A numerical research on magnetohydrodynamic mixed convection flow in a lid-driven trapezoidal enclosure at non-uniform heating of bottom wall has been studied numerically. The enclosure consists of insulated top wall ...A numerical research on magnetohydrodynamic mixed convection flow in a lid-driven trapezoidal enclosure at non-uniform heating of bottom wall has been studied numerically. The enclosure consists of insulated top wall and cold side walls, too. It also contains a heated triangular block (<em>Rot</em> = 0<span style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">°</span> - 90<span style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">°</span>) located somewhere inside the enclosure. The boundary top wall of the enclosure is moving through uniform speed <em>U</em><sub>0</sub>. The geometry of the model has been represented mathematically by coupled governing equations in accordance with proper boundary conditions and then a two-dimensional Galerkin finite element based numerical approach has been adopted to solve this paper. The numerical computations have been carried out for the wide range of parameters Prandtl number (0.5 ≤ <em>Pr</em> ≤ 2), Reynolds number (60 ≤ <em>Re</em> ≤ 120), Rayleigh number (<em>Ra</em> = 10<sup>3</sup>) and Hartmann number (<em>Ha</em> = 20) taking with different rotations of heated triangular block. The results have been shown in the form of streamlines, temperature patterns or isotherms, average Nusselt number and average bulk temperature of the fluid in the enclosure at non-uniform heating of bottom wall. It is also indicated that both the streamlines, isotherm patterns strongly depend on the aforesaid governing parameters and location of the triangular block but the thermal conductivity of the triangular block has a noteworthy role on the isotherm pattern lines. Moreover, the variation of <em>Nu</em><sub>av</sub> of hot bottom wall and <em>θ</em><sub>av</sub> in the enclosure is demonstrated here to show the characteristics of heat transfer in the enclosure.展开更多
This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster aroun...This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster around 0 or 1 under mild conditions.The limited numerical results show that the TPTS preconditioner is more efficient than the classic block-diagonal and block-triangular preconditioners when applied to the flexible generalized minimal residual(FGMRES)method.展开更多
In this paper, we provide new preconditioner for saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioner is block triangular diagonal with two variable relaxation paremeters and it i...In this paper, we provide new preconditioner for saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioner is block triangular diagonal with two variable relaxation paremeters and it is extension of results in [1] and [2]. Theoretical analysis shows that all eigenvalues of preconditioned matrix is strongly clustered. Finally, numerical tests confirm our analysis.展开更多
Mining projects especially relating to limestone deposits require an accurate knowledge of tonnage and grade,for both short and long-term planning.This is often difficult to establish as detailed exploration operation...Mining projects especially relating to limestone deposits require an accurate knowledge of tonnage and grade,for both short and long-term planning.This is often difficult to establish as detailed exploration operations,which are required to get the accurate description of the deposit,are costly and time consuming.Geologists and mining engineers usually make use of geometric and geostatistical methods,for estimating the tonnage and grade of ore reserves.However,explicit assessments into the differences between these methods have not been reported in literature.To bridge this research gap,a comparative study is carried out to compare the qualitative reserve of Oyo-Iwa limestone deposit located in Nigeria,using geometric and geostatistical methods.The geometric method computes the reserve of the limestone deposit as 74,536,820 t(mean calcite,CaO grade=52.15)and 99,674,793 t(mean calcite,CaO grade=52.32),for the Northern and Southern zones of the deposit,respectively.On the other hand,the geostatistical method calculates the reserve as 81,626,729.65 t(mean calcite,CaO grade=53.36)and 100,098,697.46 t(mean calcite,CaO grade=52.96),for the two zones,respectively.The small relative difference in tonnage estimation between the two methods(i.e.,9.51%and 0.43%),proves that the geometric method is effective for tonnage estimation.In contrast,the relative difference in grade estimation between the two methods(i.e.,2.32%and 1.26%)is not negligible,and could be crucial in maintaining the profitability of the project.The geostatistical method is,therefore,more suitable,reliable and preferable for grade estimation,since it involves the use of spatial modelling and cross-validated interpolation.In addition,the geostatistical method is used to produce quality maps and three-dimensional(3-D)perspective view of the limestone deposit.The quality maps and 3-D view of the limestone deposit reveal the variability of the limestone grade within the deposit,and it is useful for operational management of the limestone raw materials.The qualitative mapping of the limestone deposit is key to effective production scheduling and accurate projection of raw materials for cement production.展开更多
文摘A numerical research on magnetohydrodynamic mixed convection flow in a lid-driven trapezoidal enclosure at non-uniform heating of bottom wall has been studied numerically. The enclosure consists of insulated top wall and cold side walls, too. It also contains a heated triangular block (<em>Rot</em> = 0<span style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">°</span> - 90<span style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">°</span>) located somewhere inside the enclosure. The boundary top wall of the enclosure is moving through uniform speed <em>U</em><sub>0</sub>. The geometry of the model has been represented mathematically by coupled governing equations in accordance with proper boundary conditions and then a two-dimensional Galerkin finite element based numerical approach has been adopted to solve this paper. The numerical computations have been carried out for the wide range of parameters Prandtl number (0.5 ≤ <em>Pr</em> ≤ 2), Reynolds number (60 ≤ <em>Re</em> ≤ 120), Rayleigh number (<em>Ra</em> = 10<sup>3</sup>) and Hartmann number (<em>Ha</em> = 20) taking with different rotations of heated triangular block. The results have been shown in the form of streamlines, temperature patterns or isotherms, average Nusselt number and average bulk temperature of the fluid in the enclosure at non-uniform heating of bottom wall. It is also indicated that both the streamlines, isotherm patterns strongly depend on the aforesaid governing parameters and location of the triangular block but the thermal conductivity of the triangular block has a noteworthy role on the isotherm pattern lines. Moreover, the variation of <em>Nu</em><sub>av</sub> of hot bottom wall and <em>θ</em><sub>av</sub> in the enclosure is demonstrated here to show the characteristics of heat transfer in the enclosure.
基金the National Natural Science Foundation of China under Grant Nos.61273311 and 61803247.
文摘This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster around 0 or 1 under mild conditions.The limited numerical results show that the TPTS preconditioner is more efficient than the classic block-diagonal and block-triangular preconditioners when applied to the flexible generalized minimal residual(FGMRES)method.
文摘In this paper, we provide new preconditioner for saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioner is block triangular diagonal with two variable relaxation paremeters and it is extension of results in [1] and [2]. Theoretical analysis shows that all eigenvalues of preconditioned matrix is strongly clustered. Finally, numerical tests confirm our analysis.
文摘Mining projects especially relating to limestone deposits require an accurate knowledge of tonnage and grade,for both short and long-term planning.This is often difficult to establish as detailed exploration operations,which are required to get the accurate description of the deposit,are costly and time consuming.Geologists and mining engineers usually make use of geometric and geostatistical methods,for estimating the tonnage and grade of ore reserves.However,explicit assessments into the differences between these methods have not been reported in literature.To bridge this research gap,a comparative study is carried out to compare the qualitative reserve of Oyo-Iwa limestone deposit located in Nigeria,using geometric and geostatistical methods.The geometric method computes the reserve of the limestone deposit as 74,536,820 t(mean calcite,CaO grade=52.15)and 99,674,793 t(mean calcite,CaO grade=52.32),for the Northern and Southern zones of the deposit,respectively.On the other hand,the geostatistical method calculates the reserve as 81,626,729.65 t(mean calcite,CaO grade=53.36)and 100,098,697.46 t(mean calcite,CaO grade=52.96),for the two zones,respectively.The small relative difference in tonnage estimation between the two methods(i.e.,9.51%and 0.43%),proves that the geometric method is effective for tonnage estimation.In contrast,the relative difference in grade estimation between the two methods(i.e.,2.32%and 1.26%)is not negligible,and could be crucial in maintaining the profitability of the project.The geostatistical method is,therefore,more suitable,reliable and preferable for grade estimation,since it involves the use of spatial modelling and cross-validated interpolation.In addition,the geostatistical method is used to produce quality maps and three-dimensional(3-D)perspective view of the limestone deposit.The quality maps and 3-D view of the limestone deposit reveal the variability of the limestone grade within the deposit,and it is useful for operational management of the limestone raw materials.The qualitative mapping of the limestone deposit is key to effective production scheduling and accurate projection of raw materials for cement production.
