A total variation diminishing-weighted average flux （TVD-WAF）-based hybrid numerical scheme for the enhanced version of nonlinearly dispersive Boussinesq-type equations was developed. The one-dimensional governing e...A total variation diminishing-weighted average flux （TVD-WAF）-based hybrid numerical scheme for the enhanced version of nonlinearly dispersive Boussinesq-type equations was developed. The one-dimensional governing equations were rewritten in the conservative form and then discretized on a uniform grid. The finite volume method was used to discretize the flux term while the remaining terms were approximated with the finite difference method. The second-order TVD-WAF method was employed in conjunction with the Harten-Lax-van Leer （HLL） Riemann solver to calculate the numerical flux, and the variables at the cell interface for the local Riemann problem were reconstructed via the fourth- order monotone upstream-centered scheme for conservation laws （MUSCL）. The time marching scheme based on the third-order TVD Runge- Kutta method was used to obtain numerical solutions. The model was validated through a series of numerical tests, in which wave breaking and a moving shoreline were treated. The good agreement between the computed results, documented analytical solutions, and experimental data demonstrates the correct discretization of the governing equations and high accuracy of the proposed scheme, and also conforms the advantages of the proposed shock-capturing scheme for the enhanced version of the Boussinesq model, including the convenience in the treatment of wave breaking and moving shorelines and without the need for a numerical filter.展开更多
A finite-volume Total Variation Diminishing (TVD) scheme is presented formodeling dam-break flows in open channels. This method is used for solving the 2D shallow waterequations on arbitrary quadrilateral meshes, base...A finite-volume Total Variation Diminishing (TVD) scheme is presented formodeling dam-break flows in open channels. This method is used for solving the 2D shallow waterequations on arbitrary quadrilateral meshes, based upon a second-order hybrid TVD scheme with anoptimum-selected limiter in the space discretization and a two-step Runge-Kutta approach in the timediscretization. Verification for a circular dam-break problem is carried out by comparing thepresent results with others and very good agreement is shown. The present algorithm is then used topredict dam-break flow characteristics in open channels such as in furcated channels. Morecomplicated unsteady flow characteristics in these furcated channels than in the regular channelsstudied previously can observed in this work.展开更多
Flows around a circular cylinder displaying an unsteady vortex shedding process at the Reynolds numbers of 1000,3900 and 1×104 are studied using a finite-volume Total Variation Diminishing（TVD） scheme for solvi...Flows around a circular cylinder displaying an unsteady vortex shedding process at the Reynolds numbers of 1000,3900 and 1×104 are studied using a finite-volume Total Variation Diminishing（TVD） scheme for solving the Unsteady Reynolds-Averaged Navier-Stokes（URANS） equations.An Elemental Velocity Vector Transformation（EVVT） approach is proposed for the local normal and tangential velocity transformation at the interfaces of main and satellite elements.The presented method is validated by comparing with the available experimental data and numerical results.It is shown that the two-dimensional TVD finite volume method with the Renormalization Group（RNG） turbulence model can be used to determine hydrodynamic forces and captures vortex shedding characteristics very well.展开更多
A finite-difference Total Variation Diminishing （TVD） numerical simulation model for coupling the Reynolds Averaged Navier-Stokes （RANS） equations, pressure-relative continuity equation and various k-εturbulence ...A finite-difference Total Variation Diminishing （TVD） numerical simulation model for coupling the Reynolds Averaged Navier-Stokes （RANS） equations, pressure-relative continuity equation and various k-εturbulence models was developed to solve the incompressible flow based on the pseudo-compressibility method. The hyperbolicity of all these equations was studied and the discretization of the fully coupling equations with all the primal variables and source terms were made in this article. Numerical simulation for modeling the flow around a ground-mounted square rib was implemented and validated by comparing with the published wind tunnel experimental data. It is shown that such a numerical simulation method with a proper turbulence model has a very good accuracy to simulate the flow around a surface-mounted rib. It is concluded that the Renormalization Group （RNG） and Chen-Kim k-εturbulence models have much better ability to predict the characteristics of the vortex structure and flow separation than the standard k-εmodel.展开更多
为研究气体离心机取料支臂附近的流动状况,数值模拟了取料支臂附近的流场。采用矢量分裂的有限体积法求解不同出流条件下的N av ier-S tokes方程。采用二阶总变差减小原理,捕捉激波,同时将支臂外部和内部的流动结合起来进行计算。讨论...为研究气体离心机取料支臂附近的流动状况,数值模拟了取料支臂附近的流场。采用矢量分裂的有限体积法求解不同出流条件下的N av ier-S tokes方程。采用二阶总变差减小原理,捕捉激波,同时将支臂外部和内部的流动结合起来进行计算。讨论了激波和气体粘性对流场的影响。得到了不同取料情况下的流场分布图像。结果表明:所采用的计算格式很好地捕捉到了激波和边界层,验证了计算方法的有效性,为数值模拟实际离心机支臂附近的流动状况和支臂损耗的计算打下了基础。展开更多
One-dimensional open channel flows are simulated using the discontinuous Galerkin finite element method. Three different explicit time marching schemes, including multistep/multistage schemes, are evaluated for differ...One-dimensional open channel flows are simulated using the discontinuous Galerkin finite element method. Three different explicit time marching schemes, including multistep/multistage schemes, are evaluated for different channel shapes for accuracy and efficiency. The Forward Euler, second-order Adam-Bashforth （multistep）, and second-order total variation diminishing （TVD） Runge-Kutta （multistage） time marching schemes are utilized. The role of monotonized central, minmod, and zero TVD slope limiters for each of the time marching scheme is investigated. The numerical flux is approximated using HLL function. The accuracy and robustness of different time marching schemes are evaluated for steady and unsteady flows using analytical and measured data. The unsteady flows include dam break tests with wet and dry beds downstream of the dam in prismatic （rectangular, trapezoidal, triangular, and parabolic cross-sections） and non-prismatic （natural river） channels. The steady flow test involves simulation of hydraulic jump in a diverging rectangular channel. The various schemes are evaluated by comparing accuracy using statistical measures and efficiency using maximum possible time step size as well as CPU runtime. The second-order Adam-Bashforth time marching scheme is found to have the best accuracy and efficiency among the time stepping schemes tested.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.51579034)the Open Fund of the Key Laboratory of Ocean Circulation and Waves,Chinese Academy of Sciences(Grant No.KLOCW1502)
文摘A total variation diminishing-weighted average flux （TVD-WAF）-based hybrid numerical scheme for the enhanced version of nonlinearly dispersive Boussinesq-type equations was developed. The one-dimensional governing equations were rewritten in the conservative form and then discretized on a uniform grid. The finite volume method was used to discretize the flux term while the remaining terms were approximated with the finite difference method. The second-order TVD-WAF method was employed in conjunction with the Harten-Lax-van Leer （HLL） Riemann solver to calculate the numerical flux, and the variables at the cell interface for the local Riemann problem were reconstructed via the fourth- order monotone upstream-centered scheme for conservation laws （MUSCL）. The time marching scheme based on the third-order TVD Runge- Kutta method was used to obtain numerical solutions. The model was validated through a series of numerical tests, in which wave breaking and a moving shoreline were treated. The good agreement between the computed results, documented analytical solutions, and experimental data demonstrates the correct discretization of the governing equations and high accuracy of the proposed scheme, and also conforms the advantages of the proposed shock-capturing scheme for the enhanced version of the Boussinesq model, including the convenience in the treatment of wave breaking and moving shorelines and without the need for a numerical filter.
文摘A finite-volume Total Variation Diminishing (TVD) scheme is presented formodeling dam-break flows in open channels. This method is used for solving the 2D shallow waterequations on arbitrary quadrilateral meshes, based upon a second-order hybrid TVD scheme with anoptimum-selected limiter in the space discretization and a two-step Runge-Kutta approach in the timediscretization. Verification for a circular dam-break problem is carried out by comparing thepresent results with others and very good agreement is shown. The present algorithm is then used topredict dam-break flow characteristics in open channels such as in furcated channels. Morecomplicated unsteady flow characteristics in these furcated channels than in the regular channelsstudied previously can observed in this work.
基金supported by the National High Technology Research and Development Program of China (863 Program,Grant No. 2008AA09Z310)the Important National Scienceand Technology Specific Sub-Project (Grant No.2008ZX05026-001)
文摘Flows around a circular cylinder displaying an unsteady vortex shedding process at the Reynolds numbers of 1000,3900 and 1×104 are studied using a finite-volume Total Variation Diminishing（TVD） scheme for solving the Unsteady Reynolds-Averaged Navier-Stokes（URANS） equations.An Elemental Velocity Vector Transformation（EVVT） approach is proposed for the local normal and tangential velocity transformation at the interfaces of main and satellite elements.The presented method is validated by comparing with the available experimental data and numerical results.It is shown that the two-dimensional TVD finite volume method with the Renormalization Group（RNG） turbulence model can be used to determine hydrodynamic forces and captures vortex shedding characteristics very well.
文摘A finite-difference Total Variation Diminishing （TVD） numerical simulation model for coupling the Reynolds Averaged Navier-Stokes （RANS） equations, pressure-relative continuity equation and various k-εturbulence models was developed to solve the incompressible flow based on the pseudo-compressibility method. The hyperbolicity of all these equations was studied and the discretization of the fully coupling equations with all the primal variables and source terms were made in this article. Numerical simulation for modeling the flow around a ground-mounted square rib was implemented and validated by comparing with the published wind tunnel experimental data. It is shown that such a numerical simulation method with a proper turbulence model has a very good accuracy to simulate the flow around a surface-mounted rib. It is concluded that the Renormalization Group （RNG） and Chen-Kim k-εturbulence models have much better ability to predict the characteristics of the vortex structure and flow separation than the standard k-εmodel.
文摘为研究气体离心机取料支臂附近的流动状况,数值模拟了取料支臂附近的流场。采用矢量分裂的有限体积法求解不同出流条件下的N av ier-S tokes方程。采用二阶总变差减小原理,捕捉激波,同时将支臂外部和内部的流动结合起来进行计算。讨论了激波和气体粘性对流场的影响。得到了不同取料情况下的流场分布图像。结果表明:所采用的计算格式很好地捕捉到了激波和边界层,验证了计算方法的有效性,为数值模拟实际离心机支臂附近的流动状况和支臂损耗的计算打下了基础。
文摘One-dimensional open channel flows are simulated using the discontinuous Galerkin finite element method. Three different explicit time marching schemes, including multistep/multistage schemes, are evaluated for different channel shapes for accuracy and efficiency. The Forward Euler, second-order Adam-Bashforth （multistep）, and second-order total variation diminishing （TVD） Runge-Kutta （multistage） time marching schemes are utilized. The role of monotonized central, minmod, and zero TVD slope limiters for each of the time marching scheme is investigated. The numerical flux is approximated using HLL function. The accuracy and robustness of different time marching schemes are evaluated for steady and unsteady flows using analytical and measured data. The unsteady flows include dam break tests with wet and dry beds downstream of the dam in prismatic （rectangular, trapezoidal, triangular, and parabolic cross-sections） and non-prismatic （natural river） channels. The steady flow test involves simulation of hydraulic jump in a diverging rectangular channel. The various schemes are evaluated by comparing accuracy using statistical measures and efficiency using maximum possible time step size as well as CPU runtime. The second-order Adam-Bashforth time marching scheme is found to have the best accuracy and efficiency among the time stepping schemes tested.
