This paper is concerned with the mathematical model for the numerical simulation of supercritical surface flows. A boundary-fitted coordinate system was used to overcome the difficulties and inaccuracy associated w...This paper is concerned with the mathematical model for the numerical simulation of supercritical surface flows. A boundary-fitted coordinate system was used to overcome the difficulties and inaccuracy associated with the determination of flow characteristics near the fl ow boundaries. The MacCormack scheme was applied for the solution of the transfo rmed system of equations. Comparisions between computed results and experimental data show a satisfactory agreement.展开更多
In this paper, a new numerical scheme of Total Variation Diminishing (TVD) MacCormack type for MagnetoHydroDynamic (MHD) equations is proposed by taking into account of the characteristics such as convergence, stabili...In this paper, a new numerical scheme of Total Variation Diminishing (TVD) MacCormack type for MagnetoHydroDynamic (MHD) equations is proposed by taking into account of the characteristics such as convergence, stability, resolution. This new scheme is established by solving the MHD equations with a TVD modified MacCormack scheme for the purpose of developing a scheme of quick convergence as well as of TVD property. To show the validation, simplicity and practicability of the scheme for modelling MHD problems, a self-similar Cauchy problem with the discontinuous initial data consisting of constant states, and the collision of two fast MHD shocks, and two-dimensional Orszag and Tang's MHD vortex problem are discussed with the numerical results conforming to the existing results obtained by the Roe type TVD, the high-order Godunov scheme,and Weighted Essentially Non-Oscillatory (WENO) scheme. The numerical tests show that this two-step TVD MacCormack numerical scheme for MHD system is of robust operation in the presence of very strong waves, thin shock fronts, thin contact and slip surface discontinuities.展开更多
输水工程中的水锤现象是设计和运行部门极为关注的问题,数值模拟是管路系统中水锤压力预测和控制的重要环节。为了对变特性管路系统的水锤进行数值模拟,建立了基于MacCormack格式的变空间步长的水锤计算模型(V-MCS)。通过与经典的Method...输水工程中的水锤现象是设计和运行部门极为关注的问题,数值模拟是管路系统中水锤压力预测和控制的重要环节。为了对变特性管路系统的水锤进行数值模拟,建立了基于MacCormack格式的变空间步长的水锤计算模型(V-MCS)。通过与经典的Method of Characteristics(MOC)方法及固定步长的MacCormack(MTMS)方法模拟结果的对比,对V-MCS方法进行了验证。采用V-MCS方法模拟了变特性管路系统中的水锤过程,获得了管道压力与流量波动过程以及全线极值压力分布情况。结果表明,在变特性管路系统中,V-MCS方法可以有效地对复杂管路水锤现象进行模拟。该方法在空间网格划分上更为灵活,可根据计算需求对管道各个区域选取不等的空间步长,能在一定程度上减少计算断面数量,在不改变管路固有波速的情况下可实现对复杂管路系统的同步水锤模拟。展开更多
River ice is a natural phenomenon in cold regions, influenced by meteorology, geomorphology, and hydraulic conditions. River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal pro...River ice is a natural phenomenon in cold regions, influenced by meteorology, geomorphology, and hydraulic conditions. River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal processes, and they are also influenced by weather and hydrologic conditions. Because natural rivers are serpentine, with bends, narrows, and straight reaches, the commonly-used one-dimensional river ice models and two-dimensional models based on the rectangular Cartesian coordinates are incapable of simulating the physical phenomena accurately. In order to accurately simulate the complicated river geometry and overcome the difficulties of numerical simulation resulting from both complex boundaries and differences between length and width scales, a two-dimensional river ice numerical model based on a boundary-fitted coordinate transformation method was developed. The presented model considers the influence of the frazil ice accumulation under ice cover and the shape of the leading edge of ice cover during the freezing process. The model is capable of determining the velocity field, the distribution of water temperature, the concentration distribution of frazil ice, the transport of floating ice, the progression, stability, and thawing of ice cover, and the transport, accumulation, and erosion of ice under ice cover. A MacCormack scheme was used to solve the equations numerically. The model was validated with field observations from the Hequ Reach of the Yellow River. Comparison of simulation results with field data indicates that the model is capable of simulating the river ice process with high accuracy.展开更多
This paper is concerned with a new numerical method of two dimensional flow. The governing system of differential equations is transformed into an equivalent system applied over a square grid network in order to overc...This paper is concerned with a new numerical method of two dimensional flow. The governing system of differential equations is transformed into an equivalent system applied over a square grid network in order to overcome the difficulties and inaccurancies associated with the determination of characteristics near the flow boundaries. The MacCormack two step explicit scheme with second order accurancy is used for the solution of the transformed system of equations. Comparison between computed and experimental data shows a satisfactory agreement.展开更多
In this paper, the flood regulation by operating the downstream sluice gates for a reservoir with a water intake is studied. The two-dimensional depth-averaged flow equations are solved by the boundary fitted finite v...In this paper, the flood regulation by operating the downstream sluice gates for a reservoir with a water intake is studied. The two-dimensional depth-averaged flow equations are solved by the boundary fitted finite volume method (FVM) based on MacCormack prediction-correction scheme. The bed deformation caused by both the bed load and incoming suspended sediment is determined in a coupled way. The model is used to simulate the practical flood regulation operation of a reservoir. The results have been compared with the physical experiment.展开更多
基金Project Supported by China Postdoctoral Science Foundation National Natural Science Foundation of China (No:59839330), t
文摘This paper is concerned with the mathematical model for the numerical simulation of supercritical surface flows. A boundary-fitted coordinate system was used to overcome the difficulties and inaccuracy associated with the determination of flow characteristics near the fl ow boundaries. The MacCormack scheme was applied for the solution of the transfo rmed system of equations. Comparisions between computed results and experimental data show a satisfactory agreement.
基金the National Natural Science Foundation of China(No.49925412,49990450),the National Basic Research Science Foundation(No.G2000078405)
文摘In this paper, a new numerical scheme of Total Variation Diminishing (TVD) MacCormack type for MagnetoHydroDynamic (MHD) equations is proposed by taking into account of the characteristics such as convergence, stability, resolution. This new scheme is established by solving the MHD equations with a TVD modified MacCormack scheme for the purpose of developing a scheme of quick convergence as well as of TVD property. To show the validation, simplicity and practicability of the scheme for modelling MHD problems, a self-similar Cauchy problem with the discontinuous initial data consisting of constant states, and the collision of two fast MHD shocks, and two-dimensional Orszag and Tang's MHD vortex problem are discussed with the numerical results conforming to the existing results obtained by the Roe type TVD, the high-order Godunov scheme,and Weighted Essentially Non-Oscillatory (WENO) scheme. The numerical tests show that this two-step TVD MacCormack numerical scheme for MHD system is of robust operation in the presence of very strong waves, thin shock fronts, thin contact and slip surface discontinuities.
文摘输水工程中的水锤现象是设计和运行部门极为关注的问题,数值模拟是管路系统中水锤压力预测和控制的重要环节。为了对变特性管路系统的水锤进行数值模拟,建立了基于MacCormack格式的变空间步长的水锤计算模型(V-MCS)。通过与经典的Method of Characteristics(MOC)方法及固定步长的MacCormack(MTMS)方法模拟结果的对比,对V-MCS方法进行了验证。采用V-MCS方法模拟了变特性管路系统中的水锤过程,获得了管道压力与流量波动过程以及全线极值压力分布情况。结果表明,在变特性管路系统中,V-MCS方法可以有效地对复杂管路水锤现象进行模拟。该方法在空间网格划分上更为灵活,可根据计算需求对管道各个区域选取不等的空间步长,能在一定程度上减少计算断面数量,在不改变管路固有波速的情况下可实现对复杂管路系统的同步水锤模拟。
基金supported by the National Natural Science Foundation of China(Grant No.50579030)
文摘River ice is a natural phenomenon in cold regions, influenced by meteorology, geomorphology, and hydraulic conditions. River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal processes, and they are also influenced by weather and hydrologic conditions. Because natural rivers are serpentine, with bends, narrows, and straight reaches, the commonly-used one-dimensional river ice models and two-dimensional models based on the rectangular Cartesian coordinates are incapable of simulating the physical phenomena accurately. In order to accurately simulate the complicated river geometry and overcome the difficulties of numerical simulation resulting from both complex boundaries and differences between length and width scales, a two-dimensional river ice numerical model based on a boundary-fitted coordinate transformation method was developed. The presented model considers the influence of the frazil ice accumulation under ice cover and the shape of the leading edge of ice cover during the freezing process. The model is capable of determining the velocity field, the distribution of water temperature, the concentration distribution of frazil ice, the transport of floating ice, the progression, stability, and thawing of ice cover, and the transport, accumulation, and erosion of ice under ice cover. A MacCormack scheme was used to solve the equations numerically. The model was validated with field observations from the Hequ Reach of the Yellow River. Comparison of simulation results with field data indicates that the model is capable of simulating the river ice process with high accuracy.
文摘This paper is concerned with a new numerical method of two dimensional flow. The governing system of differential equations is transformed into an equivalent system applied over a square grid network in order to overcome the difficulties and inaccurancies associated with the determination of characteristics near the flow boundaries. The MacCormack two step explicit scheme with second order accurancy is used for the solution of the transformed system of equations. Comparison between computed and experimental data shows a satisfactory agreement.
文摘In this paper, the flood regulation by operating the downstream sluice gates for a reservoir with a water intake is studied. The two-dimensional depth-averaged flow equations are solved by the boundary fitted finite volume method (FVM) based on MacCormack prediction-correction scheme. The bed deformation caused by both the bed load and incoming suspended sediment is determined in a coupled way. The model is used to simulate the practical flood regulation operation of a reservoir. The results have been compared with the physical experiment.
