temperature field and material deformation field. One of the critical issues in CFD simulation of FSW is the use of the frictional boundary condition, which represents the friction between the welding tool and the workpiece in the numerical models. In this study, three-dimensional numerical simulation is conducted to analyze the heat transfer and plastic deformation behaviors during the FSW of AA2024. For comparison purposes, both the boundary velocity （BV） models and the boundary shear stress （BSS） models are employed in order to assess their performances in predicting the temperature and material deformation in FSW. It is interesting to note that different boundary conditions yield similar predictions on temperature, but quite different predictions on material deformation. The numerical predictions are compared with the experimental results. The predicted deformation zone geometry by the BSS model is consistent with the experimental results while there is large difference between the predictions by the BV models and the experimental measurements. The fact that the BSS model yields more reasonable predictions on the deformation zone geometry is attributed to its capacity to automatically adjust the contact state at the tool/workpiece interface. Based on the favorable predictions on both the temperature field and the material deformation field, the BSS model is suggested to have a better performance in numerical simulation of FSW than the BV model.

A review of down-hole tubular string buckling in well engineering

Down-hole tubular string buckling is the most classic and complex part of tubular string mechanics in well engineering. Studies of down-hole tubular string buckling not only have theoretical significance in revealing the buckling mechanism but also have prominent practical value in design and control of tubular strings. In this review, the basic principles and applicable scope of three classic research methods （the beam-column model, buck- ling differential equation, and energy method） are intro- duced. The critical buckling loads and the post-buckling behavior under different buckling modes in vertical, inclined, horizontal, and curved wellbores from different researchers are presented and compared. The current understanding of the effects of torque, boundary condi- tions, friction force, and connectors on down-hole tubular string buckling is illustrated. Meanwhile, some unsolved problems and controversial conclusions are discussed. Future research should be focused on sophisticated description of buckling behavior and the coupling effect of multiple factors. In addition, active control of down-hole tubular string buckling behavior needs some attention urgently.