Article
Computer Science, Interdisciplinary Applications
Yi Zhang, Artur Palha, Marc Gerritsma, Leo G. Rebholz
Summary: We introduce a mimetic dual-field discretization method for conserving mass, kinetic energy, and helicity in three-dimensional incompressible Navier-Stokes equations. The method utilizes a conservative dual-field mixed weak formulation and a discrete algebraic system that handles the nonlinearity. Conservation of mass, kinetic energy, and helicity is proven at the discrete level, along with proper dissipation rates in the viscous case.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mechanics
Nam Nguyen, H. Nguyen-Xuan, Jaehong Lee
Summary: In this paper, we propose an efficient approach based on flexible polygonal meshes for solving stress-constrained topology optimization problems involving both compressible and nearly incompressible materials. The approach tackles volumetric locking phenomena in nearly incompressible material limit and solves topology optimization problems with local stress constraints using an augmented Lagrangian technique. The significant contribution of this work is a unified formulation for stress-constrained topology optimization, valid for various element types, with only displacement field involved and no constraint aggregation technique required. Experimental results demonstrate the distinguishing and intriguing features of the optimized topology for nearly incompressible materials with stress constraints.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2022)
Article
Engineering, Multidisciplinary
Bosco Garcia-Archilla, Julia Novo, Samuele Rubino
Summary: In this article, we investigate the use of proper orthogonal decomposition (POD) methods for approximating the incompressible Navier-Stokes equations. We examine the effect of using different discretizations for the nonlinear term in the FOM and POD methods, and analyze the additional error term that arises. We also explore the impact of adding grad-div stabilization to both methods. Numerical experiments are conducted to validate the theoretical analysis.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Applied
Wenjia Liu, Shuo Zhang
Summary: This study investigates the minimum degree of polynomials needed to construct a stable conservative pair for incompressible Stokes problems on general triangulations. A finite element pair is proposed, which uses slightly enriched piecewise linear polynomials for velocity and piecewise constant space for pressure. The pair is shown to be the lowest-degree stable conservative pair for Stokes problems on general triangulations.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Lorenzo Botti, Francesco Carlo Massa
Summary: We propose two Hybrid High-Order (HHO) methods for the incompressible Navier-Stokes equations and investigate their robustness with respect to the Reynolds number. The two methods differ in their pressure-velocity coupling, but both have been numerically validated and shown to be effective and applicable.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Yani Feng, Qifeng Liao, David Silvester
Summary: In this paper, a nonoverlapping Robin-type multi-domain decomposition method based on stabilized Q(1)-P-0 mixed approximation (RMDD-Q(1)-P-0) is presented for incompressible flow problems. The global equations are decomposed into local problems through Robin-type domain decomposition, which are solved using the local jump stabilized Q(1)-P-0 approximation. It is proven that the RMDD-Q(1)-P-0 solutions converge to the standard global Q(1)-P-0 solutions for the Stokes problem. Numerical experiments show that RMDD-Q(1)-P-0 significantly improves the scalability of the stabilized Q(1)-P-0 approximation. The codes used in the experiments are available online.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Yanghai Yu, Jinlu Li, Zhaoyang Yin
Summary: In this paper, a new smallness hypothesis of initial data for the three-dimensional incompressible Navier-Stokes equations is derived and used to prove the existence of a unique global solution. Additionally, two examples of initial data satisfying the smallness condition are constructed, demonstrating that the norm of the initial data can be arbitrarily large.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Engineering, Multidisciplinary
Changkye Lee, Sundararajan Natarajan
Summary: This paper proposes an adaptive framework based on the edge-based strain smoothing approach with polygonal meshes for largely deformable quasi-incompressible hyperelasticity. The framework utilizes quadtree decomposition for spatial discretization and strain smoothing technique for computing the bilinear/linear form. Numerical study demonstrates the accuracy and robustness of the proposed framework with fewer degrees of freedom compared to uniform refinement.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Mathematics, Applied
Thomas Y. Hou, De Huang
Summary: In this paper, the potential singularity behavior of the 3D incompressible axisymmetric Euler equations with smooth initial data of finite energy is investigated. It is found that the introduction of numerical viscosity leads to a locally self-similar blowup phenomenon.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
Article
Engineering, Multidisciplinary
Ricardo Costa, Stephane Clain, Gaspar J. Machado, Joao M. Nobrega
Summary: The numerical solution of the incompressible Navier-Stokes equations presents challenging numerical issues. The proposed novel method uses polygonal meshes and linear piecewise elements to approximate arbitrary smooth curved boundaries, avoiding the limitations of conventional curved mesh approaches.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Marine
K. D. Do
Summary: This paper addresses the problem of global asymptotic and local exponential stabilization of a rigid body inside a viscous incompressible fluid described by Navier-Stokes equations within a bounded domain in three dimensional space provided that there is no collision between the rigid body and the boundary of the fluid domain. Due to consideration of less regular initial values of the fluid velocity, the forces and moments induced by the fluid on the rigid body are not able to bound. Therefore, the paper handles fluid work and fluid power on the rigid body in stability and convergence analysis of the closed-loop system. The control design ensures global asymptotic and local exponential stability of the rigid body while the initial fluid velocity is not required to be small and regular but only under no collision between the rigid body and the boundary of the fluid domain.
Article
Mathematics, Applied
Wei Shi, Xin-Guang Yang, Lin Shen
Summary: This paper investigates the global well-posedness of a fluid-solid interaction model with vorticity, which is described as a hyperbolic-parabolic coupled system along the conjugate boundary. The fluid is governed by the incompressible Navier-Stokes equation with vorticity, while the elastic solid is modeled by the wave equation. The global existence of weak solution and uniqueness of the coupled system are proven using the energy method, delicate estimates, and the truncation-polishing technique to overcome the lack of smoothness in the variational form. (c) 2023 Elsevier B.V. All rights reserved.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Engineering, Multidisciplinary
Costanza Arico, Marco Sinagra, Calogero Picone, Tullio Tucciarelli
Summary: A new numerical methodology is proposed for solving the 3D Navier-Stokes equations for incompressible fluids within complex boundaries and unstructured body-fitted tetrahedral mesh. The method involves a predictor step using the MAST procedure to handle non-linear terms, followed by correction steps using Mixed Hybrid Finite Elements discretization. The approach is validated with literature tests and one real-case test, showing good stability and accuracy.
ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS
(2021)
Article
Engineering, Multidisciplinary
Ricardo Costa, Stephane Clain, Gaspar J. Machado, Joao M. Nobrega, Hugo Beirao da Veiga, Francesca Crispo
Summary: This study proposes a simple and efficient method for handling slip boundary conditions on arbitrary curved boundaries in three-dimensional fluid flow problems governed by the incompressible Navier-Stokes equations. By reconstructing discrete data, slip boundary conditions are reformulated as scalar boundary conditions, and polynomial reconstructions with specific linear constraints are used to approximate arbitrary curved boundaries. Through several benchmark tests, it is confirmed that this method effectively achieves up to eighth-order convergence.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Applied
Xiaona Cui, Wei Shi, Xuezhi Li, Xin-Guang Yang
Summary: This paper investigates the tempered pullback dynamics of 3-D nonautonomous incompressible Navier-Stokes equations with nonlinear damping and delay in a bounded domain. It proves the existence and uniqueness of weak and strong solutions based on delicate priori estimates, and demonstrates the existence of the minimal family of pullback attractors under appropriate hypotheses on external forces.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Engineering, Multidisciplinary
E. Artioli, L. Beirao da Veiga, F. Dassi
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
Article
Mathematics, Applied
L. Beirao da Veiga, F. Dassi, G. Vacca
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2020)
Article
Mathematics, Applied
L. Beirao da Veiga, F. Brezzi, L. D. Marini, A. Russo
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2020)
Review
Mathematics, Applied
E. Artioli, L. Beirao da Veiga, M. Verani
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2020)
Article
Engineering, Multidisciplinary
Paola F. Antonietti, Gianmarco Manzini, Ilario Mazzieri, Hashem M. Mourad, Marco Verani
Summary: The study introduces the conforming virtual element method for numerical approximation of two-dimensional elastodynamics problem, proves stability and convergence of the method, and derives optimal error estimates under different refinements. Experimental results demonstrate the method's effectiveness on various computational meshes and show exponential convergence under p-refinement. Dispersion-dissipation analysis reveals that polygonal meshes exhibit similar properties to classical simplicial/quadrilateral grids.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
L. Beirao da Veiga, A. Pichler, G. Vacca
Summary: This paper presents a virtual element (VE) discretization for a time-dependent coupled system of nonlinear partial differential equations, aiming to investigate the capabilities of virtual element methods (VEM) for complex fluid flow problems. By combining VEM with a time stepping scheme, a theoretical analysis of the method was developed under the assumption of a regular solution. The scheme was then tested on both regular and realistic test cases to validate its effectiveness.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Applied
L. Beirao da Veiga, F. Dassi, G. Manzini, L. Mascotto
Summary: We introduce a low order virtual element discretization for time dependent Maxwell's equations, which allows for the use of general polyhedral meshes. Both the semi- and fully-discrete schemes are considered. We derive optimal a priori estimates and validate them through numerical experiments. As key findings, we discuss novel inequalities associated with de Rahm sequences of nodal, edge, and face virtual element spaces.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Mathematics, Applied
Daniele Funaro, Gianmarco Manzini
Summary: This study provides spectral approximation based on Hermite-Fourier expansion of the Vlasov-Poisson model with high-order artificial collision operators. The analysis considers the necessary conditions related to the artificial collision term, number of spectral modes, and time-step in order to ensure stability in appropriate norms. The study starts with a Hermite discretization of a simple linear problem in one dimension and extends partially to cover the complete nonlinear Vlasov-Poisson model.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
L. Beirao da Veiga, C. Canuto, R. H. Nochetto, G. Vacca
Summary: This study investigates the equilibrium of a hinged rigid leaflet with an attached rotational spring in a stationary incompressible fluid within a rigid channel using theoretical and numerical methods. Sufficient conditions for the existence and uniqueness of equilibrium positions are identified based on properties of the domain functional. The proposed numerical technique utilizes the mesh flexibility of the Virtual Element Method and proves quasi-optimal error estimates through a variety of numerical experiments.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2021)
Article
Engineering, Multidisciplinary
E. Benvenuti, A. Chiozzi, G. Manzini, N. Sukumar
Summary: In this paper, the authors propose an eXtended Virtual Element Method (X-VEM) for two-dimensional linear elastic fracture. The X-VEM allows for mesh-independent modeling of crack discontinuities and elastic crack-tip singularities on general polygonal meshes. The method involves an extended projector and additional basis functions constructed from standard virtual basis functions and enrichment fields. Numerical experiments demonstrate the accuracy and optimal convergence of the X-VEM formulation for mixed-mode linear elastic fracture problems.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Gianmarco Manzini, Annamaria Mazzia
Summary: In this paper, two conforming virtual element formulations for the numerical approximation of the Stokes problem on polygonal meshes are presented. Both formulations are inf-sup stable and have optimal convergence rates in the L2 and energy norm. The effectiveness of these numerical approximations is assessed through investigation on a representative benchmark problem.
APPLIED NUMERICAL MATHEMATICS
(2022)
Article
Mathematics, Applied
Jian Meng, Lourenco Beirao da Veiga, Lorenzo Mascotto
Summary: In this paper, we establish stability bounds for Stokes-like virtual element spaces in both two and three dimensions. These bounds are crucial for deriving optimal interpolation estimates. In addition, we conduct numerical tests to investigate the behavior of the stability constants from a practical perspective.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Engineering, Multidisciplinary
L. Beirao da Veiga, D. Mora, A. Silgado
Summary: In this paper, a fully-coupled virtual element method is proposed for solving the nonstationary Boussinesq system in 2D. The method utilizes the stream-function and temperature fields and employs C1- and C0-conforming virtual element approaches for spatial discretization. The temporal variable is discretized using a backward Euler scheme. The well-posedness and unconditional stability of the fully-discrete problem are proved, and error estimates in H2- and H1-norms are derived for the stream-function and temperature fields. Benchmark tests are conducted to validate the theoretical error bounds and demonstrate the behavior of the fully-discrete scheme.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
G. Manzini, R. Vuchkov, B. Alexandrov
Summary: Coupling the mimetic finite difference method with the tensor-train format allows for efficient low-rank numerical approximations of the solutions of the time-dependent Maxwell wave propagation equations in three dimensions. By discretizing the curl operators on the primal/dual tensor product grid complex and coupling it with a staggered-in-time second-order accurate time-marching scheme, we obtain a solver that is accurate to the second order in time and space. The use of the tensor-train format significantly improves solver performance in terms of CPU time and memory storage.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mathematics, Applied
Gianmarco Manzini, Annamaria Mazzia
Summary: This study presents a new method for the numerical approximation of the Stokes problem on polygonal meshes within the framework of the virtual element method. The numerical approximation shows optimal convergence rates in various cases, except for the lowest order on triangular meshes, and in square meshes known to be unstable.
JOURNAL OF COMPUTATIONAL DYNAMICS
(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)
