In this paper,we establish the global regularity of 2D leray-alpha regularized tropical climate models.The global strong solution to the system with a half Laplacian of the first baroclinic model of velocity(Av)and th...In this paper,we establish the global regularity of 2D leray-alpha regularized tropical climate models.The global strong solution to the system with a half Laplacian of the first baroclinic model of velocity(Av)and thermal diffusion(△θ)or with only the dissipation of the barotropic mode(-Au)are obtained.展开更多
Linear/nonlinear and Stokes based-stabilizations for the filter equations for damping out primitive variable(PV)solutions corrupted by uniformly distributed randomnoises are numerically studied through the natural con...Linear/nonlinear and Stokes based-stabilizations for the filter equations for damping out primitive variable(PV)solutions corrupted by uniformly distributed randomnoises are numerically studied through the natural convection(NC)aswell as the mixed convection(MC)environment.The most recognizable filter-scheme is based on a combination of the negative Laplace equation multiplied with the selection of the spatial scale and a linear function in order to preserve the uniqueness of the filtered solution.A more complicated filter-scheme,based on a Stokes problem which couples a filtered velocity and a filtered(artificial)pressure(or Lagrange multiplier)in order to enforce the incompressibility constraint,is also studied.Linear and Stokes basedfilters via nested iterative(NI)filters and the consistent splitting scheme(CSS)are proposed for the NC/MC problems.Inspired by the total-variation(TV)model of image diffusion,well preserved feature flow patterns from the corrupted NC/MC environment are obtained by TV-Stokes based-filters together with the CSS.Our experimental results show that our proposed algorithms are effective and efficient in eliminating the unwanted spurious oscillations and preserving the accuracy of thermal convective fluid flows.展开更多
基金partially supported by the National Natural Science Foundation of China(No.11471103).
文摘In this paper,we establish the global regularity of 2D leray-alpha regularized tropical climate models.The global strong solution to the system with a half Laplacian of the first baroclinic model of velocity(Av)and thermal diffusion(△θ)or with only the dissipation of the barotropic mode(-Au)are obtained.
文摘Linear/nonlinear and Stokes based-stabilizations for the filter equations for damping out primitive variable(PV)solutions corrupted by uniformly distributed randomnoises are numerically studied through the natural convection(NC)aswell as the mixed convection(MC)environment.The most recognizable filter-scheme is based on a combination of the negative Laplace equation multiplied with the selection of the spatial scale and a linear function in order to preserve the uniqueness of the filtered solution.A more complicated filter-scheme,based on a Stokes problem which couples a filtered velocity and a filtered(artificial)pressure(or Lagrange multiplier)in order to enforce the incompressibility constraint,is also studied.Linear and Stokes basedfilters via nested iterative(NI)filters and the consistent splitting scheme(CSS)are proposed for the NC/MC problems.Inspired by the total-variation(TV)model of image diffusion,well preserved feature flow patterns from the corrupted NC/MC environment are obtained by TV-Stokes based-filters together with the CSS.Our experimental results show that our proposed algorithms are effective and efficient in eliminating the unwanted spurious oscillations and preserving the accuracy of thermal convective fluid flows.
