Article
Mathematics, Applied
Wei-Wei Han, Yao-Lin Jiang, Zhen Miao
Summary: In this work, a first-order implicit-explicit type scheme for the EMAC formulation of the timedependent Navier-Stokes equations is constructed using the scalar auxiliary variable method. The scheme is linear and solves a series of Stokes type equations with constant coefficients at each time step. The scheme is stable without any condition on the time step and conserves momentum and angular momentum, while providing error estimates for the velocity.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Sean Ingimarson, Monika Neda, Leo G. Rebholz, Jorge Reyes, An Vu
Summary: We propose a pressure correction temporal discretization method for the incompressible Navier-Stokes equations in EMAC form. The method is proven to be stable and have error estimates for the case of mixed finite element spatial discretization. It addresses the issue of the exponential dependence of the Gronwall constant on the Reynolds number and shows advantages over other formulations in numerical tests. Additionally, extensions of the method to the Crank-Nicolson temporal discretization are discussed.
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
(2023)
Article
Mathematics, Applied
Binbin Du, Jianguo Huang, Haibiao Zheng
Summary: Three two-grid Arrow-Hurwicz (A-H) methods are proposed for solving the steady incompressible Navier-Stokes equations, which combine the existing A-H method with different one-step schemes on fine mesh to enhance efficiency. Error analyses and numerical tests demonstrate the theoretical results and efficiency of these methods.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
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
Medine Demir, Aytekin Cibik, Songul Kaya
Summary: This paper discusses the application of the backward Euler based linear time filtering method in the developed energy-momentum-angular momentum conserving formulation under weakly enforced divergence constraint. The method enhances accuracy and improves approximate solutions by adding time filtering as a post-processing step. The numerical studies confirm the theoretical findings and demonstrate the superiority of the proposed method over the unfiltered case.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Computer Science, Interdisciplinary Applications
Antonin Boisneault, Samuel Dubuis, Marco Picasso
Summary: A space-time adaptive algorithm is proposed to solve the incompressible Navier-Stokes equations. Time discretization is performed using the BDF2 method, while continuous, piecewise linear anisotropic finite elements are used for space discretization. Numerical experiments confirm the accuracy of the error indicator and the efficiency of the adaptive algorithm.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Haitao Leng
Summary: This study introduces a hybridizable discontinuous Galerkin method for solving the steady-state incompressible Navier-Stokes equations. By introducing an a posteriori error estimator and using L-2 projection and inf-sup condition, the robustness of the error estimator for global L-2 errors is proven. Several numerical examples are presented to validate the theoretical analysis.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mechanics
Bo Peng, Xiaohu Guo, Yingqing Zu, Zhenfu Tian
Summary: In this paper, a pure streamfunction high-order compact difference solver is proposed for three-dimensional steady incompressible flows. A physics-preserving pure streamfunction formulation is introduced to reduce the physics-informed loss. Fourth-order compact schemes are suggested for the partial derivatives in the streamfunction formulation, and a high-resolution HOC scheme is introduced for approximating the pure third-order partial derivatives. Numerical examples validate the accuracy, convergence, and efficiency of the proposed method, showing fourth-order accuracy, excellent convergence, high-resolution, and low computational cost at higher Reynolds number.
Article
Computer Science, Interdisciplinary Applications
Xueyu Qin, Jian Yu, Zhenhua Jiang, Lintao Huang, Chao Yan
Summary: In this paper, explicit second derivative multistep methods (SDMMs) are developed for the Euler and Navier-Stokes equations to improve computational efficiency. Third-order and fourth-order SDMMs temporal discretization methods are constructed based on order conditions. The proposed strong stability preserving (SSP) condition provides optimal parameters for SSP SDMMs. Numerical experiments show that the SDMMs achieve the designed accuracy order on smooth regions and have approximately twice the computational efficiency compared to other methods.
COMPUTERS & FLUIDS
(2024)
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
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
Edward A. Miller, Xi Chen, David M. Williams
Summary: The purpose of this paper is to extend the versatile mixed methods for isothermal flows to simulate non-isothermal incompressible flows and evaluate the proposed methods theoretically and experimentally.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Computer Science, Interdisciplinary Applications
Minmiao Wang, Pankaj Jagad, Anil N. Hirani, Ravi Samtaney
Summary: We propose a discretization scheme for incompressible two-phase flows based on discrete exterior calculus (DEC). By extending our physically-compatible exterior calculus discretization for single phase flow, we are able to simulate immiscible two-phase flows with discontinuous changes in fluid properties across the interface. Our scheme transforms the two-phase incompressible Navier-Stokes equations and conservative phase field equation into the framework of exterior calculus, and obtains the discrete counterpart by using discrete differential forms and operators. We demonstrate the effectiveness and versatility of our scheme through various test cases, showing excellent boundedness, mass conservation, convergence and the ability to handle large density and viscosity ratios as well as surface tension.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Haitao Leng
Summary: In this paper, a hybridizable discontinuous Galerkin method with divergence-free and H(div)-conforming velocity field is proposed for the stationary incompressible Navier-Stokes equations. The pressure-robustness, which ensures that the a priori error estimates of the velocity are independent of the pressure error, is satisfied. Additionally, an efficient and reliable a posteriori error estimator is derived for the L-2 errors in the velocity gradient and pressure, under a smallness assumption. Numerical examples are provided to demonstrate the pressure-robustness and the performance of the obtained a posteriori error estimator.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Computer Science, Interdisciplinary Applications
Victor DeCaria, Sigal Gottlieb, Zachary J. Grant, William J. Layton
Summary: Time accuracy has always been challenging in simulations of fluid motion. To accelerate the development of accurate methods, we propose new time stepping methods that incorporate inexpensive pre-filtering and post-filtering steps. These methods address the issues of accuracy and stability and have been tested successfully.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Maxim A. Olshanskii, Arnold Reusken, Alexander Zhiliakov
Summary: The paper introduces a trace finite element method for solving the Stokes system on a closed smooth surface. It achieves inf-sup stability through volume normal derivative stabilization and demonstrates optimal convergence and interpolation properties. Numerical examples illustrate the method's effectiveness.
MATHEMATICS OF COMPUTATION
(2021)
Article
Mathematics, Applied
Thomas Jankuhn, Maxim A. Olshanskii, Arnold Reusken, Alexander Zhiliakov
Summary: The paper introduces a higher order unfitted finite element method for the Stokes system on a surface in R-3, utilizing parametric P-k-Pk-1 finite element pairs on a tetrahedral bulk mesh. It proves stability and optimal order convergence results, including a quantification of geometric errors from approximate parametric representation of the surface. Numerical experiments demonstrate the method's effectiveness.
JOURNAL OF NUMERICAL MATHEMATICS
(2021)
Article
Biochemistry & Molecular Biology
A. Zhiliakov, Y. Wang, A. Quaini, M. Olshanskii, S. Majd
Summary: Membrane phase-separation is a mechanism used by biological membranes to concentrate specific lipid species for organizing membrane processes. The computational approach based on the surface Cahn-Hilliard phase-field model complements experimental investigations in designing patchy liposomes by providing both qualitative and accurate quantitative information about membrane organization dynamics. The computational model informed by experiments has the potential to assist in designing liposomes with spatially organized surfaces, reducing cost and time in the design process.
BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES
(2021)
Article
Mathematics, Applied
Maxim Olshanskii, Xianmin Xu, Vladimir Yushutin
Summary: The paper studies an Allen-Cahn-type equation defined on a time-dependent surface as a model of phase separation with order-disorder transition in a thin material layer. It shows that the limiting behavior of the solution is a geodesic mean curvature type flow in reference coordinates through formal inner-outer expansion. A geometrically unfitted finite element method, known as trace FEM, is considered for numerical solution with full stability and convergence analysis accounting for interpolation errors and approximate geometry recovery.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Engineering, Multidisciplinary
Yerbol Palzhanov, Alexander Zhiliakov, Annalisa Quaini, Maxim Olshanskii
Summary: This paper presents a thermodynamically consistent phase-field model of two-phase flow of incompressible viscous fluids which allows for a non-linear dependence of the fluid density on the phase-field order parameter. An unfitted finite element method is applied to discretize the system, and a fully discrete time-stepping scheme is introduced to ensure the stability of the numerical solution. Numerical examples demonstrate the stability, accuracy, and overall efficiency of the approach, revealing interesting dependencies of flow statistics on geometry in two-phase surface flows.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Applied
Maxim Olshanskii, Annalisa Quaini, Qi Sun
Summary: We propose an isoparametric unfitted finite element approach for simulating two-phase Stokes problems with slip, demonstrating stability and optimal error estimates independent of various factors. Numerical results in two and three dimensions support the theoretical findings and showcase the robustness of the approach.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Maxim A. Olshanskii, Alexander Zhiliakov
Summary: The paper discusses the reuse of matrix factorization as a building block in augmented Lagrangian and modified AL preconditioners for nonsymmetric saddle point linear algebraic systems. The strategy is applied to efficiently solve two-dimensional incompressible fluid problems independent of Reynolds number, and is tested on simulating surface fluid motion motivated by lateral fluidity of inextensible viscous membranes. New eigenvalue estimates for the AL preconditioner are derived from numerical examples including Kelvin-Helmholtz instability problems on the sphere and torus.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2022)
Article
Mathematics
Maxim Olshanskii, Yerbol Palzhanov, Annalisa Quaini
Summary: This paper investigates phase-field models for the numerical simulation of lateral phase separation and coarsening in lipid membranes, with and without lateral flow. An unfitted finite element method is used for the numerical solution of these models, allowing for complex and evolving shapes without explicit surface parametrization. The effect of lateral flow on phase evolution is examined through several numerical tests, focusing on the impact of variable line tension, viscosity, membrane composition, and surface shape on pattern formation.
VIETNAM JOURNAL OF MATHEMATICS
(2022)
Article
Biochemistry & Molecular Biology
Y. Wang, Y. Palzhanov, A. Quaini, M. Olshanskii, S. Majd
Summary: Researchers have proposed a computational platform based on the principles of continuum mechanics and thermodynamics to model the membrane coarsening dynamics of liposomes. The platform has been quantitatively validated and shown to be a valuable tool in experimental practice.
BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES
(2022)
Article
Engineering, Multidisciplinary
Alexander V. Mamonov, Maxim A. Olshanskii
Summary: This paper presents a reduced order model (ROM) for numerical integration of a dynamical system with multiple parameters. The ROM utilizes compressed tensor formats to find a low rank representation for high-fidelity snapshots of the system state. The computational cost of the online phase depends only on tensor compression ranks, making it efficient and accurate.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Alexander Lozovskiy, Maxim A. Olshanskii, Yuri V. Vassilevski
Summary: This paper investigates a finite element method for a fluid-porous structure interaction problem, with a corrected balance of stresses on the fluid-structure interface. The deformations of the elastic medium are not necessarily small and are modeled using the Saint Venant-Kirchhoff (SVK) constitutive relation. The stability of the method is proved through an energy bound for the finite element solution.
RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING
(2022)
Article
Mathematics, Applied
Maxim A. Olshanskii, Arnold Reusken, Alexander Zhiliakov
Summary: This paper studies the lateral flow of a Boussinesq-Scriven fluid on a passively evolving surface embedded in Double-struck capital R-3, and introduces a well-posed weak formulation and a numerical solution method.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2022)
Article
Mechanics
Maxim A. A. Olshanskii
Summary: The paper explores equilibrium configurations of inextensible elastic membranes that exhibit lateral fluidity. The mechanical equilibrium is described by differential equations derived from a continuum description of membrane motions using the surface Navier-Stokes equations with bending forces. The equilibrium conditions are independent of lateral viscosity and relate tension, pressure, and tangential velocity of the fluid. Only surfaces with Killing vector fields, such as axisymmetric shapes, can support non-zero stationary mass flow.
Article
Mathematics, Applied
Haoran Liu, Michael Neilan, Maxim Olshanskii
Summary: We propose a CutFEM discretization for the Stokes problem based on the Scott-Vogelius pair, where discrete piecewise polynomial spaces are defined on non-fitted macro-element triangulations. Boundary conditions are imposed through Nitsche-type discretization, and stability is ensured by adding local ghost penalty stabilization terms. The scheme exhibits stability and a divergence-free property of the discrete velocity outside an O(h) neighborhood of the boundary. Additionally, a local grad-div stabilization is introduced to mitigate the error caused by violation of the divergence-free condition. Error analysis shows optimal order error estimates with a grad-div parameter scaling like O(h(-1)).
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
(2023)
Article
Engineering, Multidisciplinary
Akshay J. Thomas, Mateusz Jaszczuk, Eduardo Barocio, Gourab Ghosh, Ilias Bilionis, R. Byron Pipes
Summary: We propose a physics-guided transfer learning approach to predict the thermal conductivity of additively manufactured short-fiber reinforced polymers using micro-structural characteristics obtained from tensile tests. A Bayesian framework is developed to transfer the thermal conductivity properties across different extrusion deposition additive manufacturing systems. The experimental results demonstrate the effectiveness and reliability of our method in accounting for epistemic and aleatory uncertainties.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Zhen Zhang, Zongren Zou, Ellen Kuhl, George Em Karniadakis
Summary: In this study, deep learning and artificial intelligence were used to discover a mathematical model for the progression of Alzheimer's disease. By analyzing longitudinal tau positron emission tomography data, a reaction-diffusion type partial differential equation for tau protein misfolding and spreading was discovered. The results showed different misfolding models for Alzheimer's and healthy control groups, indicating faster misfolding in Alzheimer's group. The study provides a foundation for early diagnosis and treatment of Alzheimer's disease and other misfolding-protein based neurodegenerative disorders using image-based technologies.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jonghyuk Baek, Jiun-Shyan Chen
Summary: This paper introduces an improved neural network-enhanced reproducing kernel particle method for modeling the localization of brittle fractures. By adding a neural network approximation to the background reproducing kernel approximation, the method allows for the automatic location and insertion of discontinuities in the function space, enhancing the modeling effectiveness. The proposed method uses an energy-based loss function for optimization and regularizes the approximation results through constraints on the spatial gradient of the parametric coordinates, ensuring convergence.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Bodhinanda Chandra, Ryota Hashimoto, Shinnosuke Matsumi, Ken Kamrin, Kenichi Soga
Summary: This paper proposes new and robust stabilization strategies for accurately modeling incompressible fluid flow problems in the material point method (MPM). The proposed approach adopts a monolithic displacement-pressure formulation and integrates two stabilization strategies to ensure stability. The effectiveness of the proposed method is validated through benchmark cases and real-world scenarios involving violent free-surface fluid motion.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Chao Peng, Alessandro Tasora, Dario Fusai, Dario Mangoni
Summary: This article discusses the importance of the tangent stiffness matrix of constraints in multibody systems and provides a general formulation based on quaternion parametrization. The article also presents the analytical expression of the tangent stiffness matrix derived through linearization. Examples demonstrate the positive effect of this additional stiffness term on static and eigenvalue analyses.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Thibaut Vadcard, Fabrice Thouverez, Alain Batailly
Summary: This contribution presents a methodology for detecting isolated branches of periodic solutions to nonlinear mechanical equations. The method combines harmonic balance method-based solving procedure with the Melnikov energy principle. It is able to predict the location of isolated branches of solutions near families of autonomous periodic solutions. The relevance and accuracy of this methodology are demonstrated through academic and industrial applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Weisheng Zhang, Yue Wang, Sung-Kie Youn, Xu Guo
Summary: This study proposes a sketch-guided topology optimization approach based on machine learning, which incorporates computer sketches as constraint functions to improve the efficiency of computer-aided structural design models and meet the design intention and requirements of designers.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Leilei Chen, Zhongwang Wang, Haojie Lian, Yujing Ma, Zhuxuan Meng, Pei Li, Chensen Ding, Stephane P. A. Bordas
Summary: This paper presents a model order reduction method for electromagnetic boundary element analysis and extends it to computer-aided design integrated shape optimization of multi-frequency electromagnetic scattering problems. The proposed method utilizes a series expansion technique and the second-order Arnoldi procedure to reduce the order of original systems. It also employs the isogeometric boundary element method to ensure geometric exactness and avoid re-meshing during shape optimization. The Grey Wolf Optimization-Artificial Neural Network is used as a surrogate model for shape optimization, with radar cross section as the objective function.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
C. Pilloton, P. N. Sun, X. Zhang, A. Colagrossi
Summary: This paper investigates the smoothed particle hydrodynamics (SPH) simulations of violent sloshing flows and discusses the impact of volume conservation errors on the simulation results. Different techniques are used to directly measure the particles' volumes and stabilization terms are introduced to control the errors. Experimental comparisons demonstrate the effectiveness of the numerical techniques.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Ye Lu, Weidong Zhu
Summary: This work presents a novel global digital image correlation (DIC) method based on a convolution finite element (C-FE) approximation. The C-FE based DIC provides highly smooth and accurate displacement and strain results with the same element size as the usual finite element (FE) based DIC. The proposed method's formulation and implementation, as well as the controlling parameters, have been discussed in detail. The C-FE method outperformed the FE method in all tested examples, demonstrating its potential for highly smooth, accurate, and robust DIC analysis.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Mojtaba Ghasemi, Mohsen Zare, Amir Zahedi, Pavel Trojovsky, Laith Abualigah, Eva Trojovska
Summary: This paper introduces Lung performance-based optimization (LPO), a novel algorithm that draws inspiration from the efficient oxygen exchange in the lungs. Through experiments and comparisons with contemporary algorithms, LPO demonstrates its effectiveness in solving complex optimization problems and shows potential for a wide range of applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jingyu Hu, Yang Liu, Huixin Huang, Shutian Liu
Summary: In this study, a new topology optimization method is proposed for structures with embedded components, considering the tension/compression asymmetric interface stress constraint. The method optimizes the topology of the host structure and the layout of embedded components simultaneously, and a new interpolation model is developed to determine interface layers between the host structure and embedded components.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Qiang Liu, Wei Zhu, Xiyu Jia, Feng Ma, Jun Wen, Yixiong Wu, Kuangqi Chen, Zhenhai Zhang, Shuang Wang
Summary: In this study, a multiscale and nonlinear turbulence characteristic extraction model using a graph neural network was designed. This model can directly compute turbulence data without resorting to simplified formulas. Experimental results demonstrate that the model has high computational performance in turbulence calculation.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jacinto Ulloa, Geert Degrande, Jose E. Andrade, Stijn Francois
Summary: This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. The proper generalized decomposition (PGD) is leveraged to decompose the displacements into multiple time scales, separating the spatial and intra-cyclic dependence from the inter-cyclic variation, thereby reducing computational burden.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Utkarsh Utkarsh, Valentin Churavy, Yingbo Ma, Tim Besard, Prakitr Srisuma, Tim Gymnich, Adam R. Gerlach, Alan Edelman, George Barbastathis, Richard D. Braatz, Christopher Rackauckas
Summary: This article presents a high-performance vendor-agnostic method for massively parallel solving of ordinary and stochastic differential equations on GPUs. The method integrates with a popular differential equation solver library and achieves state-of-the-art performance compared to hand-optimized kernels.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)