Article
Mechanics
Li-Wei Chen, Berkay A. Cakal, Xiangyu Hu, Nils Thuerey
Summary: In this study, deep learning methods were used to efficiently predict flow fields and loads for aerodynamic shape optimization. The trained U-net-based deep neural network models successfully inferred flow fields and calculated gradient flows for optimizing shapes, showing great promise for general aerodynamic design problems. The results demonstrate that the DNN models are capable of accurately predicting flow fields and generating satisfactory aerodynamic forces, even without specific training for aerodynamic forces.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Mathematics, Applied
L. Rebholz, F. Tone
Summary: This paper studies the H1-stability of the BDF2 scheme for the 2D Navier-Stokes equations for all positive time. Specifically, we discretize in time using the backward differentiation formula (BDF2) and prove the stability of the numerical scheme with the help of the discrete Gronwall lemma and the discrete uniform Gronwall lemma.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Computer Science, Interdisciplinary Applications
Shinhoo Kang, Alp Dener, Aidan Hamilton, Hong Zhang, Emil M. Constantinescu, Robert L. Jacob
Summary: This study examines multirate partitioned Runge-Kutta methods for the fluid-fluid interaction problem and demonstrates their parallel performance using the PETSc library. The results show that these methods can conserve total mass, have second-order accuracy in time, and provide favorable strong- and weak-scaling performance on modern computing architectures. The study also highlights that the speedup factors of multirate partitioned Runge-Kutta methods align with theoretical expectations.
COMPUTERS & FLUIDS
(2023)
Article
Mechanics
T. H. B. Demont, S. K. F. Stoter, E. H. van Brummelen
Summary: In this article, the behavior of the Abels-Garcke-Grun Navier-Stokes-Cahn-Hilliard diffuse-interface model for binary-fluid flows as the diffuse-interface thickness approaches zero is studied. The optimal order of the m-epsilon scaling relation and its impact on the convergence rate of the diffuse-interface solution to the sharp-interface solution are elucidated. The case of an oscillating droplet is investigated, and new analytical expressions for small-amplitude oscillations are derived. The sharp-interface limit of the Navier-Stokes-Cahn-Hilliard equations is probed using an adaptive finite-element method.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Physics, Mathematical
Masahiro Suzuki, Katherine Zhiyuan Zhang
Summary: In this paper, we investigate the compressible Navier-Stokes equation in a perturbed half-space with an outflow boundary condition and the supersonic condition. We demonstrate the unique existence of stationary solutions for the perturbed half-space, which exhibit multidirectional flow and are independent of the tangential directions. Additionally, we prove the asymptotic stability of these stationary solutions.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2021)
Article
Mechanics
Chuong V. Tran, Xinwei Yu, David G. Dritschel
Summary: Incompressible fluid flows are characterized by high correlations between velocity and pressure, as well as between vorticity and pressure. This correlation plays a significant role in maintaining regularity in Navier-Stokes flows. The study suggests that as long as global pressure minimum (or minima) and velocity maximum (or maxima) are mutually exclusive, regularity is likely to persist.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Xinjie Ji, James Gabbard, Wim M. van Rees
Summary: This paper introduces a sharp-interface approach based on the immersed interface method for handling the one- and two-way coupling between an incompressible flow and rigid bodies using the vorticity-velocity Navier-Stokes equations. The authors develop a moving boundary treatment and a two-way coupling methodology that do not require the pressure field. Extensive testing shows that the resulting solver achieves second-order accuracy and provides efficiency benefits compared to a representative first-order approach.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Sameh Abidi, Jamil Satouri
Summary: The article proposes a new numerical method to solve the problem of optimal control of the steady-state Navier-Stokes equations through the velocity-pressure formulation. A system of equations is derived using a new technique for calculating the solution. The spectral method is used to discretize the problem, and an extended relaxation method is proposed to ensure proper convergence of the system. Numerical results are provided to confirm the effectiveness of this approach.
Article
Computer Science, Interdisciplinary Applications
Ning Li, Jilian Wu, Xinlong Feng
Summary: In this paper, a filtered time-stepping method for incompressible Navier-Stokes equations with variable density is presented. By using a time filter, the time accuracy of the method is increased from first order to second order with only one backward Euler solve at each time step. The added time filter is expressed by linear combinations of the solutions at previous time levels without additional complexity. The stability of density and velocity for both the fully implicit backward Euler algorithm and the backward Euler plus time filter algorithm is proved. Furthermore, the approach is extended to a variable time stepsize BETF algorithm, and new adaptive BE algorithm and variable stepsize variable order algorithm with low cost error estimators are constructed. Experimental results demonstrate the stability and efficiency of the proposed methods.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Yanqing Wang, Yulin Ye
Summary: In this paper, an energy conservation criterion is derived for weak solutions of both the incompressible and compressible Navier-Stokes equations. The criterion is based on a combination of velocity and its gradient. For the incompressible case, it extends known results on periodic domain, including the famous Lions' energy conservation criterion. For the compressible case, it improves recent results and extends criteria for energy conservation from incompressible to compressible flow.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Li Shan, Haicheng Zhang
Summary: This report discusses the flow in dual-porosity media coupled with free flow in embedded macrofractures and conduits. It introduces a dual-porosity model for flow in the dual-porosity media and a Stokes model for flow in the conduits/macrofractures. A partitioned time stepping method is proposed to decouple the complex model into three simple sub-problems, ensuring stability and optimal error estimates of the method.
APPLIED NUMERICAL MATHEMATICS
(2022)
Article
Mechanics
Lukas Unglehrt, Michael Manhart
Summary: This study investigates the flow behavior of a hexagonal close-packed arrangement of spheres under steady and oscillatory conditions. The friction and pressure drag contributions to the momentum budget are quantified and analyzed. The findings show that for steady flow, the friction and viscous pressure drag scale with the Reynolds number, while the convective pressure drag exhibits different scaling behaviors. Under oscillatory flow conditions, the amplitudes of the drag components are similar to the steady cases at low and medium Womersley numbers, but behave differently at high Womersley numbers, indicating the need for new models beyond the current quasisteady approaches.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Mechanics
Niklas Fehn, Martin Kronbichler, Peter Munch, Wolfgang A. Wall
Summary: This study contributes to the investigation of the well-known energy dissipation anomaly in inviscid limit by conducting high-resolution numerical simulations of the three-dimensional Taylor-Green vortex problem. The interesting observation is made that the kinetic energy evolution does not tend towards exact energy conservation as the spatial resolution of numerical scheme increases. This raises the question of whether the results obtained can be seen as a numerical confirmation of the famous energy dissipation anomaly and elaborates on an indirect approach for the identification of finite-time singularities based on energy arguments.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Mathematics, Applied
Dominic Breit, Andreas Prohl
Summary: In this paper, we propose and study a temporal and a spatio-temporal discretisation method for the two-dimensional stochastic Navier-Stokes equations in bounded domains with no-slip boundary conditions. By considering additive noise, we construct the discretisation based on the solution of the related nonlinear random partial differential equation, which is solved using a transform of the solution of the stochastic Navier-Stokes equations. We show a strong rate (up to) 1 in probability for the corresponding discretisation in space and time (and space-time).
IMA JOURNAL OF NUMERICAL ANALYSIS
(2023)
Article
Mathematics, Applied
James C. Robinson
Summary: This paper considers the solutions of the three-dimensional Navier-Stokes equations on periodic domains and compares them to solutions on the whole space. It shows that under certain conditions, regularity can be transferred from the whole space to the periodic case.
Article
Physics, Multidisciplinary
Jing Yue, Jian Li, Wen Zhang, Zhangxin Chen
Summary: We propose an efficient deep learning method called coupled deep neural networks (CDNNs) for coupling the Stokes and Darcy-Forchheimer problems. Our method properly compiles the interface conditions of the coupled problems into the networks and serves as an efficient alternative to complex coupled problems. To enforce energy conservation constraints, the CDNNs use simple fully connected layers and a custom loss function for model training and physical property approximation. The method has advantages in random sampling, mesh-free implementation, and parallel computation for solving multiple variables simultaneously. Theoretical results guarantee the convergence of the loss function and the neural networks to the exact solution. Numerical experiments demonstrate the performance of the proposed method.
Article
Engineering, Chemical
Mohammadali Ahmadi, Matthew Clarke, Zhangxin Chen
Summary: Heavy oil and bitumen play a crucial role in Canada's energy resources, and in-situ thermal methods are the primary approaches used to produce them. Researchers used molecular dynamics simulation to study the rheological behavior of bitumen under different temperatures, revealing that the size and polarity of bitumen fractions affect its rheological behavior.
CANADIAN JOURNAL OF CHEMICAL ENGINEERING
(2023)
Article
Geochemistry & Geophysics
Xiaocai Shan, Zhangxin Chen, Boye Fu, Wang Zhang, Jing Li, Keliu Wu
Summary: We introduce a novel deep spatial-sequential graph convolutional network (SSGCN) for predicting total organic carbon (TOC) by leveraging cross-log topological association features and log-specific sequential features, outperforming existing methods. In the southeast Sichuan Basin, SSGCN shows better cross-validation performance and generalizability. Our SSGCN method can predict TOC with an R-2 value of 0.87 within 1 second, increasing efficiency in obtaining TOC parameter. We recommend using graph and sequential convolutions in well-log analysis deep learning architectures.
Article
Biochemistry & Molecular Biology
Mohammadali Ahmadi, Zhangxin Chen
Summary: Using molecular dynamics (MD) simulation, the study evaluated the wettability alteration during steam injection for bitumen and heavy oil recovery. It was found that higher asphaltene content led to higher adsorption energy between bitumen/heavy oil and quartz surfaces. At elevated temperatures, the quartz surfaces became more oil-wet, while at ambient conditions, they were highly water-wet. These findings provide insights into wettability alteration during in situ thermal processes for bitumen and heavy oil recovery.
Article
Mathematics, Applied
Shuaijun Liu, Pengzhan Huang
Summary: In this paper, a sparse grad-div stabilized algorithm is proposed to penalize for lack of divergence-free solution in the incompressible magnetohydrodynamics equations. This algorithm adds a minimally intrusive module that implements grad-div stabilization with a sparse block structure matrix. The unconditional stability and error estimates of the proposed algorithm are provided, and numerical tests are conducted. Compared to other grad-div stabilizations, the sparse grad-div stabilized algorithm is more efficient with some large values of grad-div parameters.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Energy & Fuels
Qiyang Gou, Shang Xu, Zhangxin Chen, Zhengbin Wu
Summary: The traditional characterization of shale oil reservoir pores is based on the classification of micro, meso, and macropores in shale gas reservoirs. However, the significant difference between oil and gas molecules results in poor applicability of this classification. This study proposes a new classification method for shale oil reservoirs, based on N2 adsorption, Soxhlet extraction, and programmed pyrolysis experiments. Compared to previous methods, this new approach reveals the correlation between shale oil attributes and pore spaces for the first time, providing more accurate evaluation results and significant implications for optimizing exploration strategies.
Article
Energy & Fuels
Gang Hui, Zhangxin Chen, Jun Yan, Muming Wang, Hai Wang, Dongmei Zhang, Fei Gu
Summary: The integrated experiment logging-based strategy is proposed to evaluate high-quality shale in the West Duvernay Shale Basin. Through core measurements and logging interpretations, the geographic distribution of high-quality shales is determined. Machine learning techniques are then used to quantify the relationships between shale productivity and reservoir characteristics and predict the spatial distribution of high-quality shales. The strategy reveals that the Duvernay shale consists of four sublayers, with the D2 and D3 sublayers considered high-quality.
Article
Energy & Fuels
Bo Liao, Jintang Wang, Jinsheng Sun, Kaihe Lv, Lei Liu, Qi Wang, Ren Wang, Xindi Lv, Yudou Wang, Zhangxin Chen
Summary: Studying the synergism effect of different hydrate inhibitors on methane hydrate formation is crucial for developing new gas hydrate inhibitors and drilling and completion fluid systems.
Article
Energy & Fuels
Zhenqian Xue, Shuo Yao, Haoming Ma, Chi Zhang, Kai Zhang, Zhangxin Chen
Summary: This study proposes an optimization framework based on Artificial Neural Network (ANN) and Differential Evolution (DE) to optimize a three-horizontal-well Enhanced Geothermal System (EGS) in the Qiabuqia field, considering the levelized cost of electricity (LCOE) as an economic performance indicator. The results show that the proposed framework can significantly save operation time and achieve the lowest LCOE among all random cases.
Review
Chemistry, Physical
Heng Zhao, Jing Liu, Na Zhong, Steve Larter, Yu Li, Md Golam Kibria, Bao-Lian Su, Zhangxin Chen, Jinguang Hu
Summary: Biomass, as a promising alternative to limited fossil feedstock, has the potential for value-added chemicals and fuels. However, the low conversion efficiency and product selectivity of biomass photoreforming due to its structural complexity and unclear reaction mechanism remain challenges. Hierarchically porous photocatalysts with adjustable surface properties have shown superiority in boosting the conversion efficiency and selectivity by improving mass transfer.
ADVANCED ENERGY MATERIALS
(2023)
Article
Mathematics, Applied
Shuaijun Liu, Pengzhan Huang, Yinnian He
Summary: In this paper, a fully discrete second-order-in-time scheme for the incompressible MHD equations is proposed, which utilizes blended BDF and extrapolation treatments for nonlinear terms. The scheme is shown to be more accurate than the traditional two-step BDF scheme, while maintaining A-stability. The unconditional stability, long-time stability, and optimal convergence rate of the scheme are discussed, and numerical experiments with comparison to the two-step BDF scheme are conducted to verify the findings.
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2023)
Article
Energy & Fuels
Feng Zhang, Long Nghiem, Zhangxin Chen
Summary: This paper introduces the use of proxy models in reservoir simulation to explore relationships between explanatory and response variables. Deep learning methods, such as Recurrent Neural Networks (RNNs), have shown remarkable advancement in predicting reservoir production. However, the limitation of RNNs being hard to parallelize makes their training process computationally expensive. Therefore, a Transformer based proxy model is proposed in this study to accelerate learning and simulation processes.
GEOENERGY SCIENCE AND ENGINEERING
(2023)
Article
Chemistry, Physical
Xi Cheng, Bo Liu, Heng Zhao, Hongguang Zhang, Jiu Wang, Zhangkang Li, Bei Li, Zhangxin Chen, Jinguang Hu
Summary: This study designed a catalyst with a strong interfacial effect to efficiently photorefine lignocellulosic biomass, producing hydrogen and value-added chemicals. By optimizing the interfacial effect, the catalyst achieved high photocatalytic hydrogen production in the presence of different electron donors. This research demonstrates the potential of photorefining raw biomass through the design and optimization of catalysts.
JOURNAL OF COLLOID AND INTERFACE SCIENCE
(2024)
Article
Thermodynamics
Weibing Tian, Keliu Wu, Yanling Gao, Jing Li, Zhangxin Chen, Wojciech Stanek
Summary: This study revealed the dynamic contact angle (DCA) effect on imbibition and its impact on enhanced oil recovery in tight reservoirs. The results showed that the DCA effect has four stages of influence on imbibition recovery with time and affects both imbibition velocity and recovery rate.
Article
Energy & Fuels
Fuhe Lin, Frank Cheng, Zhangxin Chen
Summary: Condensed water in natural gas transmission can lead to pipeline corrosion and rupture. Predicting the distribution of water film and flow characteristics is crucial for analyzing pipe elbow corrosion. In this study, a model is developed to predict water phase accumulation locations and corrosion extent. The model is validated and shows substantial agreement with previous studies. The simulation results indicate that water film is mainly distributed at the bottom, and the elbow front is more susceptible to corrosion.
GEOENERGY SCIENCE AND ENGINEERING
(2023)
