In this paper,we develop a multi-scalar auxiliary variables(MSAV)scheme for the Cahn-Hilliard Magnetohydrodynamics system by introducing two scalar auxiliary variables(SAV).This scheme is linear,fully decoupled and un...In this paper,we develop a multi-scalar auxiliary variables(MSAV)scheme for the Cahn-Hilliard Magnetohydrodynamics system by introducing two scalar auxiliary variables(SAV).This scheme is linear,fully decoupled and unconditionally stable in energy.Subsequently,we provide a detailed implementation procedure for full decoupling.Thus,at each time step,only a series of linear differential equations with constant coefficients need to be solved.To validate the effectiveness of our approach,we conduct an error analysis for this first-order scheme.Finally,some numerical experiments are provided to verify the energy dissipation of the system and the convergence of the proposed approach.展开更多
Model of Casson nanofluid flow over a nonlinear shrinking surface is considered.Model of Tiwari and Das is applied to nanofluid comprising of sodium alginate with copper and silver.The governing nonlinear equations in...Model of Casson nanofluid flow over a nonlinear shrinking surface is considered.Model of Tiwari and Das is applied to nanofluid comprising of sodium alginate with copper and silver.The governing nonlinear equations incorporating the effects of the viscous dissipation are transformed into boundary value problems (BVPs) of ordinary differential equations (ODEs) by using appropriate similarity transformations.The resulting equations are converted into initial value problems (IVPs) using the shooting method which are then solved by Runge-Kutta method of fourth order.In order to determine the stability of the dual solutions obtained,stability analysis is performed and discovered that the first (second) solution is stable (unstable) and physically realizable (unrealizable).Both the thickness of the thermal boundary layer as well as temperature increase when the Casson parameter (β) is increased in the second solution.展开更多
An analytical approach was presented for estimating the factor of safety(FS) for slope failure, with consideration of the impact of a confined aquifer. An upward-moving wetting front from the confined water was assume...An analytical approach was presented for estimating the factor of safety(FS) for slope failure, with consideration of the impact of a confined aquifer. An upward-moving wetting front from the confined water was assumed and the pore water pressure distribution was then estimated and used to obtain the analytical expression of FS. Then, the validation of the theoretical analysis was applied based on an actual case in Hong Kong. It is shown that the presence of a confined aquifer leads to a lower FS value, and the impact rate of hydrostatic pressure on FS increases as the confined water pressure increases, approaching to a maximum value determined by the ratio of water density to saturated soil density. It is also presented that the contribution of hydrostatic pressure and hydrodynamic pressure to the slope stability vary with the confined aquifer pressure.展开更多
基金Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)Basic Research Plan of Shanxi Province(202203021211129)。
文摘In this paper,we develop a multi-scalar auxiliary variables(MSAV)scheme for the Cahn-Hilliard Magnetohydrodynamics system by introducing two scalar auxiliary variables(SAV).This scheme is linear,fully decoupled and unconditionally stable in energy.Subsequently,we provide a detailed implementation procedure for full decoupling.Thus,at each time step,only a series of linear differential equations with constant coefficients need to be solved.To validate the effectiveness of our approach,we conduct an error analysis for this first-order scheme.Finally,some numerical experiments are provided to verify the energy dissipation of the system and the convergence of the proposed approach.
基金Universiti Utara Malaysia (UUM) for the moral and financial support in conducting this research
文摘Model of Casson nanofluid flow over a nonlinear shrinking surface is considered.Model of Tiwari and Das is applied to nanofluid comprising of sodium alginate with copper and silver.The governing nonlinear equations incorporating the effects of the viscous dissipation are transformed into boundary value problems (BVPs) of ordinary differential equations (ODEs) by using appropriate similarity transformations.The resulting equations are converted into initial value problems (IVPs) using the shooting method which are then solved by Runge-Kutta method of fourth order.In order to determine the stability of the dual solutions obtained,stability analysis is performed and discovered that the first (second) solution is stable (unstable) and physically realizable (unrealizable).Both the thickness of the thermal boundary layer as well as temperature increase when the Casson parameter (β) is increased in the second solution.
基金Project(R5110012)supported by Special Foundation for Distinguished Young Scholars of Zhejiang Province,ChinaProject(2009C33117)supported by The General Program of Natural Science Foundation of Zhejiang Province,China
文摘An analytical approach was presented for estimating the factor of safety(FS) for slope failure, with consideration of the impact of a confined aquifer. An upward-moving wetting front from the confined water was assumed and the pore water pressure distribution was then estimated and used to obtain the analytical expression of FS. Then, the validation of the theoretical analysis was applied based on an actual case in Hong Kong. It is shown that the presence of a confined aquifer leads to a lower FS value, and the impact rate of hydrostatic pressure on FS increases as the confined water pressure increases, approaching to a maximum value determined by the ratio of water density to saturated soil density. It is also presented that the contribution of hydrostatic pressure and hydrodynamic pressure to the slope stability vary with the confined aquifer pressure.
