We present an efficient deep learning method called coupled deep neural networks(CDNNs) for coupling of the Stokes and Darcy–Forchheimer problems. Our method compiles the interface conditions of the coupled problems ...We present an efficient deep learning method called coupled deep neural networks(CDNNs) for coupling of the Stokes and Darcy–Forchheimer problems. Our method compiles the interface conditions of the coupled problems into the networks properly and can be served as an efficient alternative to the complex coupled problems. To impose energy conservation constraints, the CDNNs utilize simple fully connected layers and a custom loss function to perform the model training process as well as the physical property of the exact solution. The approach can be beneficial for the following reasons: Firstly, we sample randomly and only input spatial coordinates without being restricted by the nature of samples.Secondly, our method is meshfree, which makes it more efficient than the traditional methods. Finally, the method is parallel and can solve multiple variables independently at the same time. We present the theoretical results to guarantee the convergence of the loss function and the convergence of the neural networks to the exact solution. Some numerical experiments are performed and discussed to demonstrate performance of the proposed method.展开更多
Finite-sized inertial spherical particles are fully-resolved with the immersed boundary projection method(IBPM)in the turbulent open-channel flow by direct numerical simulation(DNS).The accuracy of the particle surfac...Finite-sized inertial spherical particles are fully-resolved with the immersed boundary projection method(IBPM)in the turbulent open-channel flow by direct numerical simulation(DNS).The accuracy of the particle surface force models is investigated in comparison with the total force obtained via the fully-resolved method.The results show that the steady-state resistance only performs well in the streamwise direction,while the fluid acceleration force,the added-mass force,and the shear-induced Saffman lift can effectively compensate for the large-amplitude and high-frequency characteristics of the particle surface forces,especially for the wall-normal and spanwise components.The modified steady-state resistance with the correction effects of the acceleration and the fluid shear can better represent the overall forces imposed on the particles,and it is a preferable choice of the surface force model in the Lagrangian point-particle method.展开更多
The laminar boundary layer behind a constant-speed shock wave moving through a dusty gas along a solid surface is studied.The Saffman lift force acting on a spherical particle in a gas boundary layer is taken into acc...The laminar boundary layer behind a constant-speed shock wave moving through a dusty gas along a solid surface is studied.The Saffman lift force acting on a spherical particle in a gas boundary layer is taken into account.A method for calculating the density profile of dispersed phase near the wall is pro- posed and some numerical results are given.It is shown that behind the shock wave,there exists a curved thin layer where the density of particles is many times higher than the original one.This dust collection effect may be of essential importance to the problem of dust explosion in industry.展开更多
This paper introduces a new stabilized finite element method for the coupled Stokes and Darcy problem based on the nonconforming Crouzeix-Raviart element. Optimal error estimates for the fluid velocity and pressure ar...This paper introduces a new stabilized finite element method for the coupled Stokes and Darcy problem based on the nonconforming Crouzeix-Raviart element. Optimal error estimates for the fluid velocity and pressure are derived. A numerical example is presented to verify the theoretical predictions.展开更多
We derived and analyzed a new numerical scheme for the coupled Stokes and Darcy problems by using H（div） conforming elements in the entire domain. The approach employs the mixed finite element method for the Darcy e...We derived and analyzed a new numerical scheme for the coupled Stokes and Darcy problems by using H（div） conforming elements in the entire domain. The approach employs the mixed finite element method for the Darcy equations and a stabilized H（div） finite element method for the Stokes equations. Optimal error estimates for the fluid velocity and pressure are derived. The finite element solutions from the new scheme not only feature a full satisfaction of the continuity equation, which is highly demanded in scientific computing, but also satisfy the mass conservation.展开更多
针对超声速气流驱动干粉颗粒形成的缩放喷管气固两相射流,采用拉格朗日方法、气固双向耦合模型以及Shear-Stress Transport k-ω湍流模型进行数值模拟,分析了颗粒装载比、萨夫曼力和入口压力等因素对气体参数、颗粒速度以及颗粒聚集度...针对超声速气流驱动干粉颗粒形成的缩放喷管气固两相射流,采用拉格朗日方法、气固双向耦合模型以及Shear-Stress Transport k-ω湍流模型进行数值模拟,分析了颗粒装载比、萨夫曼力和入口压力等因素对气体参数、颗粒速度以及颗粒聚集度的影响。结果表明:气固双向耦合模型可以准确的分析气体与颗粒之间的相互作用。当高压气体通过缩放喷管时会产生超声速流动,从而带动颗粒作加速运动;在同一入口压力下,如果颗粒装载比较高,那么颗粒速度较小,且气体参数受颗粒的影响较大。颗粒在喷管扩张段轴线附近聚集,导致轴线到壁面附近区域内,产生沿径向向外的气流速度梯度,这可以解释萨夫曼力使轴线上气固两相的速度增大,并且在高颗粒装载比下的影响更显著的原因。不同入口压力下可能出现欠膨胀、过膨胀和完全膨胀三种不同喷管射流形态;在完全膨胀流态下,颗粒加速和气流降温的效果相对更好。研究结果可为超声速干粉灭火技术的应用提供理论支撑。展开更多
基金Project supported in part by the National Natural Science Foundation of China (Grant No.11771259)the Special Support Program to Develop Innovative Talents in the Region of Shaanxi Province+1 种基金the Innovation Team on Computationally Efficient Numerical Methods Based on New Energy Problems in Shaanxi Provincethe Innovative Team Project of Shaanxi Provincial Department of Education (Grant No.21JP013)。
文摘We present an efficient deep learning method called coupled deep neural networks(CDNNs) for coupling of the Stokes and Darcy–Forchheimer problems. Our method compiles the interface conditions of the coupled problems into the networks properly and can be served as an efficient alternative to the complex coupled problems. To impose energy conservation constraints, the CDNNs utilize simple fully connected layers and a custom loss function to perform the model training process as well as the physical property of the exact solution. The approach can be beneficial for the following reasons: Firstly, we sample randomly and only input spatial coordinates without being restricted by the nature of samples.Secondly, our method is meshfree, which makes it more efficient than the traditional methods. Finally, the method is parallel and can solve multiple variables independently at the same time. We present the theoretical results to guarantee the convergence of the loss function and the convergence of the neural networks to the exact solution. Some numerical experiments are performed and discussed to demonstrate performance of the proposed method.
基金Project supported by the National Natural Science Foundation of China(Nos.11490551,11772172,11702158)。
文摘Finite-sized inertial spherical particles are fully-resolved with the immersed boundary projection method(IBPM)in the turbulent open-channel flow by direct numerical simulation(DNS).The accuracy of the particle surface force models is investigated in comparison with the total force obtained via the fully-resolved method.The results show that the steady-state resistance only performs well in the streamwise direction,while the fluid acceleration force,the added-mass force,and the shear-induced Saffman lift can effectively compensate for the large-amplitude and high-frequency characteristics of the particle surface forces,especially for the wall-normal and spanwise components.The modified steady-state resistance with the correction effects of the acceleration and the fluid shear can better represent the overall forces imposed on the particles,and it is a preferable choice of the surface force model in the Lagrangian point-particle method.
文摘The laminar boundary layer behind a constant-speed shock wave moving through a dusty gas along a solid surface is studied.The Saffman lift force acting on a spherical particle in a gas boundary layer is taken into account.A method for calculating the density profile of dispersed phase near the wall is pro- posed and some numerical results are given.It is shown that behind the shock wave,there exists a curved thin layer where the density of particles is many times higher than the original one.This dust collection effect may be of essential importance to the problem of dust explosion in industry.
基金Project supported by the Science and Technology Foundation of Sichuan Province(No. 05GG006-006-2)
文摘This paper introduces a new stabilized finite element method for the coupled Stokes and Darcy problem based on the nonconforming Crouzeix-Raviart element. Optimal error estimates for the fluid velocity and pressure are derived. A numerical example is presented to verify the theoretical predictions.
基金The Key Technologies R&D Program ofSichuan Province (No.05GG006-0062)
文摘We derived and analyzed a new numerical scheme for the coupled Stokes and Darcy problems by using H（div） conforming elements in the entire domain. The approach employs the mixed finite element method for the Darcy equations and a stabilized H（div） finite element method for the Stokes equations. Optimal error estimates for the fluid velocity and pressure are derived. The finite element solutions from the new scheme not only feature a full satisfaction of the continuity equation, which is highly demanded in scientific computing, but also satisfy the mass conservation.
文摘针对超声速气流驱动干粉颗粒形成的缩放喷管气固两相射流,采用拉格朗日方法、气固双向耦合模型以及Shear-Stress Transport k-ω湍流模型进行数值模拟,分析了颗粒装载比、萨夫曼力和入口压力等因素对气体参数、颗粒速度以及颗粒聚集度的影响。结果表明:气固双向耦合模型可以准确的分析气体与颗粒之间的相互作用。当高压气体通过缩放喷管时会产生超声速流动,从而带动颗粒作加速运动;在同一入口压力下,如果颗粒装载比较高,那么颗粒速度较小,且气体参数受颗粒的影响较大。颗粒在喷管扩张段轴线附近聚集,导致轴线到壁面附近区域内,产生沿径向向外的气流速度梯度,这可以解释萨夫曼力使轴线上气固两相的速度增大,并且在高颗粒装载比下的影响更显著的原因。不同入口压力下可能出现欠膨胀、过膨胀和完全膨胀三种不同喷管射流形态;在完全膨胀流态下,颗粒加速和气流降温的效果相对更好。研究结果可为超声速干粉灭火技术的应用提供理论支撑。
