A class of nonlinear parabolic equation on a polygonal domain Ω R2 is inves- tigated in this paper. We introduce a finite element method on overlapping non-matching grids for the nonlinear parabolic equation based o...A class of nonlinear parabolic equation on a polygonal domain Ω R2 is inves- tigated in this paper. We introduce a finite element method on overlapping non-matching grids for the nonlinear parabolic equation based on the partition of unity method. We give the construction and convergence analysis for the semi-discrete and the fully discrete finite element methods. Moreover, we prove that the error of the discrete variational problem has good approximation properties. Our results are valid for any spatial dimensions. A numerical example to illustrate the theoretical results is also given.展开更多
In marine engineering,appendages such as fin stabilizers and/or T-foils are made to rotate and to reduce the motion of ships.Research on the hydrodynamics of ships fitted with active appendages has significantly impro...In marine engineering,appendages such as fin stabilizers and/or T-foils are made to rotate and to reduce the motion of ships.Research on the hydrodynamics of ships fitted with active appendages has significantly improved the design and control of such ships.However,most studies focus on fixed rather than rotating appendages,thereby ignoring the hydrodynamic unsteadiness of active appendages.To enhance the reliability and precision of the numerical simulations,we propose the use of overlapping grids for simulating advanced catamarans fitted with a pair of rotating T-foils under each bow.The fundamental purpose of the overlapping grid technique is to realize information exchange via regional overlap sharing in each subdomain of the computing domain,instead of using the method of boundary sharing,thus greatly alleviating the difficulty of generating the subdomain grid;moreover,the technique guarantees the quality of the subdomain grid.Within the main computational domain,a subdomain was allocated to accommodate the T-foil.Overlapping meshes near the interface between the two domains enable information flow during the simulation;the overlapping grids are updated at every iteration step because the subdomain rotates.The instantaneous trim and sinkage responses of the catamaran to the T-foil rotation were reproduced.From the moment the active T-foil stopped moving,there was no change in the ship’s sailing attitude,indicating that the response was in real time.By comparing with EFD data,the numerical results showed reasonable agreement,indicating the feasibility and effectiveness of the technique in simulating the hydrodynamics of ships fitted with active appendages.展开更多
The present study investigates the axisymmetric stagnation point radiativeflow of a Cu-Al2O3/water hybrid nanofluid over a radially stretched/shrunk disk.In this paper,a new mathematical model has been developed by ta...The present study investigates the axisymmetric stagnation point radiativeflow of a Cu-Al2O3/water hybrid nanofluid over a radially stretched/shrunk disk.In this paper,a new mathematical model has been developed by taking into consideration the concept of different nanoparticles concentration in a hybrid nanofluid,which are Brownian motion and thermophor-esis of nanoparticles.A new model for entropy generation has also been provided in the present study.The non-dimensional governing equations of the developed mathematical model are solved using newly developed and efficient overlapping grid spectral collocation method.Numerical stability and residual error test are provided here to show the accuracy of the numer-ical method in this mathematical model.The outcomes offluidflow,temperature,and two different types of concentration profiles are depicted,and described in graphical and tabular forms.For the limiting instances,comparison shows excellent agreement among current and results established in the literature.Increasing the strength of magneticfield is seen to increase the radial component offluid velocity as well as the entropy generated within the system.Two different nanofluid concentration profiles are increasing and decreasing with rising thermophor-esis and Brownian motion parameters,respectively,from a particular height above the disk because of the revised nanofluid boundary condition.Temperature profile increases here with increasing Biot number,and increasing Brinkman number causes higher entropy generation number for both stretching and shrinking disks.The enhanced thermal characteristics of the hybrid nanofluid over the single particle nanofluid has been observed.展开更多
This paper describes the use of overlapping grids for the calculation of flow around single and multiple-particle configurations at the micro scale. The basic equations for calculation are those for conservation of ma...This paper describes the use of overlapping grids for the calculation of flow around single and multiple-particle configurations at the micro scale. The basic equations for calculation are those for conservation of mass and momentum which are solved using a common Finite-Volume formulation. The hydrodynamic particle-particle and particle-wall interaction can be calculated by using an overlapping or Chimera grid scheme. With the grid structuring procedure it is possible to use simple and structured grids around the particles and the overall main grid geometry. The particle grids are lapped over the main grid such that they can move independently after each time step without remeshing the whole geometry. The paper gives results for the validation of the code developed for general test cases, for a rotating ellipsoid in simple shear flow, the flow around particles attached to a wall, the motion of a particle in the vicinity of a wall and some results for the flow through a packed bed configuration.展开更多
In this paper, we introduce a domain decomposition method with non-matching grids for solving Dirichlet exterior boundary problems by coupling of finite element method （FEM） and natural boundary element method（BEM...In this paper, we introduce a domain decomposition method with non-matching grids for solving Dirichlet exterior boundary problems by coupling of finite element method （FEM） and natural boundary element method（BEM）. We first derive the optimal energy error estimate of the nonconforming approximation generated by this method. Then we apply a Dirichlet-Neumann（D-N） alternating algorithm to solve the coupled discrete system. It will be shown that such iterative method possesses the optimal convergence. The numerical experiments testify our theoretical results.展开更多
基于重叠网格技术,VOF(volume of fluid)多相流模型以及改进型分离涡模型相结合方法,建立了基于主动通气下双体水下齐射降载增稳数值方法,分析了通气量对空泡形态、载荷特性及运动稳定性的影响规律。结果表明:在一定范围内,随着通气量...基于重叠网格技术,VOF(volume of fluid)多相流模型以及改进型分离涡模型相结合方法,建立了基于主动通气下双体水下齐射降载增稳数值方法,分析了通气量对空泡形态、载荷特性及运动稳定性的影响规律。结果表明:在一定范围内,随着通气量的增加,当通气空泡完全包裹航行体孔口下方区域后,横向载荷幅值和交变峰值均减小,同时,产生的扶偏力矩能够大幅度减小双发航行体之间狭长流域产生的流动干扰现象。另外,为了避免发生共振现象,设计航行体时应尽量使其固有频率在通气效应产生的低频范围之外。综合分析,主动通气方式对多体水下齐射运动姿态的不稳定性具有较好的改善作用。展开更多
基金Supported by the Natural Science Foundation of Hunan under Grant No. 06C713.
文摘A class of nonlinear parabolic equation on a polygonal domain Ω R2 is inves- tigated in this paper. We introduce a finite element method on overlapping non-matching grids for the nonlinear parabolic equation based on the partition of unity method. We give the construction and convergence analysis for the semi-discrete and the fully discrete finite element methods. Moreover, we prove that the error of the discrete variational problem has good approximation properties. Our results are valid for any spatial dimensions. A numerical example to illustrate the theoretical results is also given.
基金Supported by the National Natural Science Foundation of China(Grant No.51509053)
文摘In marine engineering,appendages such as fin stabilizers and/or T-foils are made to rotate and to reduce the motion of ships.Research on the hydrodynamics of ships fitted with active appendages has significantly improved the design and control of such ships.However,most studies focus on fixed rather than rotating appendages,thereby ignoring the hydrodynamic unsteadiness of active appendages.To enhance the reliability and precision of the numerical simulations,we propose the use of overlapping grids for simulating advanced catamarans fitted with a pair of rotating T-foils under each bow.The fundamental purpose of the overlapping grid technique is to realize information exchange via regional overlap sharing in each subdomain of the computing domain,instead of using the method of boundary sharing,thus greatly alleviating the difficulty of generating the subdomain grid;moreover,the technique guarantees the quality of the subdomain grid.Within the main computational domain,a subdomain was allocated to accommodate the T-foil.Overlapping meshes near the interface between the two domains enable information flow during the simulation;the overlapping grids are updated at every iteration step because the subdomain rotates.The instantaneous trim and sinkage responses of the catamaran to the T-foil rotation were reproduced.From the moment the active T-foil stopped moving,there was no change in the ship’s sailing attitude,indicating that the response was in real time.By comparing with EFD data,the numerical results showed reasonable agreement,indicating the feasibility and effectiveness of the technique in simulating the hydrodynamics of ships fitted with active appendages.
基金support of the North-Eastern Hill University,Shillong-793022,Meghalaya,Indiathe University of South Africa,Corner Christian de Wet and Pioneer Avenue,Florida Park,Roodepoort,1709,South Africa.
文摘The present study investigates the axisymmetric stagnation point radiativeflow of a Cu-Al2O3/water hybrid nanofluid over a radially stretched/shrunk disk.In this paper,a new mathematical model has been developed by taking into consideration the concept of different nanoparticles concentration in a hybrid nanofluid,which are Brownian motion and thermophor-esis of nanoparticles.A new model for entropy generation has also been provided in the present study.The non-dimensional governing equations of the developed mathematical model are solved using newly developed and efficient overlapping grid spectral collocation method.Numerical stability and residual error test are provided here to show the accuracy of the numer-ical method in this mathematical model.The outcomes offluidflow,temperature,and two different types of concentration profiles are depicted,and described in graphical and tabular forms.For the limiting instances,comparison shows excellent agreement among current and results established in the literature.Increasing the strength of magneticfield is seen to increase the radial component offluid velocity as well as the entropy generated within the system.Two different nanofluid concentration profiles are increasing and decreasing with rising thermophor-esis and Brownian motion parameters,respectively,from a particular height above the disk because of the revised nanofluid boundary condition.Temperature profile increases here with increasing Biot number,and increasing Brinkman number causes higher entropy generation number for both stretching and shrinking disks.The enhanced thermal characteristics of the hybrid nanofluid over the single particle nanofluid has been observed.
文摘This paper describes the use of overlapping grids for the calculation of flow around single and multiple-particle configurations at the micro scale. The basic equations for calculation are those for conservation of mass and momentum which are solved using a common Finite-Volume formulation. The hydrodynamic particle-particle and particle-wall interaction can be calculated by using an overlapping or Chimera grid scheme. With the grid structuring procedure it is possible to use simple and structured grids around the particles and the overall main grid geometry. The particle grids are lapped over the main grid such that they can move independently after each time step without remeshing the whole geometry. The paper gives results for the validation of the code developed for general test cases, for a rotating ellipsoid in simple shear flow, the flow around particles attached to a wall, the motion of a particle in the vicinity of a wall and some results for the flow through a packed bed configuration.
基金The work of this author was supported by Natural Science Foundation of China(G10371129) The work of this author was supported by the National Basic Research Program of China under the grant G19990328,2005CB321701 the National Natural Science Foundation of China.
文摘In this paper, we introduce a domain decomposition method with non-matching grids for solving Dirichlet exterior boundary problems by coupling of finite element method （FEM） and natural boundary element method（BEM）. We first derive the optimal energy error estimate of the nonconforming approximation generated by this method. Then we apply a Dirichlet-Neumann（D-N） alternating algorithm to solve the coupled discrete system. It will be shown that such iterative method possesses the optimal convergence. The numerical experiments testify our theoretical results.
文摘基于重叠网格技术,VOF(volume of fluid)多相流模型以及改进型分离涡模型相结合方法,建立了基于主动通气下双体水下齐射降载增稳数值方法,分析了通气量对空泡形态、载荷特性及运动稳定性的影响规律。结果表明:在一定范围内,随着通气量的增加,当通气空泡完全包裹航行体孔口下方区域后,横向载荷幅值和交变峰值均减小,同时,产生的扶偏力矩能够大幅度减小双发航行体之间狭长流域产生的流动干扰现象。另外,为了避免发生共振现象,设计航行体时应尽量使其固有频率在通气效应产生的低频范围之外。综合分析,主动通气方式对多体水下齐射运动姿态的不稳定性具有较好的改善作用。
