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MIXED DISCONTINUOUS GALERKIN METHOD FOR QUASI-NEWTONIAN STOKES flowS

Journal of Computational mathematics 2024年第3期42卷 885-910页

作者： Yanxia Qian Fei Wang Wenjing Yan School of Mathematics and Statistics Xi'an Jiaotong UniversityXi'an 710049China School of Mathematics and Statistics&State Key Laboratory of Multiphase Flow in Power Engineering Xi'an Jiaotong UniversityXi'an 710049China

In this paper,we introduce and analyze an augmented mixed discontinuous Galerkin(MDG)method for a class of quasi-Newtonian Stokes *** the mixed formulation,the unknowns are strain rate,stress and velocity,which are approximated by a discontinuous piecewise polynomial triplet ■for k≥***,the discontinuous piecewise polynomial function spaces for the field of strain rate and the stress field are designed to be *** addition,the pressure is easily recovered through simple *** the benefit of the analysis,we enrich the MDG scheme with the constitutive equation relating the stress and the strain rate,so that the well-posedness of the augmented formulation is obtained by a nonlinear functional *** k≥0,we get the optimal convergence order for the stress in broken ■(div)-norm and velocity in L^(2)-***,the error estimates of the strain rate and the stress in-norm,and the pressure in L^(2)-norm are optimal under certain ***,several numerical examples are given to show the performance of the augmented MDG method and verify the theoretical *** evidence is provided to show that the orders of convergence are sharp.

关键词： Quasi-Newtonian fows Mixed discontinuous Galerkin method Symmetric strain rate Symmetric stress Optimal convergence orders

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Adaptive Growing Randomized Neural Networks for Solving Partial Differential Equations

arXiv

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arXiv 2024年

作者： Dang, Haoning Wang, Fei Jiang, Song School of Mathematics and Statistics Xi’an Jiaotong University Shaanxi Xi’an710049 China School of Mathematics and Statistics State Key Laboratory of Multiphase Flow in Power Engineering Xi’an Jiaotong University Shaanxi Xi’an710049 China Institute of Applied Physics and Computational Mathematics Beijing100088 China

Randomized neural network (RNN) methods have been proposed for solving various partial differential equations (PDEs), demonstrating high accuracy and efficiency. However, initializing the fixed parameters remains a challenging issue. Additionally, RNNs often struggle to solve PDEs with sharp or discontinuous solutions. In this paper, we propose a novel approach called Adaptive Growing Randomized Neural Network (AG-RNN) to address these challenges. First, we establish a parameter initialization strategy based on frequency information to construct the initial RNN. After obtaining a numerical solution from this initial network, we use the residual as an error indicator. Based on the error indicator, we introduce growth strategies that expand the neural network, making it wider and deeper to improve the accuracy of the numerical solution. A key feature of AG-RNN is its adaptive strategy for determining the weights and biases of newly added neurons, enabling the network to expand in both width and depth without requiring additional training. Instead, all weights and biases are generated constructively, significantly enhancing the network’s approximation capabilities compared to conventional randomized neural network methods. In addition, a domain splitting strategy is introduced to handle the case of discontinuous solutions. Extensive numerical experiments are conducted to demonstrate the efficiency and accuracy of this innovative approach. Copyright © 2024, The Authors. All rights reserved.

关键词： Partial differential equations

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A mixed discontinuous Galerkin method with symmetric stress for Brinkman problem based on the velocity-pseudostress formulation

arXiv

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arXiv 2019年

作者： Qian, Yanxia Wu, Shuonan Wang, Fei Wang, Fei School of Mathematics and Statistics Xi'An Jiaotong University Xi'an Shaanxi710049 China School of Mathematical Sciences Peking University Beijing100871 China School of Mathematics and Statistics State Key Laboratory of Multiphase Flow in Power Engineering Xi'An Jiaotong University Xi'an Shaanxi710049 China

The Brinkman equations can be regarded as a combination of the Stokes and Darcy equations which model transitions between the fast flow in channels (governed by Stokes equations) and the slow flow in porous media (governed by Darcy?fs law). The numerical challenge for this model is the designing of a numerical scheme which is stable for both the Stokes-dominated (high permeability) and the Darcy-dominated (low permeability) equations. In this paper, we solve the Brinkman model in n dimensions (n = 2, 3) by using the mixed discontinuous Galerkin (MDG) method, which meets this challenge. This MDG method is based on the pseudostress-velocity formulation and uses a discontinuous piecewise polynomial pair PSk+1-Pk(k ≥ 0), where the stress field is symmetric. The main unknowns are the pseudostress and the velocity, whereas the pressure is easily recovered through a simple postprocessing. A key step in the analysis is to establish the parameter-robust inf-sup stability through specific parameter-dependent norms at both continuous and discrete levels. Therefore, the stability results presented here are uniform with respect to the permeability. Thanks to the parameter-robust stability analysis, we obtain optimal error estimates for the stress in broken H(div)-norm and velocity in L2-norm. Furthermore, the optimal L2 error estimate for pseudostress is derived under certain conditions. Finally, numerical experiments are provided to support the theoretical results and to show the robustness, accuracy, and flexibility of the MDG method. Copyright © 2019, The Authors. All rights reserved.

关键词： Stability

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A mixed discontinuous galerkin method for linear elasticity with strongly imposed symmetry

arXiv

引用

arXiv 2019年

作者： Wang, Fei Wu, Shuonan Xu, Jinchao School of Mathematics and Statistics and State Key Laboratory of Multiphase Flow in Power Engineering Xi'an Jiaotong University Xi'an Shaanxi710049 China School of Mathematical Sciences Peking University Beijing100871 China Department of Mathematics Pennsylvania State University University ParkPA16802 United States

In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in d-dimension (d = 2, 3). This method uses polynomials of degree k + 1 for the stress and of degree k for the displacement (k > 0). The mixed DG scheme is proved to be well-posed under proper norms. Specifically, we prove that, for any k > 0, the H(div)-like error estimate for the stress and L2 error estimate for the displacement are optimal. We further establish the optimal L2 error estimate for the stress provided that the Pk+2 - P-1 k+1 Stokes pair is stable and k > d. We also provide numerical results of MDG showing that the orders of convergence are actually sharp.65N30, 65M60 Copyright © 2019, The Authors. All rights reserved.

关键词： Galerkin methods

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Hydrothermal Hydrolysis Modeling of Lignocellulosic Biomass Using Subcritical Water for Test Packed Bed Reactor

SSRN

引用

SSRN 2023年

作者： Wu, Zhonggang Wang, Jiawei Du, Xiaocheng Su, Hanguang China Nuclear Power Operations Co. Ltd. Shenzhen518116 China Department of Mathematics Physics and Electrical Engineering Northumbria University NewcastleNE1 8ST United Kingdom State Key Laboratory of Multiphase Flow in Power Engineering Xian Jiaotong University Xi'An China School of Information Science and Engineering Northeastern University Shenyang China

In this paper, the subcritical water hydrothermal conversion process of lignocellulosic biomass as porous media in packed bed reactor was investigated by numerical simulation. The computational fluid dynamics mathematical modeling was used to describe the transient multi-physical fields formed during the instantaneous formation process of organic functional groups on the bases of experiment. The effect of inlet hydrothermal fluid velocity and temperature on the transient seepage flow, heat and transfer, and organic conversion reaction were investigated by ANSYS FLUENT® software. The results of the simulation indicate that the osmotic pressure and velocity increase with the hydrothermal fluid velocity and temperature. The surface heat transfer coefficient increases with the hydrothermal fluid velocity and temperature, and may reach the maximum within the scope of this paper. Both experimental and numerical simulation results consistently show that within the first 60 minutes of the hydrothermal reaction, the organic reaction rate is mainly determined by the combined model of turbulent-hydrothermal reaction. For a later time period after 60 minutes, the organic reaction rate mainly depends on the single model of hydrothermal reaction. Comparing the same experimental conditions and their real-time measurements, the numerical results in this paper accord with them. © 2023, The Authors. All rights reserved.

关键词： Porous materials

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PREFACE: SPECIAL ISSUE FOR THE 2ND INTERNATIONAL SYMPOSIUM ON THERMAL-FLUID DYNAMICS (ISTFD2021)

引用

Heat Transfer Research 2022年第8期53卷 V-VI页

作者： Cheng, Lixin Bai, Bofeng Guo, Zhixiong School of Energy and Power Engineering Beijing University of Technology Beijing100124 China Department of Engineering and Mathematics Sheffield Hallam University SheffieldS1 1WB United Kingdom State Key Laboratory of Multiphase Flow in Power Engineering Xi’an Jiaotong University Xi’an710049 China Department of Mechanical and Aerospace Engineering Rutgers The State University of New Jersey PiscatawayNJ08854 United States

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A study of a computational BVP for heat transfer and friction drag in magnetohydrodynamics viscous flow of a nanofluid subject to the curved surface

引用

Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical engineering 2021年

作者： Khan, M Riaz Saleel, C Ahamed Saeed, Tareq Allehiany, F.M. El-Refaey, Adel M Jing, Dengwei Mahmoud, Emad E LSEC and ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences China School of Mathematical Science University of Chinese Academy of Sciences China Department of Mechanical Engineering College of Engineering King Khalid University Saudi Arabia -Research Group Department of Mathematics Faculty of Science King Abdulaziz University Saudi Arabia Department of Mathematical Sciences College of Applied Sciences Umm Al-Qura University Saudi Arabia Department of Basic and Applied Science College of Engineering and Technology Arab Academy for Science Technology Maritime Transport Smart Village Campus Egypt State Key Laboratory of Multiphase Flow in Power Engineering Xi’an Jiaotong University China Department of Mathematics and Statistics College of Science Taif University Taif Saudi Arabia

The ongoing work investigates the features of Joule heating and convective condition over a magnetohydrodynamic stagnation point flow of (Formula presented.) nanofluid moving across a curved surface. Moreover, mass suction is supposed through the stretching/shrinking surface. The initially developed model of partial differential equations is transformed into the ordinary ones assisted by suitable similarity variables. Subsequently, the ultimate nonlinear model of ordinary differential equations is solved with the help of a built-in function bvp4c package in MATLAB. Several graphical results are plotted to see the influence of various dimensionless parameters over the velocity, temperature, heat transfer, and friction drag. We found that there exists an escalation in temperature with increasing values of curvature, Eckert number, Hartmann number, and Biot number;however, the velocity profile declines with large curvature, ratio parameter, and high concentration of nanoparticles. It is also important to note that the friction drag rises with the mass suction, and reduces with vast curvature, whereas the rate of heat transfer improves with suction and Biot number but lowers with Eckert number and Hartmann number. © IMechE 2021.

关键词： Magnetohydrodynamics

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