The steady state, two dimensional creeping flow of an upper convected Maxwell (UCM) fluid between two eccentric cylinders, with the inner one rotating,is computed by p version of EVSS/SUPG finite element method. T...The steady state, two dimensional creeping flow of an upper convected Maxwell (UCM) fluid between two eccentric cylinders, with the inner one rotating,is computed by p version of EVSS/SUPG finite element method. The solutions converge as the polynomial order of the approximation increases. An upper Deborah number (De) limit attains 30 (p≤5). With De increasing, The boundary layers form and develop in the stress, which match closely with those predicted by asymptotic analysis. The results show that numerical oscillations is caused by the boundary layers of stress and can be reduced by increasing the polynomial order of the approximation.展开更多
A streamline upwind/Petrov-Galerkin （SUPG） finite element method based on a penalty function is pro- posed for steady incompressible Navier-Stokes equations. The SUPG stabilization technique is employed for the for-...A streamline upwind/Petrov-Galerkin （SUPG） finite element method based on a penalty function is pro- posed for steady incompressible Navier-Stokes equations. The SUPG stabilization technique is employed for the for- mulation of momentum equations. Using the penalty function method, the continuity equation is simplified and the pres- sure of the momentum equations is eliminated. The lid-driven cavity flow problem is solved using the present model. It is shown that steady flow simulations are computable up to Re = 27500, and the present results agree well with previous solutions. Tabulated results for the properties of the primary vortex are also provided for benchmarking purposes.展开更多
文摘The steady state, two dimensional creeping flow of an upper convected Maxwell (UCM) fluid between two eccentric cylinders, with the inner one rotating,is computed by p version of EVSS/SUPG finite element method. The solutions converge as the polynomial order of the approximation increases. An upper Deborah number (De) limit attains 30 (p≤5). With De increasing, The boundary layers form and develop in the stress, which match closely with those predicted by asymptotic analysis. The results show that numerical oscillations is caused by the boundary layers of stress and can be reduced by increasing the polynomial order of the approximation.
基金the National Natural Science Foundation of China (Grants 41372301 and 51349011)the Preeminent Youth Talent Project of Southwest University of Science and Technology (Grant 13zx9109)
文摘A streamline upwind/Petrov-Galerkin （SUPG） finite element method based on a penalty function is pro- posed for steady incompressible Navier-Stokes equations. The SUPG stabilization technique is employed for the for- mulation of momentum equations. Using the penalty function method, the continuity equation is simplified and the pres- sure of the momentum equations is eliminated. The lid-driven cavity flow problem is solved using the present model. It is shown that steady flow simulations are computable up to Re = 27500, and the present results agree well with previous solutions. Tabulated results for the properties of the primary vortex are also provided for benchmarking purposes.
