A new mixed scheme which combines the variation of constants and the H1-Galerkin mixed finite element method is constructed for nonlinear Sobolev equation with nonlinear con- vection term. Optimal error estimates are ...A new mixed scheme which combines the variation of constants and the H1-Galerkin mixed finite element method is constructed for nonlinear Sobolev equation with nonlinear con- vection term. Optimal error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are given to confirm the theoretical analysis of the proposed method.展开更多
A boundary element method for simulating thermocapillary convection in a two-layer immiscible fluid system with flat and free interface has been developed.The divergence theorem is applied to the non-linear convective...A boundary element method for simulating thermocapillary convection in a two-layer immiscible fluid system with flat and free interface has been developed.The divergence theorem is applied to the non-linear convective volume integral of the boundary element formulation with the pressure penalty function.Consequently,velocity gradients are eliminated and the complete formulation is written in terms of velocity.This avoids the difficulty of convective discretizations and provides considerable reductions in storage and computational requirements while improving accuracy.In this paper,we give the influence of different parameters(Marangoni number, Reynolds number)on thermocapillary convection in cavity with two-layer immiscible fluids.As shown by the numerical results,when the physical parameters between liquid encapsulant and melt are chosen appropriately, the detrimental flow in the bottom melt layer can be greatly suppressed.The influence of the free interface on thermocapillary convection is also shown.展开更多
A boundary element method has been developed for analysing heat transport phenomena in solitary wave on falling thin liquid films at high Reynolds numbers. The divergence theorem is applied to the non-linear convectiv...A boundary element method has been developed for analysing heat transport phenomena in solitary wave on falling thin liquid films at high Reynolds numbers. The divergence theorem is applied to the non-linear convective volume integral of the boundary element formulation with the pressure penalty function. Consequently, velocity and temperature gradients are eliminated, and the complete formulation is written in terms of velocity and temperature. This provides considerable reduction in storage and computational requirements while improving accuracy. The non-linear equation systems of boundary element discretization are solved by the quasi-Newton iterative scheme with Broyden's update. The streamline maps and the temperature distributions in solitary wave and wavy film flow have been obtained, and the variations of Nusselt numbers along the wall-liquid interface are also given. There are large cross-flow velocities and S-shape temperature distributions in the recirculating region of solitary wave. This special flow and thermal process can be a mechanism to enhance heat transport.展开更多
基金Supported by National Natural Science Fund of China (11061021)Key Project of Chinese Ministry of Education (12024)+2 种基金Natural Science Fund of Inner Mongolia Autonomous Region (2012MS0108,2012MS0106,2011BS0102)Scientific Research Projection of Higher Schools of Inner Mongolia (NJZZ12011,NJZY13199)Program of Higher-level talents of Inner Mongolia University (125119,Z200901004,30105-125132)
文摘A new mixed scheme which combines the variation of constants and the H1-Galerkin mixed finite element method is constructed for nonlinear Sobolev equation with nonlinear con- vection term. Optimal error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are given to confirm the theoretical analysis of the proposed method.
基金Project supported by the National Natural Science Foundation of China
文摘A boundary element method for simulating thermocapillary convection in a two-layer immiscible fluid system with flat and free interface has been developed.The divergence theorem is applied to the non-linear convective volume integral of the boundary element formulation with the pressure penalty function.Consequently,velocity gradients are eliminated and the complete formulation is written in terms of velocity.This avoids the difficulty of convective discretizations and provides considerable reductions in storage and computational requirements while improving accuracy.In this paper,we give the influence of different parameters(Marangoni number, Reynolds number)on thermocapillary convection in cavity with two-layer immiscible fluids.As shown by the numerical results,when the physical parameters between liquid encapsulant and melt are chosen appropriately, the detrimental flow in the bottom melt layer can be greatly suppressed.The influence of the free interface on thermocapillary convection is also shown.
基金This project was financially supported by the National Natural Science Foundation of China
文摘A boundary element method has been developed for analysing heat transport phenomena in solitary wave on falling thin liquid films at high Reynolds numbers. The divergence theorem is applied to the non-linear convective volume integral of the boundary element formulation with the pressure penalty function. Consequently, velocity and temperature gradients are eliminated, and the complete formulation is written in terms of velocity and temperature. This provides considerable reduction in storage and computational requirements while improving accuracy. The non-linear equation systems of boundary element discretization are solved by the quasi-Newton iterative scheme with Broyden's update. The streamline maps and the temperature distributions in solitary wave and wavy film flow have been obtained, and the variations of Nusselt numbers along the wall-liquid interface are also given. There are large cross-flow velocities and S-shape temperature distributions in the recirculating region of solitary wave. This special flow and thermal process can be a mechanism to enhance heat transport.
