This study is devoted to the computational fluid dynamics (CFD) modeling of steady laminar mixed convection flow and heat transfer in lid driven cavity (10 ≤ Re ≤ 1000). The ratio of the height to the width of the c...This study is devoted to the computational fluid dynamics (CFD) modeling of steady laminar mixed convection flow and heat transfer in lid driven cavity (10 ≤ Re ≤ 1000). The ratio of the height to the width of the cavity is ranged over H/L = 0.5 to 1.5. The governing equations are solved using commercial finite volume package FLUENT to visualize the nature of the flow and estimate the heat transfer inside the cavity for different aspect ratio. The simulation results are presented in terms of average Nusselt number of the hot wall, velocity profile, and temperature contours. It was found that the average Nusselt number inside the cavity is strongly governed by the aspect ratio as well as the Reynolds number. A parametric study is conducted to demonstrate the effect of aspect ratio on the flow and heat transfer characteristics. It is found that heat transfer enhancement was obtained by decreasing the aspect ratio and/or increasing the Reynolds number.展开更多
This study presents the LES(large eddy simulation)of forced convection in laminar and two dimensional turbulent flows when the flow reaches the steady state.The main purpose is the evaluation of a developed numerical ...This study presents the LES(large eddy simulation)of forced convection in laminar and two dimensional turbulent flows when the flow reaches the steady state.The main purpose is the evaluation of a developed numerical methodology for the simulation of forced convection flows at various Reynolds numbers(100_〈Rex〈_10,000)and for a fixed Prandtl number(Pr=1.0).The hexahedral eight-node FEM(finite element method)with an explicit Taylor-Galerkin scheme is used to obtain the numerical solutions of the conservation equations of mass,momentum and energy.The Smagorinsky model is employed for the sub-grid treatment.The time-averaged velocity and temperature profiles are compared with results of literature and a CFD(computational fluid dynamics)package based on finite volume method,leading to a highest deviation of nearly 6%.Moreover,characteristics of the forced convection flows are properly obtained,e.g.,the effect of the Reynolds number over the multiplicity of scales.展开更多
In recent years, the Lattice Boltzmann Method (LBM) has developed into an alternative and promising numerical scheme for simulating fluid flows and modeling physics in fluids. In order to propose LBM for high Reynolds...In recent years, the Lattice Boltzmann Method (LBM) has developed into an alternative and promising numerical scheme for simulating fluid flows and modeling physics in fluids. In order to propose LBM for high Reynolds number fluid flow applications, a subgrid turbulence model for LBM was introduced based on standard Smagorinsky subgrid model and Lattice Bhatnagar-Gross-Krook (LBGK) model. The subgrid LBGK model was subsequently used to simulate the two-dimensional driven cavity flow at high Reynolds numbers. The simulation results including distribution of stream lines, dimensionless velocities distribution, values of stream function, as well as location of vertex center, were compared with benchmark solutions, with satisfactory agreements.展开更多
A numerical algorithm using a bilinear or linear finite element and semi-implicit three-step method is presented for the analysis of incompressible viscous fluid problems. The streamline upwind/Petrov-Galerkin (SUPG) ...A numerical algorithm using a bilinear or linear finite element and semi-implicit three-step method is presented for the analysis of incompressible viscous fluid problems. The streamline upwind/Petrov-Galerkin (SUPG) stabilization scheme is used for the formulation of the Navier-Stokes equations. For the spatial discretization, the convection term is treated explicitly, while the viscous term is treated implicitly, and for the temporal discretization, a three-step method is employed. The present method is applied to simulate the lid driven cavity problems with different geometries at low and high Reynolds numbers. The results compared with other numerical experiments are found to be feasible and satisfactory.展开更多
Multiple steady solutions and hysteresis phenomenon in the square cavity flows driven by the surface with antisymmetric velocity profile are investigated by numerical simulation and bifurcation analysis.A high order s...Multiple steady solutions and hysteresis phenomenon in the square cavity flows driven by the surface with antisymmetric velocity profile are investigated by numerical simulation and bifurcation analysis.A high order spectral element method with the matrix-free pseudo-arclength technique is used for the steady-state solution and numerical continuation.The complex flow patterns beyond the symmetry-breaking at Re≈320 are presented by a bifurcation diagram for Re<2500.The results of stable symmetric and asymmetric solutions are consistent with those reported in literature,and a new unstable asymmetric branch is obtained besides the stable branches.A novel hysteresis phenomenon is observed in the range of 2208<Re<2262,where two pairs of stable and two pairs of unstable asymmetric steady solutions beyond the stable symmetric state coexist.The vortices near the sidewall appear when the Reynolds number increases,which correspond to the bifurcation of topology structure,but not the bifurcation of Navier-Stokes equations.The hysteresis is proposed to be the result of the combined mechanisms of the competition and coalescence of secondary vortices.展开更多
When two identical QED cavities driven by the coherent fields are located in a uniform environment, in addition to dissipation, there appears an indirect coupling between the two cavities induced by the background fie...When two identical QED cavities driven by the coherent fields are located in a uniform environment, in addition to dissipation, there appears an indirect coupling between the two cavities induced by the background fields. We investigate the effects of the coherent fields, the dissipation as well as the incoherent coupling on the following dynamical properties of the system： photon transfer, reversible decoherence, and quantum state transfer, etc. We find that the photons in the cavities do not leak completely into the environment due to the collective coupling between the cavities and the enviroment, and the photons are transferred irreversibly from the cavity with more photons to the cavity with less ones due to the incoherent coupling so that they are equally distributed among the two cavities. The coherent field pumping on the two cavities increases the mean photons, complements the revived magnitude of the reversible decoherence, but hinders the quantum state transfer between the two cavities. The above phenomena may find applications in quantum communication and other basic fields.展开更多
In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split i...In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation.After the linearization of the nonlinear part by Newton’s method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.展开更多
Physics-informed neural networks(PINNs)are proved methods that are effective in solving some strongly nonlinear partial differential equations(PDEs),e.g.,Navier-Stokes equations,with a small amount of boundary or inte...Physics-informed neural networks(PINNs)are proved methods that are effective in solving some strongly nonlinear partial differential equations(PDEs),e.g.,Navier-Stokes equations,with a small amount of boundary or interior data.However,the feasibility of applying PINNs to the flow at moderate or high Reynolds numbers has rarely been reported.The present paper proposes an artificial viscosity(AV)-based PINN for solving the forward and inverse flow problems.Specifically,the AV used in PINNs is inspired by the entropy viscosity method developed in conventional computational fluid dynamics(CFD)to stabilize the simulation of flow at high Reynolds numbers.The newly developed PINN is used to solve the forward problem of the two-dimensional steady cavity flow at Re=1000 and the inverse problem derived from two-dimensional film boiling.The results show that the AV augmented PINN can solve both problems with good accuracy and substantially reduce the inference errors in the forward problem.展开更多
In present paper,the mathematic background of intrusive polynomial chaos(IPC)method and coupling process with one dimension Euler equation were introduced.The IPC method was implemented for the 2D compressible stochas...In present paper,the mathematic background of intrusive polynomial chaos(IPC)method and coupling process with one dimension Euler equation were introduced.The IPC method was implemented for the 2D compressible stochastic Navier-Stokes equations to simulate the non-deterministic behavior of a lid driven cavity flow under the influence of uncertainties.The driven velocity and fluid viscosity were supposed respectively to be the uncertain variable which has Gaussian probability distribution.Based on the validation with benchmark results,discussions were mainly focused on the statistic properties of velocity distribution.The results indicated the effect of IPC method on the simulation of propagation of uncertainty in the flow field.For the simulated results of 2D cavity flow,influence of the driven velocity uncertainty is larger than that of viscosity.展开更多
The authors establish error estimates for recently developed finite-element methods for incompressible viscous flow in domains with no-slip boundary conditions.The methods arise by discretization of a well-posed exten...The authors establish error estimates for recently developed finite-element methods for incompressible viscous flow in domains with no-slip boundary conditions.The methods arise by discretization of a well-posed extended Navier-Stokes dynamics for which pressure is determined from current velocity and force fields.The methods use C1 elements for velocity and C0 elements for pressure.A stability estimate is proved for a related finite-element projection method close to classical time-splitting methods of Orszag,Israeli,DeVille and Karniadakis.展开更多
文摘This study is devoted to the computational fluid dynamics (CFD) modeling of steady laminar mixed convection flow and heat transfer in lid driven cavity (10 ≤ Re ≤ 1000). The ratio of the height to the width of the cavity is ranged over H/L = 0.5 to 1.5. The governing equations are solved using commercial finite volume package FLUENT to visualize the nature of the flow and estimate the heat transfer inside the cavity for different aspect ratio. The simulation results are presented in terms of average Nusselt number of the hot wall, velocity profile, and temperature contours. It was found that the average Nusselt number inside the cavity is strongly governed by the aspect ratio as well as the Reynolds number. A parametric study is conducted to demonstrate the effect of aspect ratio on the flow and heat transfer characteristics. It is found that heat transfer enhancement was obtained by decreasing the aspect ratio and/or increasing the Reynolds number.
文摘This study presents the LES(large eddy simulation)of forced convection in laminar and two dimensional turbulent flows when the flow reaches the steady state.The main purpose is the evaluation of a developed numerical methodology for the simulation of forced convection flows at various Reynolds numbers(100_〈Rex〈_10,000)and for a fixed Prandtl number(Pr=1.0).The hexahedral eight-node FEM(finite element method)with an explicit Taylor-Galerkin scheme is used to obtain the numerical solutions of the conservation equations of mass,momentum and energy.The Smagorinsky model is employed for the sub-grid treatment.The time-averaged velocity and temperature profiles are compared with results of literature and a CFD(computational fluid dynamics)package based on finite volume method,leading to a highest deviation of nearly 6%.Moreover,characteristics of the forced convection flows are properly obtained,e.g.,the effect of the Reynolds number over the multiplicity of scales.
文摘In recent years, the Lattice Boltzmann Method (LBM) has developed into an alternative and promising numerical scheme for simulating fluid flows and modeling physics in fluids. In order to propose LBM for high Reynolds number fluid flow applications, a subgrid turbulence model for LBM was introduced based on standard Smagorinsky subgrid model and Lattice Bhatnagar-Gross-Krook (LBGK) model. The subgrid LBGK model was subsequently used to simulate the two-dimensional driven cavity flow at high Reynolds numbers. The simulation results including distribution of stream lines, dimensionless velocities distribution, values of stream function, as well as location of vertex center, were compared with benchmark solutions, with satisfactory agreements.
基金Project supported by the National Natural Science Foundation of China (No.51078230)the Research Fund for the Doctoral Program of Higher Education of China (No.200802480056)the Key Project of Fund of Science and Technology Development of Shanghai (No.10JC1407900),China
文摘A numerical algorithm using a bilinear or linear finite element and semi-implicit three-step method is presented for the analysis of incompressible viscous fluid problems. The streamline upwind/Petrov-Galerkin (SUPG) stabilization scheme is used for the formulation of the Navier-Stokes equations. For the spatial discretization, the convection term is treated explicitly, while the viscous term is treated implicitly, and for the temporal discretization, a three-step method is employed. The present method is applied to simulate the lid driven cavity problems with different geometries at low and high Reynolds numbers. The results compared with other numerical experiments are found to be feasible and satisfactory.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11902043 and 11772065)the Science Challenge Project(Grant No.TZ2016001).
文摘Multiple steady solutions and hysteresis phenomenon in the square cavity flows driven by the surface with antisymmetric velocity profile are investigated by numerical simulation and bifurcation analysis.A high order spectral element method with the matrix-free pseudo-arclength technique is used for the steady-state solution and numerical continuation.The complex flow patterns beyond the symmetry-breaking at Re≈320 are presented by a bifurcation diagram for Re<2500.The results of stable symmetric and asymmetric solutions are consistent with those reported in literature,and a new unstable asymmetric branch is obtained besides the stable branches.A novel hysteresis phenomenon is observed in the range of 2208<Re<2262,where two pairs of stable and two pairs of unstable asymmetric steady solutions beyond the stable symmetric state coexist.The vortices near the sidewall appear when the Reynolds number increases,which correspond to the bifurcation of topology structure,but not the bifurcation of Navier-Stokes equations.The hysteresis is proposed to be the result of the combined mechanisms of the competition and coalescence of secondary vortices.
基金The project supported in part by National Natural Science Foundation of China under Grant Nos. 10175029, 10375039, and 10647007, the Doctoral Education Fund of Ministry of Education, the Research Fund of Nuclear Theory Center of HIRFL of China, and the Science and Technology Foundation of Sichuan Province under Grant No. 02GY029-189
文摘When two identical QED cavities driven by the coherent fields are located in a uniform environment, in addition to dissipation, there appears an indirect coupling between the two cavities induced by the background fields. We investigate the effects of the coherent fields, the dissipation as well as the incoherent coupling on the following dynamical properties of the system： photon transfer, reversible decoherence, and quantum state transfer, etc. We find that the photons in the cavities do not leak completely into the environment due to the collective coupling between the cavities and the enviroment, and the photons are transferred irreversibly from the cavity with more photons to the cavity with less ones due to the incoherent coupling so that they are equally distributed among the two cavities. The coherent field pumping on the two cavities increases the mean photons, complements the revived magnitude of the reversible decoherence, but hinders the quantum state transfer between the two cavities. The above phenomena may find applications in quantum communication and other basic fields.
基金financially supported by the National Natural Science Foundation of China(Grant No.51349011)the Foundation of Si’chuan Educational Committee(Grant No.17ZB0452)+1 种基金the Innovation Team Project of Si’chuan Educational Committee(Grant No.18TD0019)the Longshan Academic Talent Research Support Program of the Southwest of Science and Technology(Grant Nos.18LZX715 and 18LZX410)
文摘In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation.After the linearization of the nonlinear part by Newton’s method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.
基金Project supported by the Fundamental Research Funds for the Central Universities of China(No.DUT21RC(3)063)the National Natural Science Foundation of China(No.51720105007)the Baidu Foundation(No.ghfund202202014542)。
文摘Physics-informed neural networks(PINNs)are proved methods that are effective in solving some strongly nonlinear partial differential equations(PDEs),e.g.,Navier-Stokes equations,with a small amount of boundary or interior data.However,the feasibility of applying PINNs to the flow at moderate or high Reynolds numbers has rarely been reported.The present paper proposes an artificial viscosity(AV)-based PINN for solving the forward and inverse flow problems.Specifically,the AV used in PINNs is inspired by the entropy viscosity method developed in conventional computational fluid dynamics(CFD)to stabilize the simulation of flow at high Reynolds numbers.The newly developed PINN is used to solve the forward problem of the two-dimensional steady cavity flow at Re=1000 and the inverse problem derived from two-dimensional film boiling.The results show that the AV augmented PINN can solve both problems with good accuracy and substantially reduce the inference errors in the forward problem.
基金supported by the National Natural Science Foundation of China(Grant No.90718025)the EU Six Frame Project(Grant No.AST5-CT-2006-030959)
文摘In present paper,the mathematic background of intrusive polynomial chaos(IPC)method and coupling process with one dimension Euler equation were introduced.The IPC method was implemented for the 2D compressible stochastic Navier-Stokes equations to simulate the non-deterministic behavior of a lid driven cavity flow under the influence of uncertainties.The driven velocity and fluid viscosity were supposed respectively to be the uncertain variable which has Gaussian probability distribution.Based on the validation with benchmark results,discussions were mainly focused on the statistic properties of velocity distribution.The results indicated the effect of IPC method on the simulation of propagation of uncertainty in the flow field.For the simulated results of 2D cavity flow,influence of the driven velocity uncertainty is larger than that of viscosity.
基金Project supported by the National Science Foundation(Nos.DMS 06-04420(RLP),DMS 08-11177(JGL))the Center for Nonlinear Analysis(CNA)under National Science Foundation Grant(Nos.0405343,0635983)
文摘The authors establish error estimates for recently developed finite-element methods for incompressible viscous flow in domains with no-slip boundary conditions.The methods arise by discretization of a well-posed extended Navier-Stokes dynamics for which pressure is determined from current velocity and force fields.The methods use C1 elements for velocity and C0 elements for pressure.A stability estimate is proved for a related finite-element projection method close to classical time-splitting methods of Orszag,Israeli,DeVille and Karniadakis.
