Article
Engineering, Multidisciplinary
Yizhong Sun, Weiwei Sun, Haibiao Zheng
Summary: In this paper, a parallel domain decomposition method is proposed for solving the fully-mixed Stokes-Darcy coupled problem with the Beavers-Joseph-Saffman interface conditions. The method decouples the original problem into two independent subproblems with newly constructed Robin-type boundary conditions and modified weak formulation. Convergence analysis and numerical examples demonstrate the effectiveness of the proposed method.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Kevin Williamson, Heyrim Cho, Bedrich Sousedik
Summary: This paper discusses the numerical solution of the Stokes-Brinkman equations in highly heterogeneous porous media with stochastic permeabilities. It introduces a truncated anchored ANOVA decomposition and stochastic collocation for estimating the moments of the velocity and pressure solutions. Adaptive procedures are used to reduce the number of collocation points needed for accurate estimation, and reduced basis methods are applied to alleviate computational burden and provide rigorous a posteriori error estimates for the approximation. The methods are applied to 2D problems considering isotropic and anisotropic permeabilities.
COMPUTATIONAL GEOSCIENCES
(2021)
Article
Mathematics, Applied
A. Chakib, H. Ouaissa
Summary: This paper focuses on the numerical resolution of an inverse Cauchy problem governed by Stokes equation modeling the airflow in the lungs, particularly in determining the air velocity and pressure on the artificial boundaries of the bronchial tree. The study extends regularizing, stable, and fast iterative algorithms for solving the problem based on the domain decomposition approach, and evaluates the efficiency and feasibility of the proposed approach through numerical tests using different domain decomposition algorithms. Ultimately, the Robin-Robin algorithm is chosen for the numerical simulation of airflow in the bronchial tree configuration.
COMPUTATIONAL & APPLIED MATHEMATICS
(2021)
Article
Physics, Multidisciplinary
Cheng Huang, Karthik Duraisamy, Charles Merkle
Summary: In this paper, a reduced-order modeling framework is developed to accurately predict large-scale engineering systems. By decomposing the system into different components and using reduced-order models for each component, the framework can model the full system and achieve accurate predictions for complex systems.
FRONTIERS IN PHYSICS
(2022)
Article
Mathematics, Applied
Felipe Lepe, Gonzalo Rivera, Jesus Vellojin
Summary: In this paper, we analyze mixed finite element methods for a velocity-pressure-pseudostress formulation of the Stokes eigenvalue problem. The methods approximate the velocity and pressure with piecewise polynomials, and use the Raviart-Thomas and Brezzi-Douglas-Marini elements to approximate the pseudostress. By utilizing the classic spectral theory for compact operators, we prove that our method does not introduce spurious modes and obtain convergence and error estimates. Numerical results are presented to compare the accuracy and robustness of both numerical schemes.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Computer Science, Interdisciplinary Applications
Marziyeh Saffarian, Akbar Mohebbi
Summary: In this paper, we investigated the Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivatives, which plays a crucial role in describing the dynamic behavior of non-Newtonian fluids. We proposed a high order numerical method to solve the two-dimensional case of this equation on regular and irregular regions, and demonstrated its accuracy and efficiency through numerical simulations.
ENGINEERING WITH COMPUTERS
(2023)
Article
Operations Research & Management Science
Fabian Hoppe, Ira Neitzel
Summary: The study provides a posteriori error estimates for reduced-order modeling of quasilinear parabolic PDEs with non-monotone nonlinearity. It incorporates reduced basis, empirical interpolation, and time discretization errors, using the solution of a semi-discrete in space equation as a reference. The results are illustrated through numerical experiments.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2021)
Article
Engineering, Multidisciplinary
Spenser Anderson, Cristina White, Charbel Farhat
Summary: This article presents an alternative and complementary approach to accelerate projection-based model order reduction (PMOR) methods by introducing sparsity into the reduced-order basis. The proposed approach enhances computational efficiency by partitioning the computational domain and demonstrates significant acceleration and CPU time speedup compared to high-dimensional models in turbulent flow applications.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
K. R. Maryada, S. E. Norris
Summary: The parallel algorithm proposed in this study reduces communication costs for deterministic dynamic mode decomposition of large datasets, achieving notable savings in computational costs as well. By compressing high-dimensional snapshot data using horizontal-slicing and parallel Tall and Skinny QR factorisation, the algorithm constructs the Koopman operator with only one communication step. Additionally, avoiding the computation of the orthonormal matrix during the parallel QR factorisation results in significant computational savings, making the current algorithm up to 2.5 times faster than existing parallel approaches without sacrificing accuracy.
JOURNAL OF COMPUTATIONAL SCIENCE
(2022)
Article
Mathematics, Applied
Junpeng Song, Hongxing Rui
Summary: This paper establishes a reduced-order finite element (ROFE) method with very few degrees of freedom for the incompressible miscible displacement problem. By constructing a finite element (FE) method with second-order accuracy in time and applying the proper orthogonal decomposition (POD) technique, the method effectively reduces degrees of freedom and CPU time while proving optimal a priori error estimates for the solutions. Numerical examples verify the feasibility and effectiveness of the proposed method for solving the problem.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Felipe Lepe, Gonzalo Rivera, Jesus Vellojin
Summary: The aim of this paper is to analyze a mixed formulation for the two dimensional Stokes eigenvalue problem, where the stress and velocity are the unknowns and the pressure can be recovered through postprocessing. The paper proposes a mixed numerical method using suitable finite elements for stress approximation and piecewise polynomials for velocity approximation. Convergence and spectral correctness of the proposed method are derived using compact operators theory. Additionally, a reliable and efficient a posteriori error estimator is proposed for achieving optimal convergence order in the presence of non-sufficient smooth eigenfunctions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Xuyang Na, Xuejun Xu
Summary: This paper presents a nonoverlapping domain decomposition method for Stokes equations using mixed finite elements with discontinuous pressures. Both conforming and nonconforming finite element spaces are considered for velocities. By employing Robin boundary conditions, the indefinite Stokes problem is reduced to a positive definite problem for the interface Robin transmission data. A new preconditioner for the Stokes problem is proposed based on the Robin-type domain decomposition method, with numerical results provided to support the theoretical findings.
APPLIED NUMERICAL MATHEMATICS
(2022)
Article
Mechanics
R. Selvi, Deepak Kumar Maurya, Pankaj Shukla
Summary: The objective of this investigation is to analyze the flow behavior of an incompressible couple stress fluid through a Reiner-Rivlin liquid covered by a permeable medium. The study considers the influence of dimensionless parameter, couple stress parameter, and parameter impacting viscosity. The findings demonstrate the impact of the couple stress parameter and couple stress viscosity on the drag and pressure, and show that the Reiner-Rivlin liquid completely penetrates the couple stress fluid.
Article
Mathematics, Applied
Junpeng Song, Hongxing Rui
Summary: In this paper, a reduced-order finite element (ROFE) method with few unknowns is proposed for solving the parabolic optimal control problem. The proper orthogonal decomposition (POD) technique is applied to construct two unsteady systems, significantly reducing the number of unknowns and computational costs. Optimal a priori error estimates for the state, co-state, and control approximations are derived, and numerical examples are provided to demonstrate the accuracy and efficiency of the ROFE method.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Minqiang Xu, Kai Liu, Lei Zhang
Summary: In this paper, a staggered finite volume element method (FVEM) based marker and cell method (MAC) is proposed for solving 3D Stokes equations on non-uniform cuboid grids with a proper quadrature scheme. The stability of the proposed MAC scheme is proven using the Petrov-Galerkin method. By establishing a connection between MAC and FVEM, the superconvergence property and optimal order L2 error estimate are rigorously proved. Numerical results are provided to verify the theoretical findings.
APPLIED NUMERICAL MATHEMATICS
(2023)
Article
Engineering, Multidisciplinary
Marco Tezzele, Lorenzo Fabris, Matteo Sidari, Mauro Sicchiero, Gianluigi Rozza
Summary: This study presents a structural optimization pipeline for modern passenger ship hulls, focusing on reducing metal raw materials used during manufacturing. Using advanced model order reduction techniques, the dimensionality of input parameters and outputs of interest is reduced. The method incorporates parameter space reduction through active subspaces into the proper orthogonal decomposition with interpolation method in a multi-fidelity setting. Comprehensive testing and error analysis demonstrate the effectiveness and usefulness of the method, especially during the preliminary design phase with high dimensional parameterizations.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Mathematics, Applied
Michele Girfoglio, Annalisa Quaini, Gianluigi Rozza
Summary: In this study, a Large Eddy Simulation (LES) approach based on a nonlinear differential low-pass filter is proposed for the simulation of two-dimensional barotropic flows. The numerical experiments demonstrate that this approach, even with under-refined meshes, is capable of recovering the characteristics of the time-averaged stream function and providing an average kinetic energy that compares well with a Direct Numerical Simulation.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Monica Nonino, Francesco Ballarin, Gianluigi Rozza, Yvon Maday
Summary: This manuscript presents a reduced order model based on POD-Galerkin for unsteady fluid-structure interaction problems. The model utilizes a partitioned algorithm with semi-implicit treatment of coupling conditions. It extends existing works on reduced order models for fluid-structure interaction to unsteady problems.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
Pierfrancesco Siena, Michele Girfoglio, Francesco Ballarin, Gianluigi Rozza
Summary: In this work, a machine learning-based Reduced Order Model (ROM) is proposed for the investigation of hemodynamics in a patient-specific configuration of Coronary Artery Bypass Graft (CABG). The ROM method extracts a reduced basis space using a Proper Orthogonal Decomposition (POD) algorithm and employs Artificial Neural Networks (ANNs) for computation. The Full Order Model (FOM) is represented by the Navier-Stokes equations discretized using a Finite Volume (FV) technique. The novelties of this study include the use of FV method in a patient-specific configuration, a data-driven ROM technique, and a mesh deformation strategy based on Free Form Deformation (FFD) technique. The performance of the ROM approach is analyzed in terms of error and speed-up achieved.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Engineering, Civil
Armin Sheidani, Sajad Salavatidezfouli, Giovanni Stabile, Gianluigi Rozza
Summary: In this paper, high-fidelity CFD simulations were used to examine the wake characteristics of an H-shaped vertical-axis wind turbine. Proper Orthogonal Decomposition (POD) was applied to analyze the computed flow field in the near wake of the rotor. The performance of different turbulence models was assessed, and the significant time and length scales of the predictions were highlighted using the extracted POD modes.
JOURNAL OF WIND ENGINEERING AND INDUSTRIAL AERODYNAMICS
(2023)
Article
Mathematics, Applied
Martin W. W. Hess, Annalisa Quaini, Gianluigi Rozza
Summary: This work presents a new approach for reducing the models of time-dependent parametric partial differential equations based on data. By using a multi-step procedure, the proposed method can accurately recover field solutions from a limited number of large-scale simulations. Numerical experiments on the Rayleigh-Benard cavity problem demonstrate the effectiveness of this approach in both medium and high Grashof number regimes, especially in the latter regime approaching turbulent and chaotic behavior. One major advantage of this method is its ability to recover frequencies that are not present in the sampled data.
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Dario Coscia, Laura Meneghetti, Nicola Demo, Giovanni Stabile, Gianluigi Rozza
Summary: Convolutional Neural Network (CNN) is a crucial architecture in deep learning, with trainable filters used for convolution on discrete input data. This paper introduces a continuous version of a trainable convolutional filter that can handle unstructured data. The new framework expands the usage of CNNs for more complex problems beyond discrete domains. Experimental results demonstrate that the continuous filter achieves comparable accuracy to state-of-the-art discrete filters and can be utilized as a building block in current deep learning architectures for solving problems in unstructured domains as well.
COMPUTATIONAL MECHANICS
(2023)
Article
Nanoscience & Nanotechnology
Michele Girfoglio, Annalisa Quaini, Gianluigi Rozza
Summary: This paper introduces a pressure-based solver developed within OpenFOAM for the Euler equations. The solver uses conservative form equations with density, momentum, and total energy as variables. Two Large Eddy Simulation models are considered for stabilization and sub-grid process capturing. Numerical results demonstrate the accuracy of the approach.
Article
Engineering, Multidisciplinary
F. Mohammadizadeh, S. G. Georgiev, G. Rozza, E. Tohidi, S. Shateyi
Summary: This paper introduces the 0-Hilfer fractional Black-Scholes (0-HFBS) equation, and focuses on the existence of solutions and numerical methods. The equation is converted into a system of linear algebraic equations by collocating it with the boundary and initial conditions at Chebyshev-Gauss-Lobato points. The convergence of the method is proved, and some test problems are provided to demonstrate the effectiveness of the approach.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Engineering, Multidisciplinary
Andrea Mola, Nicola Giuliani, Oscar Crego, Gianluigi Rozza
Summary: This work discusses the correct modeling of fully nonlinear free surface boundary conditions in water wave flow simulations. The main goal is to identify a mathematical formulation and numerical treatment for both transient simulations and steady solutions. The study focuses on the kinematic and dynamic fully nonlinear free surface boundary conditions, and proves that the kinematic condition can be manipulated to derive an alternative non-penetration boundary condition. The implemented solver successfully solves steady potential flow problems and accurately reproduces results of classical steady flow solvers.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Mathematics, Applied
Anna Ivagnes, Giovanni Stabile, Andrea Mola, Traian Iliescu, Gianluigi Rozza
Summary: In this paper, hybrid data-driven ROM closures for fluid flows are proposed. These closures combine two fundamentally different strategies: purely data-driven closures and physically based, eddy viscosity data-driven closures. The hybrid model is applied to investigate a two-dimensional flow past a circular cylinder at Re = 50,000, and the numerical results show that it is more accurate than both the purely data-driven ROM and the eddy viscosity ROM.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Nicola Clinco, Michele Girfoglio, Annalisa Quaini, Gianluigi Rozza
Summary: In this paper, a filter stabilization technique for the mildly compressible Euler equations is presented, which relies on an indicator function to identify the regions where artificial viscosity is needed. By adopting the Evolve Filter-Relax (EFR) algorithm, the proposed technique shows superior stability and less dissipation compared to linear filter and Smagorinsky-like models, especially when using a function based on approximate deconvolution operators.
COMPUTERS & FLUIDS
(2023)
Article
Mathematics, Applied
Nicola Demo, Maria Strazzullo, Gianluigi Rozza
Summary: In this work, we propose applying physics informed supervised learning strategies to parametric partial differential equations. Our main goal is to simulate parametrized phenomena in a short amount of time by utilizing physics information for learning. This is achieved through the use of physics information in the loss function (standard physics informed neural networks), augmented input (extra feature employment), and guiding the construction of an effective neural network structure (physics informed architecture). The methodology has been tested for various equations and optimal control framework.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Review
Engineering, Multidisciplinary
Francesco Romor, Marco Tezzele, Markus Mrosek, Carsten Othmer, Gianluigi Rozza
Summary: Multi-fidelity models are important for combining information from different numerical simulations, surrogates, and sensors. This study focuses on approximating high-dimensional scalar functions with low intrinsic dimensionality. By introducing a low-dimensional bias, the curse of dimensionality can be overcome, especially for many-query applications. A gradient-based reduction of the parameter space through active subspaces or a nonlinear transformation of the input space is used to build a low-fidelity response surface, enabling nonlinear autoregressive multi-fidelity Gaussian process regression without the need for new simulations. This approach has great potential in engineering applications with limited data.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Mathematics, Applied
Francesco Andreuzzi, Nicola Demo, Gianluigi Rozza
Summary: This paper proposes an extension of Dynamic Mode Decomposition (DMD) to parameterized dynamical systems and demonstrates its capability in forecasting the output of interest in a parametric context. By projecting snapshots onto a reduced space and using regression techniques, DMD can approximate the output for future untested parameter configurations.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
(2023)
