A physics-informed neural network(PINN)is a powerful tool for solving differential equations in solid and fluid mechanics.However,it suffers from singularly perturbed boundary-layer problems in which there exist sharp...A physics-informed neural network(PINN)is a powerful tool for solving differential equations in solid and fluid mechanics.However,it suffers from singularly perturbed boundary-layer problems in which there exist sharp changes caused by a small perturbation parameter multiplying the highest-order derivatives.In this paper,we introduce Chien's composite expansion method into PINNs,and propose a novel architecture for the PINNs,namely,the Chien-PINN(C-PINN)method.This novel PINN method is validated by singularly perturbed differential equations,and successfully solves the wellknown thin plate bending problems.In particular,no cumbersome matching conditions are needed for the C-PINN method,compared with the previous studies based on matched asymptotic expansions.展开更多
Contaminants released from sediment into rivers are one of the main problems to study in environmental hydrodynamics. For contaminants released into the overlying water under different hydrodynamic conditions, the mec...Contaminants released from sediment into rivers are one of the main problems to study in environmental hydrodynamics. For contaminants released into the overlying water under different hydrodynamic conditions, the mechanical mechanisms involved can be roughly divided into convective diffusion, molecular diffusion, and adsorption/desorption. Because of the obvious environmental influence of fine sediment （D90 = 0.06 mm）, non-cohesive fine sediment, and cohesive fine sediment are researched in this paper, and phosphorus is chosen for a typical adsorption of a contaminant. Through theoretical analysis of the contaminant release process, according to different hydraulic conditions, the contaminant release coupling mathematical model can be established by the N-S equation, the Darcy equation, the solute transport equation, and the adsorption/desorption equation. Then, the experiments are completed in an open water flume. The simulation results and experimental results show that convective diffusion dominates the contaminant release both in non-cohesive and cohesive fine sediment after their suspension, and that they contribute more than 90 % of the total release. Molecular diffusion and desorption have more of a contribution for contaminant release from unsuspended sediment. In unsuspension sediment, convective diffusion is about 10-50 times larger than molecular diffusion during the initial stages under high velocity; it is close to molecular diffusion in the later stages. Convective diffusion is about 6 times larger than molecular diffusion during the initial stages under low velocity, it is about a quarter of mole- cular diffusion in later stages, and has a similar level with desorption/adsorption. In unsuspended sediment, a seepage boundary layer exists below the water-sediment interface, and various release mechanisms in that layer mostly dominate the contaminant release process. In non-cohesive fine sediment, the depth of that layer increases linearly with shear stress. In cohesive fine sediment, the range seepage boundary is different from that in non-cohesive sediment, and that phenomenon is more obvious under a lower shear stress.展开更多
为更加精确地模拟复杂地形地区大气边界层中气象要素,将NASA发布的SRTM3(约90m分辨率)地形高度数据引入中尺度气象模式WRF(weather research and forecasting)中,结合四种边界层参数化方案(YSU、ACM2、MYN2.5level TKE(简称MYN)、Bougea...为更加精确地模拟复杂地形地区大气边界层中气象要素,将NASA发布的SRTM3(约90m分辨率)地形高度数据引入中尺度气象模式WRF(weather research and forecasting)中,结合四种边界层参数化方案(YSU、ACM2、MYN2.5level TKE(简称MYN)、Bougeault and Lacarrere TKE(简称BL))及模式自带地形数据GTOPO30(约1km分辨率),模拟了2008年4月24—25日安徽黄山及周边地区大气边界层气象要素场变化特征,并对模式输出的2m气温、2m露点温度、10m风速、湿度廓线与模拟区域内19个气象站及2个探空站数据进行比较。结果表明,无论采用哪种地形数据,四种边界层参数化方案中,YSU方案模拟的2m气温误差最小,ACM2方案模拟的2m露点温度和10m风速误差最小;采用SRTM3数据后,四种边界层参数化方案模拟的2m气温平均均方根误差(root mean squared error,RMSE)分别降低了3.79%(YSU方案)、2.48%(ACM2方案)、3.8%(MYN方案)、0.87%(BL方案);对2m露点温度模拟,除MYN方案模拟平均RMSE降低了0.59%外,其他三种方案模拟误差分别增加了1.39%(YSU方案)、0.49%(BL方案)、0.89%(ACM2方案);而对10m风速的模拟结果,除ACM2方案模拟平均RMSE降低了2.28%外,其他三种方案模拟误差分别增加了0.22%(YSU方案)、2.32%(MYN方案)、2.45%(BL方案);对2个探空站点湿度廓线的模拟显示,各边界层方案均能模拟出水汽的垂直变化趋势,但模拟效果总体表现为偏湿,采用SRTM3地形数据之后,ACM2方案模拟部分时刻的低层水汽廓线有所改善。展开更多
将两方程k-ωSST湍流模型和Sagaut的混合尺度亚格子模型通过一个混合函数相结合,构造出一种混合大涡/雷诺平均N-S方程模拟方法(hybird large eddy simulation/reynolds-averaged navier-stokes,HybridLES/RANS),采用这种混合模拟方法结...将两方程k-ωSST湍流模型和Sagaut的混合尺度亚格子模型通过一个混合函数相结合,构造出一种混合大涡/雷诺平均N-S方程模拟方法(hybird large eddy simulation/reynolds-averaged navier-stokes,HybridLES/RANS),采用这种混合模拟方法结合5阶WENO格式对Ma=2.8平板湍流边界层进行了数值模拟,并在计算区域上游入口处采用"回收/调节"方法生成湍流脉动边界条件,通过考查RANS区域向LES区域的过渡参数及网格分辨率对这种混合模拟方法进行了评价.计算结果表明:该文采用的混合模拟方法可以捕捉到湍流边界层中的大尺度结构且入口边界层平均参数不会发生漂移,混合函数应当将RANS区域和LES区域的过渡点设置在对数律层和尾迹律层的交界处,而过渡应当迅速以获得正确的雷诺剪切应力分布,在该文采用的模型及数值方法的条件下,流向及展向的网格小至与Escudier混合长相当时,能够获得可以接受的脉动速度的单点-二阶统计值.展开更多
Recent advances in modeling of tornadoes and twisters consist of significant achievements in mathematical calculation of occurrence and evolution of a violent F5-class tornado on the Fujita scale, and four-dimensional...Recent advances in modeling of tornadoes and twisters consist of significant achievements in mathematical calculation of occurrence and evolution of a violent F5-class tornado on the Fujita scale, and four-dimensional mathematical modeling of a tornado with the fourth coordinate time multiplied by its characteristic velocity. Such a tornado can arise in a thunderstorm supercell filled with turbulent whirlwinds. A theory of the squall storms is proposed. The squall storm is modeled by running pertur- bation of the temperature inversion on the lower boundary of cloudiness. This perturbation is induced by the action of strong, hurricane winds in the upper and middle troposphere, and looks like a running solitary wave （soliton）; which is developed also in a field of pressure and velocity of a wind. If a soliton of a squall storm gets into the thunderstorm supercell then this soliton is captured by supercell. It leads to additional pressure fall of air inside a storm supercell and stimulate amplification of wind velocity here. As a result, a cyclostrophic balance inside a storm supercell generates a tornado. Comparison of the radial distribution of wind velocity inside a tornado calculated by using the new formulas and equations with radar observations of the wind velocity inside Texas Tornado Dummit in 1995 and inside the 3 May 1999 Oklahoma City Tornado shows good correspondence.展开更多
A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. Th...A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incompressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classification with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.展开更多
基金Project supported by the National Natural Science Foundation of China Basic Science Center Program for“Multiscale Problems in Nonlinear Mechanics”(No.11988102)the National Natural Science Foundation of China(No.12202451)。
文摘A physics-informed neural network(PINN)is a powerful tool for solving differential equations in solid and fluid mechanics.However,it suffers from singularly perturbed boundary-layer problems in which there exist sharp changes caused by a small perturbation parameter multiplying the highest-order derivatives.In this paper,we introduce Chien's composite expansion method into PINNs,and propose a novel architecture for the PINNs,namely,the Chien-PINN(C-PINN)method.This novel PINN method is validated by singularly perturbed differential equations,and successfully solves the wellknown thin plate bending problems.In particular,no cumbersome matching conditions are needed for the C-PINN method,compared with the previous studies based on matched asymptotic expansions.
基金supported by the National Key Program of the National Natural Science Foundation of China (Grant 11032007)
文摘Contaminants released from sediment into rivers are one of the main problems to study in environmental hydrodynamics. For contaminants released into the overlying water under different hydrodynamic conditions, the mechanical mechanisms involved can be roughly divided into convective diffusion, molecular diffusion, and adsorption/desorption. Because of the obvious environmental influence of fine sediment （D90 = 0.06 mm）, non-cohesive fine sediment, and cohesive fine sediment are researched in this paper, and phosphorus is chosen for a typical adsorption of a contaminant. Through theoretical analysis of the contaminant release process, according to different hydraulic conditions, the contaminant release coupling mathematical model can be established by the N-S equation, the Darcy equation, the solute transport equation, and the adsorption/desorption equation. Then, the experiments are completed in an open water flume. The simulation results and experimental results show that convective diffusion dominates the contaminant release both in non-cohesive and cohesive fine sediment after their suspension, and that they contribute more than 90 % of the total release. Molecular diffusion and desorption have more of a contribution for contaminant release from unsuspended sediment. In unsuspension sediment, convective diffusion is about 10-50 times larger than molecular diffusion during the initial stages under high velocity; it is close to molecular diffusion in the later stages. Convective diffusion is about 6 times larger than molecular diffusion during the initial stages under low velocity, it is about a quarter of mole- cular diffusion in later stages, and has a similar level with desorption/adsorption. In unsuspended sediment, a seepage boundary layer exists below the water-sediment interface, and various release mechanisms in that layer mostly dominate the contaminant release process. In non-cohesive fine sediment, the depth of that layer increases linearly with shear stress. In cohesive fine sediment, the range seepage boundary is different from that in non-cohesive sediment, and that phenomenon is more obvious under a lower shear stress.
文摘为更加精确地模拟复杂地形地区大气边界层中气象要素,将NASA发布的SRTM3(约90m分辨率)地形高度数据引入中尺度气象模式WRF(weather research and forecasting)中,结合四种边界层参数化方案(YSU、ACM2、MYN2.5level TKE(简称MYN)、Bougeault and Lacarrere TKE(简称BL))及模式自带地形数据GTOPO30(约1km分辨率),模拟了2008年4月24—25日安徽黄山及周边地区大气边界层气象要素场变化特征,并对模式输出的2m气温、2m露点温度、10m风速、湿度廓线与模拟区域内19个气象站及2个探空站数据进行比较。结果表明,无论采用哪种地形数据,四种边界层参数化方案中,YSU方案模拟的2m气温误差最小,ACM2方案模拟的2m露点温度和10m风速误差最小;采用SRTM3数据后,四种边界层参数化方案模拟的2m气温平均均方根误差(root mean squared error,RMSE)分别降低了3.79%(YSU方案)、2.48%(ACM2方案)、3.8%(MYN方案)、0.87%(BL方案);对2m露点温度模拟,除MYN方案模拟平均RMSE降低了0.59%外,其他三种方案模拟误差分别增加了1.39%(YSU方案)、0.49%(BL方案)、0.89%(ACM2方案);而对10m风速的模拟结果,除ACM2方案模拟平均RMSE降低了2.28%外,其他三种方案模拟误差分别增加了0.22%(YSU方案)、2.32%(MYN方案)、2.45%(BL方案);对2个探空站点湿度廓线的模拟显示,各边界层方案均能模拟出水汽的垂直变化趋势,但模拟效果总体表现为偏湿,采用SRTM3地形数据之后,ACM2方案模拟部分时刻的低层水汽廓线有所改善。
文摘将两方程k-ωSST湍流模型和Sagaut的混合尺度亚格子模型通过一个混合函数相结合,构造出一种混合大涡/雷诺平均N-S方程模拟方法(hybird large eddy simulation/reynolds-averaged navier-stokes,HybridLES/RANS),采用这种混合模拟方法结合5阶WENO格式对Ma=2.8平板湍流边界层进行了数值模拟,并在计算区域上游入口处采用"回收/调节"方法生成湍流脉动边界条件,通过考查RANS区域向LES区域的过渡参数及网格分辨率对这种混合模拟方法进行了评价.计算结果表明:该文采用的混合模拟方法可以捕捉到湍流边界层中的大尺度结构且入口边界层平均参数不会发生漂移,混合函数应当将RANS区域和LES区域的过渡点设置在对数律层和尾迹律层的交界处,而过渡应当迅速以获得正确的雷诺剪切应力分布,在该文采用的模型及数值方法的条件下,流向及展向的网格小至与Escudier混合长相当时,能够获得可以接受的脉动速度的单点-二阶统计值.
基金supported by the Presidium of the Russian Academy of Sciences in the framework of the theme 'Disasters'
文摘Recent advances in modeling of tornadoes and twisters consist of significant achievements in mathematical calculation of occurrence and evolution of a violent F5-class tornado on the Fujita scale, and four-dimensional mathematical modeling of a tornado with the fourth coordinate time multiplied by its characteristic velocity. Such a tornado can arise in a thunderstorm supercell filled with turbulent whirlwinds. A theory of the squall storms is proposed. The squall storm is modeled by running pertur- bation of the temperature inversion on the lower boundary of cloudiness. This perturbation is induced by the action of strong, hurricane winds in the upper and middle troposphere, and looks like a running solitary wave （soliton）; which is developed also in a field of pressure and velocity of a wind. If a soliton of a squall storm gets into the thunderstorm supercell then this soliton is captured by supercell. It leads to additional pressure fall of air inside a storm supercell and stimulate amplification of wind velocity here. As a result, a cyclostrophic balance inside a storm supercell generates a tornado. Comparison of the radial distribution of wind velocity inside a tornado calculated by using the new formulas and equations with radar observations of the wind velocity inside Texas Tornado Dummit in 1995 and inside the 3 May 1999 Oklahoma City Tornado shows good correspondence.
文摘A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incompressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classification with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.
