The lower-upper symmetric Gauss-Seidel （LU-SGS） implicit relaxation has been widely used because it has the merits of less dependency on grid topology, low numerical complexity and modest memory requirements. In ori...The lower-upper symmetric Gauss-Seidel （LU-SGS） implicit relaxation has been widely used because it has the merits of less dependency on grid topology, low numerical complexity and modest memory requirements. In original LU-SGS scheme, the implicit system matrix is constructed based on the splitting of convective flux Jacobian according to its spectral radius. Although this treatment has the merit of reducing computational complexity and helps to ensure the diagonally dominant property of the implicit system matrix, it can also cause serious distortions on the implicit system matrix because too many approximations are introduced by this splitting method if the contravariant velocity is small or close to sonic speed. To overcome this shortcoming, an improved LU-SGS scheme with a hybrid construction method for the implicit system matrix is developed in this paper. The hybrid way is that： on the cell faces having small contravariant velocity or transonic contravariant velocity, the accurate derivative of the convective flux term is used to construct more accurate implicit system matrix, while the original Jacobian splitting method is adopted on the other cell faces to reduce computational complexity and ensure the diagonally dominant property of the implicit system matrix. To investigate the convergence performance of the improved LU-SGS scheme, 2D and 3D turbulent flows around the NACA0012 airfoil, RAE2822 airfoil and LANN wing are simulated on hybrid unstructured meshes. The nu- merical results show that the improved LU-SGS scheme is significantly more efficient than the original LU-SGS scheme.展开更多
The rheological properties of high and low density polyethylene(HDPE and LDPE)melts were investigated by using capillary rheometer,and preliminary verification for the half natural converging angle equation of non-New...The rheological properties of high and low density polyethylene(HDPE and LDPE)melts were investigated by using capillary rheometer,and preliminary verification for the half natural converging angle equation of non-Newtonian fluids which was derived in a prerious work was made.The results showed that the natural convergent angles of the sample melts calculated by using the equation were in correspondence with the values reported in the literature under the relevant conditions.展开更多
In this paper,we first establish a new fractional magnetohydrodynamic(MHD)coupled flow and heat transfer model for a generalized second-grade fluid.This coupled model consists of a fractional momentum equation and a h...In this paper,we first establish a new fractional magnetohydrodynamic(MHD)coupled flow and heat transfer model for a generalized second-grade fluid.This coupled model consists of a fractional momentum equation and a heat conduction equation with a generalized form of Fourier law.The second-order fractional backward difference formula is applied to the temporal discretization and the Legendre spectral method is used for the spatial discretization.The fully discrete scheme is proved to be stable and convergent with an accuracy of O(τ^(2)+N-r),whereτis the time step-size and N is the polynomial degree.To reduce the memory requirements and computational cost,a fast method is developed,which is based on a globally uniform approximation of the trapezoidal rule for integrals on the real line.The strict convergence of the numerical scheme with this fast method is proved.We present the results of several numerical experiments to verify the effectiveness of the proposed method.Finally,we simulate the unsteady fractional MHD flow and heat transfer of the generalized second-grade fluid through a porous medium.The effects of the relevant parameters on the velocity and temperature are presented and analyzed in detail.展开更多
Conversion of hourly dispatch cases derived using DC optimal power flow(DCOPF)to AC power flow(ACPF)case is often challenging and requires arduous human analysis and intervention.This paper proposes an automated two-s...Conversion of hourly dispatch cases derived using DC optimal power flow(DCOPF)to AC power flow(ACPF)case is often challenging and requires arduous human analysis and intervention.This paper proposes an automated two-stage approach to solve ACPF formulated from DCOPF dispatch cases.The first stage involved the use of the conventional Newton Raphson method to solve the ACPF from flat start,then ACPF cases that are unsolvable in the first stage are subjected to a hotstarting incremental method,based on homotopy continuation,in the second stage.Critical tasks such as the addition of reactive power compensation and tuning of voltage setpoints that typically require human intervention were automated using a criteriabased selection method and optimal power flow respectively.Two datasets with hourly dispatches for the 243-bus reduced WECC system were used to test the proposed method.The algorithm was able to convert 100%of the first set of dispatch cases to solved ACPF cases.In the second dataset with suspect dispatch cases to represent an extreme conversion scenario,the algorithm created solved ACPF cases that satisfied a defined success criterion for 77.8%of the dispatch cases.The average run time for the hotstarting algorithm to create a solved ACPF case for a dispatch was less than 1 minute for the reduced WECC system.展开更多
The numerical solution of compressible flows has become more prevalent than that of incompressible flows.With the help of the artificial compressibility approach,incompressible flows can be solved numerically using th...The numerical solution of compressible flows has become more prevalent than that of incompressible flows.With the help of the artificial compressibility approach,incompressible flows can be solved numerically using the same methods as compressible ones.The artificial compressibility scheme is thus widely used to numerically solve incompressible Navier-Stokes equations.Any numerical method highly depends on its accuracy and speed of convergence.Although the artificial compressibility approach is utilized in several numerical simulations,the effect of the compressibility factor on the accuracy of results and convergence speed has not been investigated for nanofluid flows in previous studies.Therefore,this paper assesses the effect of this factor on the convergence speed and accuracy of results for various types of thermo-flow.To improve the stability and convergence speed of time discretizations,the fifth-order Runge-Kutta method is applied.A computer program has been written in FORTRAN to solve the discretized equations in different Reynolds and Grashof numbers for various grids.The results demonstrate that the artificial compressibility factor has a noticeable effect on the accuracy and convergence rate of the simulation.The optimum artificial compressibility is found to be between 1 and 5.These findings can be utilized to enhance the performance of commercial numerical simulation tools,including ANSYS and COMSOL.展开更多
Power flow calculation is the basis of power grid planning and many system analysis tasks require convergent power flow conditions.To address the unsolvable power flow problem caused by the reactive power imbalance,a ...Power flow calculation is the basis of power grid planning and many system analysis tasks require convergent power flow conditions.To address the unsolvable power flow problem caused by the reactive power imbalance,a method for adjusting reactive power flow convergence based on deep reinforcement learning is proposed.The deep reinforcement learning method takes switching parallel reactive compensation as the action space and sets the reward value based on the power flow convergence and reactive power adjustment.For the non-convergence power flow,the 500 kV nodes with reactive power compensation devices on the low-voltage side are converted into PV nodes by node type switching.And the quantified reactive power non-convergence index is acquired.Then,the action space and reward value of deep reinforcement learning are reasonably designed and the adjustment strategy is obtained by taking the reactive power non-convergence index as the algorithm state space.Finally,the effectiveness of the power flow convergence adjustment algorithm is verified by an actual power grid system in a province.展开更多
In[Dai et al.,Multi.Model.Simul.18(4)(2020)],a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn-Sham density functional theory,based on which a linearized method was deve...In[Dai et al.,Multi.Model.Simul.18(4)(2020)],a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn-Sham density functional theory,based on which a linearized method was developed in[Hu et al.,EAJAM.13(2)(2023)]for further improving the numerical efficiency.In this paper,a complete convergence analysis is delivered for such a linearized method for the all-electron Kohn-Sham model.Temporally,the convergence,the asymptotic stability,as well as the structure-preserving property of the linearized numerical scheme in the method is discussed following previous works,while spatially,the convergence of the h-adaptive mesh method is demonstrated following[Chen et al.,Multi.Model.Simul.12(2014)],with a key study on the boundedness of the Kohn-Sham potential for the all-electron Kohn-Sham model.Numerical examples confirm the theoretical results very well.展开更多
基金Foundation item： National Natural Science Foundation of China （10802067）
文摘The lower-upper symmetric Gauss-Seidel （LU-SGS） implicit relaxation has been widely used because it has the merits of less dependency on grid topology, low numerical complexity and modest memory requirements. In original LU-SGS scheme, the implicit system matrix is constructed based on the splitting of convective flux Jacobian according to its spectral radius. Although this treatment has the merit of reducing computational complexity and helps to ensure the diagonally dominant property of the implicit system matrix, it can also cause serious distortions on the implicit system matrix because too many approximations are introduced by this splitting method if the contravariant velocity is small or close to sonic speed. To overcome this shortcoming, an improved LU-SGS scheme with a hybrid construction method for the implicit system matrix is developed in this paper. The hybrid way is that： on the cell faces having small contravariant velocity or transonic contravariant velocity, the accurate derivative of the convective flux term is used to construct more accurate implicit system matrix, while the original Jacobian splitting method is adopted on the other cell faces to reduce computational complexity and ensure the diagonally dominant property of the implicit system matrix. To investigate the convergence performance of the improved LU-SGS scheme, 2D and 3D turbulent flows around the NACA0012 airfoil, RAE2822 airfoil and LANN wing are simulated on hybrid unstructured meshes. The nu- merical results show that the improved LU-SGS scheme is significantly more efficient than the original LU-SGS scheme.
文摘The rheological properties of high and low density polyethylene(HDPE and LDPE)melts were investigated by using capillary rheometer,and preliminary verification for the half natural converging angle equation of non-Newtonian fluids which was derived in a prerious work was made.The results showed that the natural convergent angles of the sample melts calculated by using the equation were in correspondence with the values reported in the literature under the relevant conditions.
基金supported by the Project of the National Key R&D Program(Grant No.2021YFA1000202)National Natural Science Foundation of China(Grant Nos.12120101001,12001326 and 12171283)+2 种基金Natural Science Foundation of Shandong Province(Grant Nos.ZR2021ZD03,ZR2020QA032 and ZR2019ZD42)China Postdoctoral Science Foundation(Grant Nos.BX20190191 and 2020M672038)the Startup Fund from Shandong University(Grant No.11140082063130)。
文摘In this paper,we first establish a new fractional magnetohydrodynamic(MHD)coupled flow and heat transfer model for a generalized second-grade fluid.This coupled model consists of a fractional momentum equation and a heat conduction equation with a generalized form of Fourier law.The second-order fractional backward difference formula is applied to the temporal discretization and the Legendre spectral method is used for the spatial discretization.The fully discrete scheme is proved to be stable and convergent with an accuracy of O(τ^(2)+N-r),whereτis the time step-size and N is the polynomial degree.To reduce the memory requirements and computational cost,a fast method is developed,which is based on a globally uniform approximation of the trapezoidal rule for integrals on the real line.The strict convergence of the numerical scheme with this fast method is proved.We present the results of several numerical experiments to verify the effectiveness of the proposed method.Finally,we simulate the unsteady fractional MHD flow and heat transfer of the generalized second-grade fluid through a porous medium.The effects of the relevant parameters on the velocity and temperature are presented and analyzed in detail.
基金This work was supported by the ERC Program of the National Science Foundation and DOE under NSF Award Number EEC-1041877the CURENT Industry Partnership Program,and the Bredesen Centre,University of Tennessee,Knoxville.
文摘Conversion of hourly dispatch cases derived using DC optimal power flow(DCOPF)to AC power flow(ACPF)case is often challenging and requires arduous human analysis and intervention.This paper proposes an automated two-stage approach to solve ACPF formulated from DCOPF dispatch cases.The first stage involved the use of the conventional Newton Raphson method to solve the ACPF from flat start,then ACPF cases that are unsolvable in the first stage are subjected to a hotstarting incremental method,based on homotopy continuation,in the second stage.Critical tasks such as the addition of reactive power compensation and tuning of voltage setpoints that typically require human intervention were automated using a criteriabased selection method and optimal power flow respectively.Two datasets with hourly dispatches for the 243-bus reduced WECC system were used to test the proposed method.The algorithm was able to convert 100%of the first set of dispatch cases to solved ACPF cases.In the second dataset with suspect dispatch cases to represent an extreme conversion scenario,the algorithm created solved ACPF cases that satisfied a defined success criterion for 77.8%of the dispatch cases.The average run time for the hotstarting algorithm to create a solved ACPF case for a dispatch was less than 1 minute for the reduced WECC system.
基金The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through the Large Groups Project under grant number RGP.2/235/43.
文摘The numerical solution of compressible flows has become more prevalent than that of incompressible flows.With the help of the artificial compressibility approach,incompressible flows can be solved numerically using the same methods as compressible ones.The artificial compressibility scheme is thus widely used to numerically solve incompressible Navier-Stokes equations.Any numerical method highly depends on its accuracy and speed of convergence.Although the artificial compressibility approach is utilized in several numerical simulations,the effect of the compressibility factor on the accuracy of results and convergence speed has not been investigated for nanofluid flows in previous studies.Therefore,this paper assesses the effect of this factor on the convergence speed and accuracy of results for various types of thermo-flow.To improve the stability and convergence speed of time discretizations,the fifth-order Runge-Kutta method is applied.A computer program has been written in FORTRAN to solve the discretized equations in different Reynolds and Grashof numbers for various grids.The results demonstrate that the artificial compressibility factor has a noticeable effect on the accuracy and convergence rate of the simulation.The optimum artificial compressibility is found to be between 1 and 5.These findings can be utilized to enhance the performance of commercial numerical simulation tools,including ANSYS and COMSOL.
基金This work was partly supported by the Technology Project of State Grid Jiangsu Electric Power Co.,Ltd.,China,under Grant No.J2022095.
文摘Power flow calculation is the basis of power grid planning and many system analysis tasks require convergent power flow conditions.To address the unsolvable power flow problem caused by the reactive power imbalance,a method for adjusting reactive power flow convergence based on deep reinforcement learning is proposed.The deep reinforcement learning method takes switching parallel reactive compensation as the action space and sets the reward value based on the power flow convergence and reactive power adjustment.For the non-convergence power flow,the 500 kV nodes with reactive power compensation devices on the low-voltage side are converted into PV nodes by node type switching.And the quantified reactive power non-convergence index is acquired.Then,the action space and reward value of deep reinforcement learning are reasonably designed and the adjustment strategy is obtained by taking the reactive power non-convergence index as the algorithm state space.Finally,the effectiveness of the power flow convergence adjustment algorithm is verified by an actual power grid system in a province.
基金partially funded by the Hunan National Applied Mathematics Center of Hunan Provincial Science and Technology Department(Grant No.2020ZYT003)by the RSF-NSFC Cooperation project(Grant No.12261131501)+4 种基金by the Excellent youth project of the Hunan Education Department(Grant No.19B543)partially supported by the National Natural Science Foundation of China(Grant Nos.11922120 and 11871489)by the FDCT of Macao SAR(Grant No.0082/2020/A2)by the MYRG of the University of Macao(Grant No.MYRG2020-00265-FST)by the Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications(Grant No.2020B1212030001).
文摘In[Dai et al.,Multi.Model.Simul.18(4)(2020)],a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn-Sham density functional theory,based on which a linearized method was developed in[Hu et al.,EAJAM.13(2)(2023)]for further improving the numerical efficiency.In this paper,a complete convergence analysis is delivered for such a linearized method for the all-electron Kohn-Sham model.Temporally,the convergence,the asymptotic stability,as well as the structure-preserving property of the linearized numerical scheme in the method is discussed following previous works,while spatially,the convergence of the h-adaptive mesh method is demonstrated following[Chen et al.,Multi.Model.Simul.12(2014)],with a key study on the boundedness of the Kohn-Sham potential for the all-electron Kohn-Sham model.Numerical examples confirm the theoretical results very well.
