In this paper,we design a decoupled,linear,stable scheme with variable time step for solving a ferrohydrodynamics system.Based on the backward Euler scheme with variable time step for time discretization,this scheme d...In this paper,we design a decoupled,linear,stable scheme with variable time step for solving a ferrohydrodynamics system.Based on the backward Euler scheme with variable time step for time discretization,this scheme deals with nonlinear terms by explicit treatment.Meanwhile,we show the stability of the proposed scheme.Finally,some numerical experiments are provided to illustrate the accuracy and stability of the proposed scheme.展开更多
In this work, an unconditionally stable, decoupled, variable time step scheme is presentedfor the incompressible Navier-Stokes equations. Based on a scalar auxiliary variablein exponential function, this fully discret...In this work, an unconditionally stable, decoupled, variable time step scheme is presentedfor the incompressible Navier-Stokes equations. Based on a scalar auxiliary variablein exponential function, this fully discrete scheme combines the backward Euler schemefor temporal discretization with variable time step and a mixed finite element method forspatial discretization, where the nonlinear term is treated explicitly. Moreover, withoutany restriction on the time step, stability of the proposed scheme is discussed. Besides,error estimate is provided. Finally, some numerical results are presented to illustrate theperformances of the considered numerical scheme.展开更多
To reduce energy consumption on summer air conditioning,a novel seasonal soil cold storage mode using natural energy is presented and two-dimensional transient heat transfer model of U-tube is developed. The three pro...To reduce energy consumption on summer air conditioning,a novel seasonal soil cold storage mode using natural energy is presented and two-dimensional transient heat transfer model of U-tube is developed. The three processes of cold storage in winter,shut-down in transition season and cold extraction in summer are simulated by using sensitive heat capacity method with variable time step. The changing of U-tube outlet water temperature in different periods,daily cold storage and cold extraction are estimated. The temperature field of the U-tube and soil around the tube is investigated. Simulations show that seasonal soil cold storage using natural cold energy is feasible in the north to Changchun,which provides theoretical support for seasonal soil cold storage application.展开更多
基金supported by the Tianshan Talent Training Program of Xinjiang Uygur Autonomous Region(2023TSYCCX0103).
文摘In this paper,we design a decoupled,linear,stable scheme with variable time step for solving a ferrohydrodynamics system.Based on the backward Euler scheme with variable time step for time discretization,this scheme deals with nonlinear terms by explicit treatment.Meanwhile,we show the stability of the proposed scheme.Finally,some numerical experiments are provided to illustrate the accuracy and stability of the proposed scheme.
基金supported by the Natural Science Foundation of China(Grant No.12361077)by the Tianshan Talent Training Program of Xinjiang Uygur Autonomous Region(Grant No.2023TSYCCX0103)by the Natural Science Foundation of Xinjiang Uygur Autonomous Region(Grant No.2023D14014).
文摘In this work, an unconditionally stable, decoupled, variable time step scheme is presentedfor the incompressible Navier-Stokes equations. Based on a scalar auxiliary variablein exponential function, this fully discrete scheme combines the backward Euler schemefor temporal discretization with variable time step and a mixed finite element method forspatial discretization, where the nonlinear term is treated explicitly. Moreover, withoutany restriction on the time step, stability of the proposed scheme is discussed. Besides,error estimate is provided. Finally, some numerical results are presented to illustrate theperformances of the considered numerical scheme.
基金Sponsored by Heilongjiang Province Emphasis Science and Technology Project ( Grant No 2006G1662-00)
文摘To reduce energy consumption on summer air conditioning,a novel seasonal soil cold storage mode using natural energy is presented and two-dimensional transient heat transfer model of U-tube is developed. The three processes of cold storage in winter,shut-down in transition season and cold extraction in summer are simulated by using sensitive heat capacity method with variable time step. The changing of U-tube outlet water temperature in different periods,daily cold storage and cold extraction are estimated. The temperature field of the U-tube and soil around the tube is investigated. Simulations show that seasonal soil cold storage using natural cold energy is feasible in the north to Changchun,which provides theoretical support for seasonal soil cold storage application.
