Article
Computer Science, Interdisciplinary Applications
Sohail Reddy, Maciej Waruszewski, Felipe A. V. de Braganca Alves, Francis X. Giraldo
Summary: This work presents IMplicit-EXplicit (IMEX) formulations for discontinuous Galerkin (DG) discretizations of the compressible Euler equations governing non-hydrostatic atmospheric flows. Two different IMEX formulations are proposed to address the stiffness problem caused by the governing dynamics and the domain discretization. Efficient Schur complements are derived for both equation sets, and their performance is studied on 2D and 3D test problems, showing their convergence rates and efficiency in mesoscale and global applications.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Maxim A. Olshanskii, Arnold Reusken, Alexander Zhiliakov
Summary: This paper studies the lateral flow of a Boussinesq-Scriven fluid on a passively evolving surface embedded in Double-struck capital R-3, and introduces a well-posed weak formulation and a numerical solution method.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2022)
Article
Computer Science, Interdisciplinary Applications
Mustafa E. Danis, Jue Yan
Summary: This study proposes a new formula for the nonlinear viscous numerical flux and extends it to the compressible Navier-Stokes equations using the direct discontinuous Galerkin method with interface correction (DDGIC). The new method simplifies the implementation and enables accurate calculation of physical quantities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Gulnur Hacat, Fikriye Yilmaz, Aytekin Cibik, Songul Kaya
Summary: This paper presents a family of implicit-explicit time stepping scheme for the optimal control problem of the unsteady Navier-Stokes equations. The scheme utilizes discrete curvature to stabilize the optimization problem and provides stability and error analyses for the state, adjoint, and control variables.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Alejandro Allendes, Gabriel R. Barrenechea, Julia Novo
Summary: This work focuses on the finite element discretization of the incompressible Navier-Stokes equations, using a low order stabilized finite element method with piecewise linear continuous discrete velocities and piecewise constant pressures. The modified continuity equation involves a stabilizing bilinear form based on the jumps of the pressure, resulting in a divergence-free velocity field. The stability of the discrete problem is proven without needing to rewrite the convective field in its skew-symmetric way, and error estimates with constants independent of viscosity are established and validated through numerous numerical experiments.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Medine Demir, Aytekin Cibik, Songul Kaya
Summary: This paper discusses the application of the backward Euler based linear time filtering method in the developed energy-momentum-angular momentum conserving formulation under weakly enforced divergence constraint. The method enhances accuracy and improves approximate solutions by adding time filtering as a post-processing step. The numerical studies confirm the theoretical findings and demonstrate the superiority of the proposed method over the unfiltered case.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Engineering, Multidisciplinary
Leo G. Rebholz, Duygu Vargun, Mengying Xiao
Summary: This paper enhances the classical IPP method for incompressible NavierStokes equations by using Anderson acceleration to improve convergence properties. By analyzing the fixed point operator associated with IPP iteration and applying a general theory for AA, it is shown that the linear convergence rate of IPP can be significantly improved with AA enhancement. Numerical tests demonstrate the effectiveness of IPP with penalty parameter 1 enhanced by AA.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Applied
Leo G. Rebholz, Camille Zerfas
Summary: The paper introduces, analyzes, and tests an interpolation operator for continuous data assimilation of evolution equations. The operator is proven to be effective and accurate in fluid transport and incompressible Navier-Stokes data assimilation, demonstrating its practical utility in solving real-world problems.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
J. K. Djoko, J. Koko, M. Mbehou, Toni Sayah
Summary: In this study, the equations of Stokes and Navier-Stokes under power law slip boundary condition are examined theoretically and numerically. The existence and convergence of solutions are established for both problems, and optimal and sub-optimal a priori error estimates are derived in the finite element approximations. Iterative schemes for solving the nonlinear problems are formulated, and their convergence is studied. The theoretical findings are confirmed by numerical experiments.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
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
Mathematics, Applied
Pelin G. Geredeli, Leo G. Rebholz, Duygu Vargun, Ahmed Zytoon
Summary: This article introduces two modifications, namely grad-div stabilization and Anderson acceleration, to accelerate the Arrow-Hurwicz (AH) iteration for solving the incompressible steady Navier-Stokes equations. By applying these modifications, the convergence of AH is improved. Analytical and numerical results demonstrate that each method enhances the convergence of AH, and their combination yields an efficient and effective method that can compete with commonly used solvers. (c) 2022 Elsevier B.V. All rights reserved.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Eid Wassim, Bo Zheng, Yueqiang Shang
Summary: Based on two-grid discretizations, this paper proposes a parallel finite element method for solving the 2D/3D Navier-Stokes equations with damping. The method solves a fully nonlinear problem on a global coarse grid and then updates the coarse grid solution by solving linearized residual subproblems in overlapping fine grid subdomains using local and parallel procedures. The proposed method's errors are estimated with the help of a local a priori estimate for the finite element solution, and its performance is demonstrated through numerical tests.
ENGINEERING WITH COMPUTERS
(2023)
Article
Mathematics, Applied
Buyang LI, Shu Ma, Katharina Schratz
Summary: This article proposes a new type of low-regularity integrator for the Navier-Stokes equations. Unlike other existing numerical methods, this method is a semi-implicit exponential method in time, which helps preserve the energy-decay structure of the equations. It demonstrates first-order convergence under weaker regularity conditions than other methods.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2022)
Article
Mathematics, Applied
Y. Rong, J. A. Fiordilino, F. Shi, Y. Cao
Summary: We study a modular Crank-Nicolson based Voigt regularization algorithm for the Navier-Stokes equations. The algorithm adds a minimally intrusive module that implements Voigt regularization and numerical dissipation, improving stability and accuracy in large-scale dynamics.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Bo Zheng, Yueqiang Shang
Summary: This paper presents and studies three two-grid stabilized quadratic equal-order finite element algorithms based on two local Gauss integrations for the steady Navier-Stokes equations with damping. The algorithms first solve a stabilized nonlinear problem on a coarse grid and then pass the coarse grid solution to a fine grid for solving a stabilized linear problem. The stability of the algorithms is analyzed using nonlinear analysis techniques, and optimal order error estimates of the approximate solutions are derived. Theoretical and numerical results demonstrate that the accuracy of the approximate solutions computed by the two-grid stabilized algorithms is comparable to solving a fully stabilized nonlinear problem on the same fine grid, while saving a significant amount of CPU time compared to the one-grid stabilized algorithm.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Water Resources
A. Hamzehloo, M. L. Bahlali, P. Salinas, C. Jacquemyn, C. C. Pain, A. P. Butler, M. D. Jackson
Summary: This study tests the feasibility of using dynamic mesh optimization in a parallel computational framework for simulating saline intrusion. The results show that this new method outperforms fixed-mesh approaches, which has significant implications for aquifer management and resource regulation.
ADVANCES IN WATER RESOURCES
(2022)
Article
Computer Science, Artificial Intelligence
Pin Wu, Kaikai Pan, Lulu Ji, Siquan Gong, Weibing Feng, Wenyan Yuan, Christopher Pain
Summary: The paper introduces a novel deep learning model integrated with physical information to reduce computational cost and optimize model performance by adding the Navier-Stokes Equation to the loss function of the generator. Experimental results demonstrate significant improvements over similar models, with the effectiveness of introducing physics loss also verified.
NEURAL COMPUTING & APPLICATIONS
(2022)
Article
Mathematics, Applied
Vinicius L. S. Silva, Claire E. Heaney, Yaqi Li, Christopher C. Pain
Summary: We propose a new application of generative adversarial networks (GANs) for time prediction (PredGAN) and measurement assimilation (DA-PredGAN). GANs have recently gained attention for their ability to generate realistic-looking images. In this study, we explore how GANs can be used in computational modeling and data assimilation. We apply these methods to a compartmental model in epidemiology to simulate the spread of COVID-19 in an idealized town, and the results show accurate predictions and efficient assimilation of observed data.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
Sibo Cheng, Jianhua Chen, Charitos Anastasiou, Panagiota Angeli, Omar K. K. Matar, Yi-Ke Guo, Christopher C. C. Pain, Rossella Arcucci
Summary: In this paper, a system is proposed that combines reduced-order surrogate models with a novel data assimilation technique to incorporate real-time observations from different physical spaces into high-dimensional dynamical systems. The system uses local smooth surrogate functions to link the encoded system variables and the current observations, enabling variational data assimilation at low computational cost. The proposed approach improves the efficiency provided by reduced-order modeling and the accuracy of data assimilation.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Nuclear Science & Technology
Akash Venkateshwaran, Mahendhar Kumar, M. B. Shyam Kumar, D. Davidson Jebaseelan, R. Sivakumar, Aniket Joshi, Christopher Pain
Summary: In-vessel melt retention is a crucial safety design in nuclear reactors to prevent radiation release during beyond-design basis accidents. This study analyzes the effects of forced convection cooling and natural convection cooling through simulating the COPRA experiment, and also examines the impact of varying reactor pressure vessel (RPV) geometry sizes. The results provide valuable insights for future severe accident experiments and the design of reactors.
PROGRESS IN NUCLEAR ENERGY
(2023)
Article
Environmental Sciences
Prashant Kumar, Juan C. Zavala-Reyes, Gopinath Kalaiarasan, Hisham Abubakar-Waziri, Gloria Young, Ian Mudway, Claire Dilliway, Ramzi Lakhdar, Sharon Mumby, Michal M. Klosowski, Christopher C. Pain, Ian M. Adcock, Jonathan S. Watson, Mark A. Sephton, Kian Fan Chung, Alexandra E. Porter
Summary: The study examined the distribution characteristics of ultrafine particles in a London underground platform, finding that particle number concentrations gradually increased and reached a peak between 18:00 and 21:00. Harmful organic compounds and metal mixtures were also identified, highlighting the need for improved ventilation conditions in underground railway systems.
SCIENCE OF THE TOTAL ENVIRONMENT
(2023)
Article
Public, Environmental & Occupational Health
Sida Chen, Zixue Tai, Jianping Liu
Summary: This study examined the factors influencing the dissemination of Tai Ji Quan (TJQ) to diverse practicing communities in China. The findings showed that individual and environmental factors play important roles in shaping personal decisions in TJQ engagement. The study highlights the need for an ecological approach to promote the spread of TJQ to the general population.
JOURNAL OF PHYSICAL ACTIVITY & HEALTH
(2023)
Article
Computer Science, Interdisciplinary Applications
Rossella Arcucci, Dunhui Xiao, Fangxin Fang, Ionel Michael Navon, Pin Wu, Christopher C. Pain, Yi-Ke Guo
Summary: Numerical simulations are widely used for predicting complex air flows and pollution transport. Non-Intrusive Reduced Order Model (NIROM) has been proven to be an efficient method for numerical forecasting. However, the reduced space of the model leads to uncertainties, and computational methodologies also contribute to uncertainty. Taking these uncertainties into account is crucial for the acceptance of numerical simulations.
COMPUTERS & FLUIDS
(2023)
Correction
Mathematics, Applied
Vinicius L. S. Silva, Claire E. Heaney, Yaqi Li, Christopher C. Pain
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Mechanics
Xiaofei Wu, Hisham Abubakar-Waziri, Fangxin Fang, Claire Dilliway, Pin Wu, Jinxi Li, Runming Yao, Pankaj Bhavsar, Prashant Kumar, Christopher C. Pain, Kian Fan Chung
Summary: We modeled the transmission of SARS-CoV-2 in an isolation room at the Royal Brompton Hospital in London, using an adaptive mesh computational fluid dynamics model. The model was based on data collected during the patient's stay and aimed to optimize the design layout of the isolation room, considering the location of the air extractor, filtration rates, bed location of the patient, and the health and safety of the staff working in the area.
Article
Respiratory System
Hisham Abubakar-Waziri, Gopinath Kalaiarasan, Rebecca Wawman, Faye Hobbs, Ian Adcock, Claire Dilliway, Fangxin Fang, Christopher Pain, Alexandra Porter, Pankaj K. Bhavsar, Emma Ransome, Vincent Savolainen, Prashant Kumar, Kian Fan Chung
Summary: During the easing of COVID-19 pandemic restrictions in London, SARS-CoV2 RNA was detected in the air of hospital waiting areas, wards, and London Underground train carriages. This suggests that airborne transmission may be an important mode of spread. Further research is needed to determine the transmission potential of SARS-CoV2 detected in the air.
BMJ OPEN RESPIRATORY RESEARCH
(2023)
Article
Engineering, Multidisciplinary
Toby R. F. Phillips, Claire E. Heaney, Boyang Chen, Andrew G. Buchan, Christopher C. Pain
Summary: This paper presents a new approach that uses AI software libraries as an alternative method for solving discretized partial differential equations (PDEs). The approach represents numerical discretizations from finite volume and finite element methods by pre-determining weights within a neural network. No training of the network is required as the weights are defined by the discretization scheme. The solutions obtained using this approach are identical to those obtained with standard codes often written in Fortran or C++, and can run on different computer architectures without modification.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Environmental Sciences
Meiling Cheng, Fangxin Fang, Ionel Michael Navon, Jie Zheng, Jiang Zhu, Christopher Pain
Summary: In this study, machine learning models were used to accurately predict the spatiotemporal ozone concentration in the Beijing-Tianjin-Hebei region from 2013 to 2018. The results showed that these models achieved better prediction performance under various meteorological conditions.
SCIENCE OF THE TOTAL ENVIRONMENT
(2023)
Article
Environmental Sciences
H. Woodward, A. Schroeder, A. de Nazelle, C. C. Pain, M. E. J. Stettler, H. ApSimon, A. Robins, P. F. Linden
Summary: The spatio-temporal variability of exposure to harmful pollutants in roadside areas is often neglected in assessments of pedestrian and cyclist exposures. This study aims to fully describe this variability and evaluate the benefits of high spatio-temporal resolution over high spatial resolution only. The study also compares high resolution vehicle emissions modeling to using a constant volume source. The findings highlight the impact of peak exposures and emphasize the importance of considering high resolution temporal air pollution variability for accurate characterization of pedestrian and cyclist exposures.
SCIENCE OF THE TOTAL ENVIRONMENT
(2023)
Article
Geosciences, Multidisciplinary
D. Rhodri Davies, Stephan C. Kramer, Sia Ghelichkhan, Angus Gibson
Summary: Firedrake is an automated system for solving partial differential equations using the finite-element method. It provides accurate, efficient, flexible, and scalable research software for simulating various problems in geophysical fluid dynamics. The system's capabilities are demonstrated through comparisons and scalability tests, and its versatility is highlighted by its application to different physical and geometrical scenarios. Firedrake is also proven to be suitable for addressing research problems in global mantle dynamics.
GEOSCIENTIFIC MODEL DEVELOPMENT
(2022)
