Article
Mathematics
Maria Luminita Scutaru, Sohaib Guendaoui, Ouadie Koubaiti, Lahcen El Ouadefli, Abdeslam El Akkad, Ahmed Elkhalfi, Sorin Vlase
Summary: This article discusses a study that compares the isogeometric analysis B-spline method with the traditional finite element method in solving a nonlinear problem in fluid dynamics. The study highlights the advantages of the IGA method, including its ability to accurately capture complex flow behavior and reduced computation time compared to FEM. The results provide valuable insights for fluid dynamics and practical implications for engineering simulations.
Article
Computer Science, Interdisciplinary Applications
Xinyi L. D. Huang, Naman Jain, Mahdi Abkar, Robert F. Kunz, Xiang I. A. Yang
Summary: The study addresses the challenge of determining if model improvement based on calibration data generalizes to other flow conditions by using global epistemic Uncertainty Quantification (UQ). The global epistemic UQ method evaluates potential improvements in terms of effectiveness and inconsistency, allowing for the classification of improvements into four quadrants to determine if they would generalize. The study successfully applies the global epistemic UQ to predict the growth of a stratified shear layer and demonstrates the model's ability to generalize under certain conditions.
COMPUTERS & FLUIDS
(2021)
Article
Mathematics, Applied
Yaoyao Chen, Yunqing Huang, Nianyu Yi
Summary: This paper carries out error analysis for a totally decoupled, linear, and unconditionally energy stable finite element method to solve the Cahn-Hilliard-Navier-Stokes equations. The a priori error analysis is derived for the phase field, velocity field, and pressure variable in the fully discrete scheme.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mechanics
Y. Marchenay, F. Chedevergne, M. Olazabal Loume
Summary: A new modeling strategy is proposed to predict the combined effects of roughness and blowing boundary conditions. Analysis of experimental data reveals deficiencies in existing roughness corrections when predicting the effect of blowing in the presence of surface roughness.
Article
Engineering, Multidisciplinary
Xueying Zhang, Yangjiong Wu
Summary: This paper proposes a high resolution strategy for the localized method of approximate particular solutions (LMAPS). The strategy aims to improve the accuracy and stability of numerical calculation by selecting upwind interpolation templates. Numerical results demonstrate that the proposed high-resolution LMAPS is effective and accurate, especially for solving the Navier-Stokes equations with high Reynolds number.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)
Article
Mechanics
Igal Cohen, Yuri Kligerman, Roman Goltsberg
Summary: The study investigates the validity of Reynolds equation for the lubrication flow in a ringless piston-cylinder system with dynamic effects. The effects of perturbed motion on a stepped profiled piston are analyzed to assess its stability. Different geometries and conditions are considered using Reynolds equation and Navier-Stokes based model, with normalized parameters established to determine validity. The findings suggest that the steady state solution obtained from Reynolds equation is valid for higher values of the reduced Reynolds number, while the transient response indicates that Reynolds equation is not valid for S & BULL; Re* > 0.05.
Article
Mathematics, Applied
Arnold Reusken
Summary: This paper studies the finite element discretizations of a surface vector-Laplace eigenproblem. Two known classes of finite element methods are considered, with a focus on the penalization method used to enforce tangentiality of the vector field. The paper presents a general abstract framework for such nonconforming discretizations of eigenproblems, and derives error bounds and convergence properties through numerical experiments.
MATHEMATICS OF COMPUTATION
(2022)
Article
Physics, Mathematical
Yaoyao Chen, Yunqing Huang, Nianyu Yi
Summary: An adaptive finite element method is proposed, analyzed and numerically validated for the Cahn-Hilliard-Navier-Stokes equations. The method is shown to be reliable and efficient through numerical experiments.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Yuming Qin, Xiuqing Wang
Summary: This paper establishes the existence of a trajectory attractor for the Navier-Stokes-Voight (NSV) equation and proves the upper semicontinuity of trajectory attractors for the 3D incompressible Navier-Stokes equation when the 3D NSV equation is considered as a perturbative equation of the 3D incompressible Navier-Stokes equation.
APPLIED MATHEMATICS AND OPTIMIZATION
(2021)
Article
Mathematics, Applied
Nityananda Roy, Karunia Putra Wijaya, Thomas Gotz, S. Sundar
Summary: This study investigates the short-range transport of microplastic particles in freshwater by simulating a lid-driven cavity with a biofilm-covering obstacle. It is found that microplastic particles are trapped in the biofilm and regions with negative Okubo-Weiss numbers, where relative vorticity dominates against local strains.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Mathematics, Applied
Biao Zeng
Summary: The aim of this paper is to study a new class of fractional evolutionary equations involving the time-fractional order integral and nonlinear weakly continuous operators. By utilizing the Rothe method and a surjectivity result for weakly continuous operators, the solvability for the problem is established. The result is then applied to prove the existence of solutions to time-fractional nonstationary incompressible Navier-Stokes equation and Navier-Stokes-Voigt equation.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2022)
Article
Computer Science, Interdisciplinary Applications
Thomas Frachon, Sara Zahedi
Summary: This article proposes a new unfitted finite element method for simulating two-phase flows with insoluble surfactant. The method features discrete conservation of surfactant mass, the possibility of using non-conforming meshes, and accurate approximation of quantities across evolving geometries. The method combines a space-time cut finite element formulation with quadrature in time and a stabilization term for function extension. Numerical simulations in different dimensions are presented, including the interaction between two drops.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Julia Calatayud, Juan Carlos Cortes, Marc Jornet
Summary: Incorporating randomness into mathematical models is necessary due to the variability of data and incomplete knowledge of true physics. Deterministic numerical methods may fail to capture uncertainty propagation in this context. The generalized polynomial chaos method has been successfully used for certain problems, while classical perturbation methods may not give reliable results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Paola F. Antonietti, Giuseppe Vacca, Marco Verani
Summary: In this paper, we consider the virtual element discretization of the coupled Navier-Stokes equations and heat equation with temperature-dependent viscosity. We present the virtual element discretization method, prove its well-posedness and provide optimal error estimates. Numerical experiments are conducted to validate the theoretical error bounds.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2022)
Article
Chemistry, Multidisciplinary
Viola Rossano, Giuliano De Stefano
Summary: The present study used the generalized k-omega formulation to calibrate the aerodynamic design of a mid-range commercial airplane. By comparing the simulations with experimental and numerical data, the performance of the method in predicting aerodynamic loading was examined, and the optimal model parameters were determined.
APPLIED SCIENCES-BASEL
(2023)