In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-d...In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+t2)is obtained,which is verified by the numerical results.展开更多
A three-dimensional, first order turbulence closure, thermal diffusion model is described in this paper. The governing equations consist of an equation of continuity, three components of momentum, conservation equatio...A three-dimensional, first order turbulence closure, thermal diffusion model is described in this paper. The governing equations consist of an equation of continuity, three components of momentum, conservation equations for salt, temperature and subgridscale energy, and an equation of state. In the model, according to the hypothesis of Kolmogorov and Prandtl, the viscosity coefficient of turbulent flow of homogeneous fluid is related to the local turbulent energy, and the horizontal and vertical exchange coefficients of mass, heat and momentum are computed with the introduction of subgridscale turbulence energy. The governing equations are solved by finite difference techniques. This model is applied to the Jiaozhou bay to predict thermal pollution by the Huangdao power plant. An instantaneous tidal current field is computed, then the distribution of temperature increment is predicted, and finally the effect of wind stress on thermal discharge is discussed.展开更多
基金the National Natural Science Fund(11661058,11761053)Natural Science Fund of Inner Mongolia Autonomous Region(2016MS0102,2017MS0107)+1 种基金Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-17-A07)National Undergraduate Innovative Training Project of Inner Mongolia University(201710126026).
文摘In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+t2)is obtained,which is verified by the numerical results.
基金This project was financially supported by the National Committee of Science and Technology Grants/903-85-08-05
文摘A three-dimensional, first order turbulence closure, thermal diffusion model is described in this paper. The governing equations consist of an equation of continuity, three components of momentum, conservation equations for salt, temperature and subgridscale energy, and an equation of state. In the model, according to the hypothesis of Kolmogorov and Prandtl, the viscosity coefficient of turbulent flow of homogeneous fluid is related to the local turbulent energy, and the horizontal and vertical exchange coefficients of mass, heat and momentum are computed with the introduction of subgridscale turbulence energy. The governing equations are solved by finite difference techniques. This model is applied to the Jiaozhou bay to predict thermal pollution by the Huangdao power plant. An instantaneous tidal current field is computed, then the distribution of temperature increment is predicted, and finally the effect of wind stress on thermal discharge is discussed.
