Article
Computer Science, Interdisciplinary Applications
Soonpil Kang, Arif Masud
Summary: This paper presents an immersed boundary method for weak enforcement of Dirichlet boundary conditions on immersed surfaces. The method combines the Variational Multiscale Discontinuous Galerkin method and an interface stabilized form. A significant contribution of this work is the analytically derived Lagrange multiplier for weak enforcement of the Dirichlet boundary conditions. Numerical experiments demonstrate the method's effectiveness with different types of meshes, and the norm of the stabilization tensor varies with the flow physics.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mechanics
Xi Chen, Corina Drapaca
Summary: This paper presents a systematic construction of H(div)-conforming numerical dissipation for time-dependent incompressible Euler and Navier-Stokes equations to improve the performance of the central flux scheme. The method generalizes the upwind flux scheme from a dissipation point of view, utilizing discontinuity of numerical quantities across interior edges. Experimental results demonstrate the effectiveness of the added dissipation in reducing errors and preserving physics.
Article
Computer Science, Interdisciplinary Applications
Guelnur Hacat, Mine Akbas, Aytekin cibik
Summary: In this study, a continuous data assimilation (CDA) scheme is proposed to combine observable data with a numerical method, resulting in better solutions that closely resemble the current state of the system. The scheme is applied to a Navier-Stokes system, discretized in time using the two-step Backward Differentiation Formula (BDF2) and in space using finite element method. To improve accuracy and prevent non-physical oscillations, a projection-based variational multiscale method (VMS) is also employed. Detailed long-time stability and convergence analyses are presented, along with numerical tests to support theoretical findings and demonstrate the potential of the method.
JOURNAL OF COMPUTATIONAL SCIENCE
(2023)
Article
Mechanics
Ningyu Zhan, Rongqian Chen, Yancheng You
Summary: The meshfree method based on DGKS, named meshfree-DGKS, is proposed for simulating incompressible/compressible flows. Discretization is done using the least squares-based finite difference approach, with the concept of numerical flux introduced to handle compressible problems with discontinuities effectively. The method allows for capturing shock waves easily by reconstructing fluxes at mid-points based on the local solution of the Boltzmann equation.
Article
Mechanics
Soonpil Kang, Arif Masud
Summary: This paper introduces a new stabilized form of incompressible Navier-Stokes equations for weak enforcement of Dirichlet boundary conditions at immersed boundaries, derived using the VMS method without user defined parameters. Through a set of benchmark problems, it is shown that the proposed method is mathematically robust and computationally stable and accurate.
Article
Engineering, Multidisciplinary
Chaemin Lee, Minam Moon, Jongho Park
Summary: This paper studies gradient smoothing methods (GSMs) with improved convergence behaviors for high-contrast problems such as the flow in heterogeneous porous media. The proposed GSM is adaptive to the heterogeneity of the problem and a multiscale variant is also introduced. The improved performance of the proposed methods is demonstrated through various numerical examples.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Jie Wan
Summary: This paper proves the existence of two-parameter multiscale V-states in a disk, concentrating near two points and not symmetric about the origin. The existence of multiscale V-states with N-folds for N >= 2 is also demonstrated.
JOURNAL OF MATHEMATICAL FLUID MECHANICS
(2021)
Article
Mathematics, Applied
Hongtao Ran, Bo Zheng, Yueqiang Shang
Summary: A parallel finite element variational multiscale method for the NavierStokes equations with nonlinear slip boundary conditions is proposed and analyzed. Error estimates in H-1-norm of velocity and L-2-norm of pressure are derived using a technical tool of local a priori estimate for the finite element solution. Numerical results verify the validity of the theoretical predictions and show the high efficiency of the proposed method.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Applied
Gaspard Jankowiak, Alexei Lozinski
Summary: This paper presents a rigorous numerical analysis of a Multiscale Finite Element Method (MsFEM) for the Stokes system in highly heterogeneous media, based on the approach proposed by B.P. Muljadi et al. The method extends the classical Crouzeix-Raviart approach by generalizing it to arbitrary sets of weighting functions for enforcing continuity across mesh edges. Error bounds are provided for a specific set of weighting functions in a periodic setting, using an accurate estimate of the homogenization error. Numerical experiments demonstrate improved accuracy compared to Part I, both in the periodic case and in a broader setting.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2023)
Article
Engineering, Multidisciplinary
Namshad Thekkethil, Simone Rossi, Hao Gao, Scott I. Heath Richardson, Boyce E. Griffith, Xiaoyu Luo
Summary: This paper proposes a variational multiscale method to stabilize a linear finite element method for nonlinear poroelasticity. The method is suitable for implicit time integration of anisotropic and incompressible poroelastic formulations. A detailed numerical methodology is presented for a monolithic formulation that includes both structural dynamics and Darcy flow. The method is verified using benchmark cases and demonstrated to have second-order accuracy.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Jonathan Jung, Vincent Perrier
Summary: This article aims to thoroughly identify the spurious mode that jeopardizes the convergence of usual upwind numerical schemes for compressible flows when the Mach number goes to 0. The spurious mode is shown to be the long time limit of a wave system, and a filtering method is developed to remove it from the solution of stationary low Mach number compressible flow, significantly improving the accuracy of an inaccurate solution.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Yiran Wang, Eric Chung, Lina Zhao
Summary: The paper introduces the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) for parabolic equations with heterogeneous diffusion coefficients, showing that the method relies on two multiscale spaces and is proven to converge based only on coarse grid size. Using different permeability fields in numerical simulations, the method is demonstrated to be effective in providing efficient and accurate numerical solutions.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Mathematics, Applied
Bo Zheng, Yueqiang Shang
Summary: A parallel stabilized finite element variational multiscale method for the incompressible Navier-Stokes equations is proposed, utilizing a fully overlapping domain decomposition approach. The method computes a stabilized solution in a given subdomain using a locally refined global mesh, without the need for substantial recoding of the existing Navier-Stokes sequential solver. Error bounds for the approximate solutions are estimated using local a priori error estimates for the stabilized solution.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Applied
Minam Moon
Summary: In this paper, a generalized multiscale hybridizable discontinuous Galerkin (GMsHDG) method is proposed for nonlinear porous media. The method modifies the existing HDG framework and introduces linearization and generating reduced dimensional multiscale spaces. The error analysis demonstrates that the error decreases with the increasing eigenvalue of the local eigenvalue problem. Numerical experiments confirm the reliability and efficiency of the proposed method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Multidisciplinary Sciences
Yann Brenier, Ivan Moyano
Summary: This article explores a more relevant set of relaxed Euler equations by studying the multi-stream pressure-less gravitational Euler-Poisson system, which allows for the recovery of a large class of smooth solutions for short enough times.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Editorial Material
Environmental Sciences
Dene Bowdalo, Herve Petetin, Oriol Jorba, Marc Guevara, Albert Soret, Dragana Bojovic, Marta Terrado, Xavier Querol, Carlos Perez Garcia-Pando
ENVIRONMENTAL RESEARCH LETTERS
(2022)
Article
Engineering, Civil
Abhishek Mukherjee, Juan Carlos Cajas, Guillaume Houzeaux, Oriol Lehmkuhl, Jenny Suckale, Simone Marras
Summary: This study investigates the impact of rigidity and vegetation density on energy reflection and dissipation in coastal forests using a three-dimensional computational fluid dynamics model. The results reveal that the blockage area created by multiple tree trunks, rather than rigidity, plays a dominant role in energy reflection. The presence of trees alters the flow field, causing turbulent kinetic energy generation and flow energy dissipation. Therefore, coastal forests reduce the onshore energy flux of tsunamis through both reflection and dissipation.
COASTAL ENGINEERING
(2023)
Article
Pharmacology & Pharmacy
Hadrien Calmet, Damien Dosimont, David Oks, Guillaume Houzeaux, Brenda Vara Almirall, Kiao Inthavong
Summary: Targeted nasal drug delivery can be improved by adjusting spray parameters. This study investigated the effects of different values of six spray parameters on particle deposition. Sensitivity analysis showed that particle size significantly affected deposition in the olfactory and posterior regions, while spray device insertion angle had a significant impact on deposition in the anterior and middle regions. Machine learning models based on 384 cases provided accurate predictions despite the small sample dataset.
INTERNATIONAL JOURNAL OF PHARMACEUTICS
(2023)
Article
Engineering, Marine
Ruixue Liu, Cosan Daskiran, Abhishek Mukherjee, Qin Xin, Fangda Cui, Simone Marras, Hena Farooqi, Heather Dettman, Michel Boufadel
Summary: A mesoscale oil spill test tank was used to study the mixing energy and particle behavior near the shorelines. Different types of waves were generated and their velocities and energy dissipation rates were measured. Large-Eddy Simulation (LES) was conducted to further analyze the particle movement under typical wave conditions. The results showed that droplet inertia had a significant impact on particle accumulation.
Article
Mechanics
J. C. Cajas, I. Rodriguez, E. Salcedo, O. Lehmkuhl, G. Houzeaux, C. Trevino
Summary: The effect of aspect ratio on vortex induced vibrations (VIV) of a pivoted circular cylinder with different length-to-diameter ratios was studied. The study found that the aspect ratio influenced the oscillation amplitudes, synchronization region, and wake structures. At lower reduced velocities, steady symmetrical flow was obtained for cylinders with small aspect ratios, but became unstable at higher velocities.
Article
Environmental Sciences
Maria Goncalves Ageitos, Vincenzo Obiso, Ron L. Miller, Oriol Jorba, Martina Klose, Matt Dawson, Yves Balkanski, Jan Perlwitz, Sara Basart, Enza Di Tomaso, Jeronimo Escribano, Francesca Macchia, Gilbert Montane, Natalie M. Mahowald, Robert O. Green, David R. Thompson, Carlos Perez Garcia-Pando
Summary: Soil dust aerosols have a significant impact on the climate system by interacting with radiation, altering cloud formation, affecting atmospheric chemistry, and playing a role in biogeochemical cycles. The composition of dust varies regionally, depending on the source region. However, current Earth system models often treat dust mineralogy as invariant, ignoring its spatial variability.
ATMOSPHERIC CHEMISTRY AND PHYSICS
(2023)
Article
Environmental Sciences
Marc Guevara, Herve Petetin, Oriol Jorba, Hugo Denier van der Gon, Jeroen Kuenen, Ingrid Super, Claire Granier, Thierno Doumbia, Philippe Ciais, Zhu Liu, Robin D. Lamboll, Sabine Schindlbacher, Bradley Matthews, Carlos Perez Garcia-Pando
Summary: The COVID-19 crisis in 2020 led to a significant decrease in anthropogenic emissions of air pollutants and greenhouse gases. This study compares near-real-time emission estimates with official inventories and reveals discrepancies at the sector and country level. The findings highlight the uncertainties in near-real-time emissions and their importance in modeling and monitoring applications.
ATMOSPHERIC CHEMISTRY AND PHYSICS
(2023)
Article
Environmental Sciences
Michail Mytilinaios, Sara Basart, Sergio Ciamprone, Juan Cuesta, Claudio Dema, Enza Di Tomaso, Paola Formenti, Antonis Gkikas, Oriol Jorba, Ralph Kahn, Carlos Perez Garcia-Pando, Serena Trippetta, Lucia Mona
Summary: This article compares and assesses a high-resolution regional desert dust reanalysis with satellite-based and ground-based observations. The assessment shows that the reanalysis is consistent with satellite and ground-based data in capturing dust sources and seasonal variations. However, the reanalysis slightly overestimates dust emissions from source regions and underestimates transported dust over outflow regions. Rating: 8 out of 10
ATMOSPHERIC CHEMISTRY AND PHYSICS
(2023)
Article
Geosciences, Multidisciplinary
Aleksander Lacima, Herve Petetin, Albert Soret, Dene Bowdalo, Oriol Jorba, Zhaoyue Chen, Raul F. Mendez Turrubiates, Hicham Achebak, Joan Ballester, Carlos Perez Garcia-Pando
Summary: Urbanization and fossil-fueled transportation have led to a significant increase in air pollution, making it crucial to understand its spatiotemporal variability for effective pollution reduction policies. Two global atmospheric composition reanalyses, CAMSRA and MERRA-2, were evaluated against surface measurements over Europe. Both reanalyses showed significant biases for most pollutants, with CAMSRA outperforming MERRA-2 in capturing the variability of pollutants. However, biases and limitations still exist due to factors such as emission inventory errors, lack of surface data assimilation, and coarse resolution.
GEOSCIENTIFIC MODEL DEVELOPMENT
(2023)
Article
Geosciences, Multidisciplinary
Alvaro Criado, Jan Mateu Armengol, Herve Petetin, Daniel Rodriguez-Rey, Jaime Benavides, Marc Guevara, Carlos Perez Garcia-Pando, Albert Soret, Oriol Jorba
Summary: Comprehensive monitoring of NO2 exceedances in urban areas is challenging due to low density air quality monitoring stations and uncertainties in air quality models. We propose a data fusion workflow that combines observational data from different sources with a dispersion model to obtain bias-corrected NO2 hourly maps at the street scale. Our approach includes a kriging-based fusion method and a machine-learning-based land use regression model. The results show significant improvements in correlation coefficient and root mean square error when merging the monitoring stations and including microscale information.
GEOSCIENTIFIC MODEL DEVELOPMENT
(2023)
Article
Environmental Sciences
Herve Petetin, Marc Guevara, Steven Compernolle, Dene Bowdalo, Pierre-Antoine Bretonniere, Santiago Enciso, Oriol Jorba, Franco Lopez, Albert Soret, Carlos Perez Garcia-Pando
Summary: The Tropospheric Monitoring Instrument (TROPOMI) has been used to monitor nitrogen dioxide (NO2) pollution in the troposphere. This study analyzed the spatio-temporal variability of TROPOMI NO2 tropospheric columns (TrC-NO2) over the Iberian Peninsula. The study found that TROPOMI observations are well correlated with surface NO2 measurements and show differences in weekly and monthly variability depending on the level of urbanization.
ATMOSPHERIC CHEMISTRY AND PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
David Oks, Guillaume Houzeaux, Mariano Vazquez, Michael Neidlin, Cristobal Samaniego
Summary: This study evaluates the effect of TAVR commissural alignment on coronary perfusion and device performance using a computational fluid-structure interaction model.
COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE
(2023)
Article
Environmental Sciences
Herve Petetin, Marc Guevara, Roger Garatachea, Franco Lopez, Kevin Oliveira, Santiago Enciso, Oriol Jorba, Xavier Querol, Jordi Massague, Andres Alastuey, Carlos Perez Garcia-Pando
Summary: Tropospheric ozone is a serious air pollutant that affects human health, vegetation, and climate in countries like Spain. A study conducted to support the Spanish O3 Mitigation Plan found that road transport and maritime traffic are the main contributors to ozone pollution. Although emission scenarios can reduce ozone concentrations, exceedances of air quality thresholds will still occur.
SCIENCE OF THE TOTAL ENVIRONMENT
(2023)
Article
Energy & Fuels
Abel Gargallo-Peiro, Gonzalo Revilla, Matias Avila, Guillaume Houzeaux
Summary: A novel approach for wind farm simulation is presented, featuring realignment and mesh adaptation. The method utilizes actuator discs to model turbines and combines a level-set-based simulation framework with an adaptation cycle. The results demonstrate the accuracy and efficiency of the proposed approach in simulating complex wind farm configurations.
Article
Environmental Sciences
Jeronimo Escribano, Enza Di Tomaso, Oriol Jorba, Martina Klose, Maria Goncalves Ageitos, Francesca Macchia, Vassilis Amiridis, Holger Baars, Eleni Marinou, Emmanouil Proestakis, Claudia Urbanneck, Dietrich Althausen, Johannes Buehl, Rodanthi-Elisavet Mamouri, Carlos Perez Garcia-Pando
Summary: This study explores the potential and added value of assimilating satellite vertical dust profiles to improve desert dust forecasts. The results show that assimilating dust extinction profiles provides better performance in the analyses and forecasts compared to assimilating column-integrated aerosol optical depth (AOD).
ATMOSPHERIC CHEMISTRY AND PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Tian Liang, Lin Fu
Summary: In this work, a new shock-capturing framework is proposed based on a new candidate stencil arrangement and the combination of infinitely differentiable non-polynomial RBF-based reconstruction in smooth regions with jump-like non-polynomial interpolation for genuine discontinuities. The resulting scheme achieves high order accuracy and resolves genuine discontinuities with sub-cell resolution.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Lukas Lundgren, Murtazo Nazarov
Summary: In this paper, a high-order accurate finite element method for incompressible variable density flow is introduced. The method addresses the issues of saddle point system and stability problem through Schur complement preconditioning and artificial compressibility approaches, and it is validated to have high-order accuracy for smooth problems and accurately resolve discontinuities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Gabriele Ciaramella, Laurence Halpern, Luca Mechelli
Summary: This paper presents a novel convergence analysis of the optimized Schwarz waveform relaxation method for solving optimal control problems governed by periodic parabolic PDEs. The analysis is based on a Fourier-type technique applied to a semidiscrete-in-time form of the optimality condition, which enables a precise characterization of the convergence factor at the semidiscrete level. The behavior of the optimal transmission condition parameter is also analyzed in detail as the time discretization approaches zero.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jonas A. Actor, Xiaozhe Hu, Andy Huang, Scott A. Roberts, Nathaniel Trask
Summary: This article introduces a scientific machine learning framework that uses a partition of unity architecture to model physics through control volume analysis. The framework can extract reduced models from full field data while preserving the physics. It is applicable to manifolds in arbitrary dimension and has been demonstrated effective in specific problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Nozomi Magome, Naoki Morita, Shigeki Kaneko, Naoto Mitsume
Summary: This paper proposes a novel strategy called B-spline based SFEM to fundamentally solve the problems of the conventional SFEM. It uses different basis functions and cubic B-spline basis functions with C-2-continuity to improve the accuracy of numerical integration and avoid matrix singularity. Numerical results show that the proposed method is superior to conventional methods in terms of accuracy and convergence.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Timothy R. Law, Philip T. Barton
Summary: This paper presents a practical cell-centred volume-of-fluid method for simulating compressible solid-fluid problems within a pure Eulerian setting. The method incorporates a mixed-cell update to maintain sharp interfaces, and can be easily extended to include other coupled physics. Various challenging test problems are used to validate the method, and its robustness and application in a multi-physics context are demonstrated.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu
Summary: This paper presents the development of a third-order compact gas-kinetic scheme for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme demonstrates robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Alsadig Ali, Abdullah Al-Mamun, Felipe Pereira, Arunasalam Rahunanthan
Summary: This paper presents a novel Bayesian statistical framework for the characterization of natural subsurface formations, and introduces the concept of multiscale sampling to localize the search in the stochastic space. The results show that the proposed framework performs well in solving inverse problems related to porous media flows.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jacob Rains, Yi Wang, Alec House, Andrew L. Kaminsky, Nathan A. Tison, Vamshi M. Korivi
Summary: This paper presents a novel method called constrained optimized DMD with Control (cOptDMDc), which extends the optimized DMD method to systems with exogenous inputs and can enforce the stability of the resulting reduced order model (ROM). The proposed method optimally places eigenvalues within the stable region, thus mitigating spurious eigenvalue issues. Comparative studies show that cOptDMDc achieves high accuracy and robustness.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Andrea La Spina, Jacob Fish
Summary: This work introduces a hybridizable discontinuous Galerkin formulation for simulating ideal plasmas. The proposed method couples the fluid and electromagnetic subproblems monolithically based on source and employs a fully implicit time integration scheme. The approach also utilizes a projection-based divergence correction method to enforce the Gauss laws in challenging scenarios. Numerical examples demonstrate the high-order accuracy, efficiency, and robustness of the proposed formulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Junhong Yue, Peijun Li
Summary: This paper proposes two numerical methods (IP-FEM and BP-FEM) to study the flexural wave scattering problem of an arbitrary-shaped cavity on an infinite thin plate. These methods successfully decompose the fourth-order plate wave equation into the Helmholtz and modified Helmholtz equations with coupled conditions on the cavity boundary, providing an effective solution to this challenging problem.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
William Anderson, Mohammad Farazmand
Summary: We develop fast and scalable methods, called RONS, for computing reduced-order nonlinear solutions. These methods have been proven to be highly effective in tackling challenging problems, but become computationally prohibitive as the number of parameters grows. To address this issue, three separate methods are proposed and their efficacy is demonstrated through examples. The application of RONS to neural networks is also discussed.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Marco Caliari, Fabio Cassini
Summary: In this paper, a second order exponential scheme for stiff evolutionary advection-diffusion-reaction equations is proposed. The scheme is based on a directional splitting approach and uses computation of small sized exponential-like functions and tensor-matrix products for efficient implementation. Numerical examples demonstrate the advantage of the proposed approach over state-of-the-art techniques.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Sebastiano Boscarino, Seung Yeon Cho, Giovanni Russo
Summary: This work proposes a high order conservative semi-Lagrangian method for the inhomogeneous Boltzmann equation of rarefied gas dynamics. The method combines a semi-Lagrangian scheme for the convection term, a fast spectral method for computation of the collision operator, and a high order conservative reconstruction and a weighted optimization technique to preserve conservative quantities. Numerical tests demonstrate the accuracy and efficiency of the proposed method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jialei Li, Xiaodong Liu, Qingxiang Shi
Summary: This study shows that the number, centers, scattering strengths, inner and outer diameters of spherical shell-structured sources can be uniquely determined from the far field patterns. A numerical scheme is proposed for reconstructing the spherical shell-structured sources, which includes a migration series method for locating the centers and an iterative method for computing the inner and outer diameters without computing derivatives.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)