Based on the finite element method(FEM), some iterative methods related to different Reynolds numbers are designed and analyzed for solving the 2D/3D stationary incompressible magnetohydrodynamics(MHD) numerically. Tw...Based on the finite element method(FEM), some iterative methods related to different Reynolds numbers are designed and analyzed for solving the 2D/3D stationary incompressible magnetohydrodynamics(MHD) numerically. Two-level finite element iterative methods, consisting of the classical m-iteration methods on a coarse grid and corrections on a fine grid, are designed to solve the system at low Reynolds numbers under the strong uniqueness condition. One-level Oseen-type iterative method is investigated on a fine mesh at high Reynolds numbers under the weak uniqueness condition. Furthermore, the uniform stability and convergence of these methods with respect to equation parameters R_e, R_m, S_c, mesh sizes h, H and iterative step m are provided. Finally, the efficiency of the proposed methods is confirmed by numerical investigations.展开更多
We investigate initial-boundary-value problem for three-dimensional magnetohydrodynamic （MHD） system of compressible viscous heat-conductive flows and the three-dimensional full compressible Navier-Stokes equations....We investigate initial-boundary-value problem for three-dimensional magnetohydrodynamic （MHD） system of compressible viscous heat-conductive flows and the three-dimensional full compressible Navier-Stokes equations. We establish a blowup criterion only in terms of the derivative of velocity field, similar to the Beale^Kato-Majda type criterion for compressible viscous barotropic flows by Huang et al. （2011）. The results indicate that the nature of the blowup for compressible MHD models of viscous media is similar to the barotropic compressible Navier-Stokes equations and does not depend on further sophistication of the MHD model, in particular, it is independent of the temperature and magnetic field. It also reveals that the deformation tensor of the velocity field plays a more dominant role than the electromagnetic field and the temperature in regularity theory. Especially, the similar results also hold for compressible viscous heat-conductive Navier-Stokes flows, which extend the results established by Fan et al. （2010）, and I-Iuang and Li （2009）. In addition, the viscous coefficients are only restricted by the physical conditions in this paper.展开更多
基金National Natural Science Foundation of China (Grant Nos. 11271298 and 11362021)
文摘Based on the finite element method(FEM), some iterative methods related to different Reynolds numbers are designed and analyzed for solving the 2D/3D stationary incompressible magnetohydrodynamics(MHD) numerically. Two-level finite element iterative methods, consisting of the classical m-iteration methods on a coarse grid and corrections on a fine grid, are designed to solve the system at low Reynolds numbers under the strong uniqueness condition. One-level Oseen-type iterative method is investigated on a fine mesh at high Reynolds numbers under the weak uniqueness condition. Furthermore, the uniform stability and convergence of these methods with respect to equation parameters R_e, R_m, S_c, mesh sizes h, H and iterative step m are provided. Finally, the efficiency of the proposed methods is confirmed by numerical investigations.
基金supported by National Natural Science Foundation of China(Grant Nos.11171236 and 71372189)Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT1273)+1 种基金Sichuan Youth Science and Technology Foundation(Grant No.2014JQ0003)China Postdoctoral Science Foundation(Grant No.2013M542285)
文摘We investigate initial-boundary-value problem for three-dimensional magnetohydrodynamic （MHD） system of compressible viscous heat-conductive flows and the three-dimensional full compressible Navier-Stokes equations. We establish a blowup criterion only in terms of the derivative of velocity field, similar to the Beale^Kato-Majda type criterion for compressible viscous barotropic flows by Huang et al. （2011）. The results indicate that the nature of the blowup for compressible MHD models of viscous media is similar to the barotropic compressible Navier-Stokes equations and does not depend on further sophistication of the MHD model, in particular, it is independent of the temperature and magnetic field. It also reveals that the deformation tensor of the velocity field plays a more dominant role than the electromagnetic field and the temperature in regularity theory. Especially, the similar results also hold for compressible viscous heat-conductive Navier-Stokes flows, which extend the results established by Fan et al. （2010）, and I-Iuang and Li （2009）. In addition, the viscous coefficients are only restricted by the physical conditions in this paper.
