Article
Mathematics, Applied
Wei Li, Pengzhan Huang
Summary: "In this paper, a fully discrete finite element scheme with two-order temporal accuracy is proposed for solving the Navier-Stokes/Navier-Stokes equations. The scheme consists of two coupled Navier-Stokes equations and a linear interface condition. The paper presents the specific steps of the scheme and establishes the stability and error estimates. Numerical experiments verify the theoretical findings and efficiency of the scheme."
APPLIED NUMERICAL MATHEMATICS
(2023)
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
Anuj Kumar
Summary: This paper investigates the optimal upper bound on mean quantities (torque, dissipation and the Nusselt number) in Taylor-Couette flow using the background method. It analyzes the energy stability of laminar flow and shows that below a certain radius ratio, the marginally stable perturbations are not axisymmetric Taylor vortices but fully three-dimensional flow. The main result of the paper is an analytical expression of the optimal bound as a function of the radius ratio. The analytical result is found to agree well with direct numerical simulations data. Additionally, the paper discusses the limitations of the background method in certain flow problems.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Engineering, Multidisciplinary
Philsu Kim, Soyoon Bak
Summary: This paper proposes a novel trajectory-approximation technique as a time-integration scheme for solving advectional partial differential equations in engineering and physics, saving computational costs and achieving third-order accuracy. The method demonstrates superior performance in simulating benchmark test flows.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(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
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
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
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
Amin Fereidooni, Abbas Moameni, Anant Grewal
Summary: The objective of this paper is to develop and utilize a minimax principle to prove the existence of symmetric solutions for the stationary Navier-Stokes equations. This minimax principle is broad enough to capture other types of solutions as long as the equation and external force are compatible under a family of operations, including compact group invariance. The subset of functions compatible under this family of operations does not need to be a linear subspace, but a closed convex set suffices for the purpose.
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Juan Vicente Gutierrez-Santacreu, Marko Antonio Rojas-Medar
Summary: The Navier-Stokes-alpha equations are a type of LES models that aim to capture the influence of small scales on large ones without calculating the entire flow range. The parameter α represents the smallest resolvable scale by the model. When α=0, the classical Navier-Stokes equations for viscous, incompressible, Newtonian fluids are recovered. These equations can also be seen as a regularization of the Navier-Stokes equations, where α stands for the regularization parameter.
PHYSICA D-NONLINEAR PHENOMENA
(2023)
Article
Engineering, Multidisciplinary
Mustafa Aggul, Alexander E. Labovsky, Kyle J. Schwiebert
Summary: This paper proposes a method to address the fluid-fluid interaction problem, where two flows are coupled through a nonlinear rigid lid condition, and one or both flows have high Reynolds numbers. The model combines the NS-omega turbulence model with a partitioning method, allowing for efficient decoupling, usage of preexisting solvers, and resolving high Reynolds number flows. The model is unconditionally stable and has optimal convergence properties. It also allows for non-filtered velocity in the interface terms, which improves the quality of the model's solution.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Review
Engineering, Multidisciplinary
Guillermo Hauke, Diego Irisarri
Summary: This article outlines the research on the application of the variational multiscale theory (VMS) to a posteriori error estimation. The technology involves splitting the exact solution into resolved and unresolved scales, and utilizing the stabilization parameters and terms to obtain explicit and implicit error estimates. This approach can be utilized for various purposes such as generating adapted meshes, deriving reduced order models, and verification and validation algorithms.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mechanics
Yuri V. Lvov, Victor S. L'vov
Summary: The researchers used the Dyson-Wyld diagrammatic technique to analyze the infinite series for the correlation functions of velocity in hydrodynamic turbulence. They found that the triple correlator of velocity plays a fundamental role in determining the statistical characteristics of the turbulence. All higher-order correlation functions can be expressed through the triple correlator. The study also showed that the suggested triangular re-summation of the infinite diagrammatic series can explain why the inverse cascade of two-dimensional hydrodynamic turbulence is close to Gaussian, supporting the idea that the flux of energy is one of the main characteristics of hydrodynamic turbulence, as proposed by Kolmogorov in 1941.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Mechanics
Mengze Wang, Gregory L. Eyink, Tamer A. Zaki
Summary: Boundary-layer transition is rigorously explained using the stochastic Lagrangian formulation of the Navier-Stokes equations, and the increase in skin friction is analyzed. It is found that the stretching of near-wall spanwise vorticity is the dominant source of increased skin friction during laminar-to-turbulent transition.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Mechanics
Warren R. Smith, Qianxi Wang
Summary: Small viscous effects in high-Reynolds-number rotational flows accumulate over time to have a leading-order effect, making the high-Reynolds-number limit for the Navier-Stokes equations singular. Investigating whether a solution of the Euler equations can approximate a real flow at large Reynolds number is crucial. The neglect of these facts leads to the use of Euler equations to simulate laminar rotational flows at large Reynolds number.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Mathematics
Alfio Quarteroni, Luca Dede, Francesco Regazzoni
Summary: In this paper, we present the electromechanical mathematical model of the human heart and discuss the establishment of numerical methods and challenges. Numerical tests demonstrate the expected theoretical convergence rate of the numerical solutions and prove the preliminary valuable application of our model in tackling clinical problems.
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Computer Science, Interdisciplinary Applications
F. Regazzoni, M. Salvador, P. C. Africa, M. Fedele, L. Dede, A. Quarteroni
Summary: This article proposes a novel mathematical and numerical model for cardiac electromechanics, which combines biophysically detailed core models, an Artificial Neural Network model, and appropriate coupling schemes. The model accurately simulates cardiac function and quantifies the utilization, dissipation, and transfer of energy in the cardiovascular network. Additionally, a robust algorithm is proposed for reconstructing the stress-free reference configuration and validating energy indicators used in clinical practice.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Engineering, Multidisciplinary
F. Regazzoni, M. Salvador, L. Dede, A. Quarteroni
Summary: This study proposes a machine learning-based method to build a differential equation system that approximates the dynamics of 3D electromechanical models for the human heart, considering a set of parameters. The method allows for the creation of a reduced-order model written as a system of ordinary differential equations, which can be coupled with hemodynamic models for real-time numerical simulations of cardiac function at a significantly lower computational cost.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Roberto Piersanti, Francesco Regazzoni, Matteo Salvador, Antonio F. Corno, Luca Dede, Christian Vergara, Alfio Quarteroni
Summary: Two crucial factors for accurate numerical simulations of cardiac electromechanics are addressed in this study: accounting for the interaction between the heart and the circulatory system, and reconstructing the muscular fiber architecture. The proposed 3D biventricular electromechanical model coupled with a 0D closed-loop model of the whole cardiovascular system successfully addresses these factors and produces results that match experimental data.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Biology
Matteo Salvador, Francesco Regazzoni, Stefano Pagani, Luca Dede', Natalia Trayanova, Alfio Quarteroni
Summary: This paper investigates the effects of mechano-electric feedbacks (MEFs) on myocardial deformation and nonselective stretch-activated channels (SACs). Numerical simulations show that all MEFs can alter the propagation of transmembrane potential. Introduction of myocardial deformation changes the basic cycle length and conduction velocity of ventricular tachycardia (VT), while nonselective SACs may turn a stable VT into an unstable one.
COMPUTERS IN BIOLOGY AND MEDICINE
(2022)
Article
Mathematics, Applied
Simone Stella, Francesco Regazzonit, Christian Vergara, Luca Dede, Alfio Quarteroni
Summary: We present a new model for human cardiac electromechanics that accurately describes the electrophysiology and tissue mechanics of the left ventricle. The proposed model significantly reduces computational time and provides physiological responses to changes in certain variables. It also reproduces the results of the monodomain model with high accuracy.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Nicolas Alejandro Barnafi Wittwer, Simone DI Gregorio, Luca Dede, Paolo Zunino, Christian Vergara, Alfio Quarteroni
Summary: The importance of myocardial perfusion in the early stage of cardiac disease is not well researched. This study proposes a mathematical model that considers the interactions among the systemic circulation, coronary vessels, and myocardium. By decoupling the computational cost, the model accurately simulates a heartbeat under healthy conditions and effectively captures phenomena arising from the interaction of multiple components.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Matteo Salvador, Francesco Regazzoni, Luca Dede, Alfio Quarteroni
Summary: In this study, a Bayesian statistical approach combining Maximum a Posteriori estimation and Hamiltonian Monte Carlo is used to quickly and accurately estimate model parameters of the cardiac function. The use of an Artificial Neural Network surrogate model allows for fast simulations and minimal hardware requirements. The approach is suitable for clinical applications and is compliant with Green Computing practices.
COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE
(2023)
Article
Engineering, Biomedical
Michele Bucelli, Alberto Zingaro, Pasquale Claudio Africa, Ivan Fumagalli, Luca Dede', Alfio Quarteroni
Summary: We have developed a mathematical and numerical model that simulates the various processes involved in heart function, including electrophysiology, mechanics, and hemodynamics. The model also considers the interactions between the different processes, such as electro-mechanical and mechano-electrical feedback. By using a coupled fluid-structure interaction approach, we are able to represent the three-dimensional nature of the heart muscle and hemodynamics. The model has been validated using a realistic human left heart model and shows qualitative and quantitative agreement with physiological ranges and medical images.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING
(2023)
Article
Mathematics
Paola F. Antonietti, Matteo Caldana, Luca Dede'
Summary: We propose a novel deep learning-based algorithm, using Artificial Neural Networks (ANNs), to accelerate the convergence of Algebraic Multigrid (AMG) methods for solving linear systems of equations from finite element discretizations of Partial Differential Equations (PDEs). By predicting the strong connection parameter with ANNs, we maximize the convergence factor of the AMG scheme. We demonstrate the effectiveness of our algorithm, called AMG-ANN, through solving two-dimensional model problems with highly heterogeneous diffusion coefficients and stationary Stokes equations.
VIETNAM JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics
Fabio Marcinno', Alberto Zingaro, Ivan Fumagalli, Luca Dede', Christian Vergara
Summary: In this work, the blood dynamics in the pulmonary arteries is studied using a 3D-0D geometric multiscale approach, and three strategies for the numerical solution of the 3D-0D coupled problem are proposed. Numerical experiments are performed using a patient-specific 3D domain and a physiologically calibrated 0D model, and the effects of connection methods and numerical strategies are discussed. The results demonstrate the potential of this method in clinical applications.
VIETNAM JOURNAL OF MATHEMATICS
(2023)
Article
Engineering, Multidisciplinary
Marco Fedele, Roberto Piersanti, Francesco Regazzoni, Matteo Salvador, Pasquale Claudio Africa, Michele Bucelli, Alberto Zingaro, Luca Dede, Alfio Quarteroni
Summary: This paper presents a biophysically detailed electromechanical model of the whole human heart, considering both atrial and ventricular contraction, as well as the bioelectromechanical interaction within the heart. The model is able to reproduce the healthy cardiac function for all chambers and demonstrates the importance of atrial contraction, fibers-stretch-rate feedback, and stabilization techniques.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Michele Bucelli, Francesco Regazzoni, Luca Dede, Alfio Quarteroni
Summary: This paper proposes a novel method that combines rescaled localized RBF interpolation with SVD to accurately, robustly and efficiently transfer the deformation gradient tensor between meshes of different resolution in cardiac electromechanics simulations. The method overcomes limitations of existing interpolation methods and enhances the flexibility and accuracy of electromechanical simulations.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Mattia Corti, Francesca Bonizzoni, Luca Dede, Alfio M. Quarteroni, Paola F. Antonietti
Summary: This paper presents a numerical modelling of the misfolding process of a-synuclein in Parkinson's disease, using a discontinuous Galerkin method. The results demonstrate the stability and accuracy of the proposed method in simulating the spreading of prion proteins, providing valuable insights for understanding the neurodegeneration process.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Interdisciplinary Applications
Tommaso Tassi, Alberto Zingaro, Luca Dede
Summary: This paper proposes using machine learning and artificial neural networks to enhance stabilization methods for advection-dominated differential problems. By generating a dataset and using the neural network to choose the optimal stabilization parameter, our approach yields more accurate solutions than conventional methods.
MATHEMATICS IN ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Jin Bao, Zhaoli Guo
Summary: At the equilibrium state of a two-phase fluid system, the chemical potential is constant and the velocity is zero. However, it is challenging to capture this equilibrium state accurately in numerical simulations, resulting in inconsistent thermodynamic interfacial properties and spurious velocities. Therefore, numerical schemes with well-balanced properties are preferred for simulating two-phase flows.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Brian C. Vermeire
Summary: This study presents a framework for implicit large eddy simulation (ILES) of incompressible flows by combining the entropically damped artificial compressibility (EDAC) method with the flux reconstruction (FR) approach. Experimental results demonstrate that the method is accurate and stable for low-order solutions, while higher-order solutions exhibit significantly higher accuracy and lower divergence error compared to reference direct numerical simulation.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Mijian Li, Rui Wang, Xinyu Guo, Xinyu Liu, Lianzhou Wang
Summary: In this study, the flow mechanisms around wall-mounted structures were investigated using Large Eddy Simulation (LES). The impact of inflow turbulence on the flow physics, dynamic response, and hydrodynamic performance was explored. The results revealed strong interference between velocity fluctuations and the wake past the cylinder, as well as significant convection effects in the far wake region.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Donatella Passiatore, Luca Sciacovelli, Paola Cinnella, Giuseppe Pascazio
Summary: A high-order shock-capturing central finite-difference scheme is evaluated for numerical simulations of hyper-sonic high-enthalpy flows out of thermochemical equilibrium. The scheme utilizes a tenth-order accurate central-difference approximation of inviscid fluxes, along with high-order artificial dissipation and shock-capturing terms. The proposed approach demonstrates accuracy and robustness for a variety of thermochemical non-equilibrium configurations.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Philipp Bahavar, Claus Wagner
Summary: Condensation is an important aspect in flow applications, and simulating the gas phase and tracking the deposition rates of condensate droplets can capture the effects of surface droplets on the flow while reducing computational costs.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Andras Szabo, Gyorgy Paal
Summary: This paper introduces an efficient calculation method, the parabolized stability equations (PSE), for solving stability equations. By calculating LU factorization once in each marching step, the time spent on solving linear systems of equations can be significantly reduced. Numerical experiments demonstrate the effectiveness of this method in reducing the solution time for linear equations, and its applicability to similar problems.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
A. Khalifa, M. Breuer
Summary: This study evaluates a recently developed data-driven model for collision-induced agglomerate breakup in high mass loading flows. The model uses artificial neural networks to predict the post-collision behavior of agglomerates, reducing computational costs compared to coupled CFD-DEM simulations.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Chunmei Du, Maojun Li
Summary: This paper considers the bilayer shallow water wave equations in one-dimensional space and presents an invariant domain preserving DG method to avoid Kelvin-Helmholtz instability.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jean-Michel Tucny, Mihir Durve, Andrea Montessori, Sauro Succi
Summary: The prediction of non-equilibrium transport phenomena in disordered media is a challenging problem for conventional numerical methods. Physics-informed neural networks (PINNs) show potential for solving this inverse problem. In this study, PINNs were used to successfully predict the velocity field of rarefied gas flow, and AdamW was found to be the best optimizer.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Min Gao, Pascal Mossier, Claus-Dieter Munz
Summary: In recent decades, the arbitrary Lagrangian-Eulerian (ALE) approach has gained popularity in dealing with fluid flows with moving boundaries. This paper presents a novel algorithm that combines the ALE finite volume (FV) and ALE discontinuous Galerkin (DG) methods into a stable and efficient hybrid approach. The main challenge of this mixed ALE FV and ALE DG method is reducing the inconsistency between the two discretizations. The proposed algorithm is implemented into a loosely-coupled fluid-structure interaction (FSI) framework and is demonstrated through various benchmark test cases and complex scenarios.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Dawid Strzelczyk, Maciej Matyka
Summary: In this study, the numerical convergence of the Meshless Lattice Boltzmann Method (MLBM) is investigated through three benchmark tests. The results are compared to the standard Lattice Boltzmann Method (LBM) and the analytical solution of the Navier-Stokes equation. It is found that MLBM outperforms LBM in terms of error value for the same number of nodes discretizing the domain.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Kanishka Bhattacharya, Tapan Jana, Amit Shaw, L. S. Ramachandra, Vishal Mehra
Summary: In this work, an adaptive algorithm is developed to address the issue of tensile instability in Smoothed Particle Hydrodynamics (SPH) by adjusting the shape of the kernel function to satisfy stability conditions. The effectiveness of the algorithm is demonstrated through dispersion analysis and fluid dynamics simulations.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Luis Laguarda, Stefan Hickel
Summary: We propose several enhancements to improve the accuracy and performance of the digital filter turbulent inflow generation technique, such as introducing a more realistic correlation function and varying target length scales. Additionally, we suggest generating inflow data in parallel at a prescribed time interval to improve computational performance. Based on the results of large-eddy simulations, these enhancements have shown to be beneficial. Suppressing streamwise velocity fluctuations at the inflow leads to the fastest relaxation of pressure fluctuations. However, this approach increases the adaptation length, which can be shortened by artificially increasing the wall-normal Reynolds stresses.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Constantin Zenz, Michele Buttazzoni, Tobias Florian, Katherine Elizabeth Crespo Armijos, Rodrigo Gomez Vazquez, Gerhard Liedl, Andreas Otto
Summary: A new model for compressible multiphase flows involving sharp interfaces and phase change is presented, with a focus on the treatment of compressibility and phase change in the multiphase fluid flow model. The model's accuracy and suitability are demonstrated through comparisons with experimental observations.
COMPUTERS & FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Joseph O'Connor, Sylvain Laizet, Andrew Wynn, Wouter Edeling, Peter V. Coveney
Summary: This article aims to apply uncertainty quantification and sensitivity analysis to the direct numerical simulation (DNS) of low Reynolds number wall-bounded turbulent channel flow. By using a highly scalable DNS framework and UQ techniques, the study evaluates the influence of different numerical parameters on the simulation results without explicitly modifying the code. The findings provide guidance for numerical simulations of wall-bounded turbulent flows.
COMPUTERS & FLUIDS
(2024)
