Article
Mathematics, Interdisciplinary Applications
Levent Aydinbakar, Kenji Takizawa, Tayfun E. Tezduyar, Daisaku Matsuda
Summary: The study tests the ST-VMS method with U-duct turbulent flow benchmark problem, utilizing ST isogeometric discretization to improve geometric representation accuracy and flow solution accuracy, showing good accuracy in this class of flow problems.
COMPUTATIONAL MECHANICS
(2021)
Article
Mathematics, Applied
Takashi Kuraishi, Kenji Takizawa, Tayfun E. E. Tezduyar
Summary: The study focuses on boundary layer mesh resolution in flow computation with the ST-VMS method and isogeometric discretization for 2D flow past a circular cylinder. By varying element lengths near the cylinder and adjusting lengths for other layers, the study evaluates velocity profiles and stabilization parameters for proper mesh resolution. The data and observations generated are expected to be valuable for VMS-based computations with isogeometric discretization, even with moving meshes.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2022)
Article
Computer Science, Interdisciplinary Applications
Soonpil Kang, Arif Masud
Summary: This paper presents an immersed boundary method for weak enforcement of Dirichlet boundary conditions on immersed surfaces. The method combines the Variational Multiscale Discontinuous Galerkin method and an interface stabilized form. A significant contribution of this work is the analytically derived Lagrange multiplier for weak enforcement of the Dirichlet boundary conditions. Numerical experiments demonstrate the method's effectiveness with different types of meshes, and the norm of the stabilization tensor varies with the flow physics.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Marcin Los, Maciej Wozniak, Keshav Pingali, Luis Emilio Garcia Castillo, Julen Alvarez-Arramberri, David Pardo, Maciej Paszynski
Summary: In this paper, a simulator for time-dependent Maxwell's equations with linear computational cost is proposed. The simulator employs B-spline basis functions and alternating-directions splitting strategy, and uses a second-order accurate time-integration scheme in a weak form. The discretization of the simulator results in a stiffness matrix with a Kronecker product structure, enabling linear computational cost LU factorization. In addition, a formulation for absorbing boundary conditions suitable for direction splitting is derived and verified through numerical simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Engineering, Multidisciplinary
Juan F. Giraldo, Victor M. Calo
Summary: This paper interprets the stabilized finite element method as a variational multiscale method, approximating the solution to partial differential equations using discrete spaces. It utilizes adaptive methods and residual minimization to compute coarse-scale and fine-scale approximations, resulting in stable solutions and robust error estimates. The framework is tested in challenging scenarios and demonstrates optimal convergence rates and stability in the solution.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
H. Cen, Q. Zhou, A. Korobenko
Summary: The study evaluates a turbulence modeling framework applied to stable stratified turbulent channel flow, finding that the framework is able to faithfully capture flow structures, replicate intermittent flow dynamics, and improve numerical accuracy in simulations.
COMPUTERS & FLUIDS
(2021)
Article
Mathematics, Interdisciplinary Applications
Takashi Kuraishi, Fulin Zhang, Kenji Takizawa, Tayfun E. Tezduyar
Summary: This article presents a framework for wind turbine wake computation, which combines ST-VMS method, ST isogeometric discretization, and Multidomain Method (MDM) to accurately represent long-wake vortex patterns in a computationally efficient way. By utilizing these methods, the computational cost is reduced while maintaining high accuracy in flow solution.
COMPUTATIONAL MECHANICS
(2021)
Article
Mathematics, Applied
Haoyang Cen, Qi Zhou, Artem Korobenko
Summary: This article introduces a computational framework for numerical modeling of stratified boundary layer over complex terrain. The framework is validated against experiments and shows good agreement with the actual situation, and it is able to handle different degrees of stratified flow. The study also found that the weak imposition of Dirichlet boundary condition has an effect on the performance of the framework.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Huayi Huang, Yunqing Huang, Qili Tang
Summary: This paper proposes a variational multiscale method for solving flow problems at high Reynolds numbers and proves its stability and convergence.
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
(2022)
Article
Environmental Sciences
A. Bayram, A. Korobenko
Summary: This paper presents a modeling method for the dispersion and deposition of expelled particles in an indoor environment. The model is validated against experimental measurements and numerical data, and is applied to simulate a coughing event under different ventilation scenarios. The results demonstrate the effectiveness and robustness of the presented formulation.
ATMOSPHERIC ENVIRONMENT
(2022)
Article
Mathematics, Interdisciplinary Applications
Takashi Kuraishi, Fulin Zhang, Kenji Takizawa, Tayfun E. Tezduyar
Summary: This article presents extensive studies on spatial and temporal resolution in wind turbine wake computation, along with a computational framework that accurately represents turbine long-wake vortex patterns in an efficient way. The framework consists of the Space-Time Variational Multiscale (ST-VMS) method, ST isogeometric discretization, and the Multidomain Method (MDM), providing high-fidelity solutions with practical efficiency in wind turbine long-wake computations.
COMPUTATIONAL 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
Xin Su, Sai-Mang Pun
Summary: This paper introduces a multiscale method for solving the Signorini problem with a heterogeneous field. By constructing multiscale basis functions and utilizing the GMsFEM framework, the method effectively handles the unilateral condition of the problem, with theoretical analysis and numerical results provided.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Interdisciplinary Applications
A. Bayram, A. Korobenko
Summary: A numerical approach for modelling cavitating flows over moving hydrodynamic surfaces is presented, using various models and methods, and detailed comparisons and experimental validations are conducted.
COMPUTATIONAL MECHANICS
(2021)
Article
Engineering, Aerospace
Jamshid Fazilati, Vahid Khalafi
Summary: Bonded repair techniques are commonly used in aviation maintenance, with Isogeometric Analysis offering a cost-effective tool for analyzing complex geometries. The study focuses on free vibration analysis of perforated plates repaired with bonded composite patches, using a multi-patch geometry modeling approach and ensuring geometry integrity through a Nitsche method. Results show the influence of geometric and material parameters on the dynamic response of repaired perforated plates.
CHINESE JOURNAL OF AERONAUTICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Yang Liu, Kenji Takizawa, Tayfun E. Tezduyar, Takashi Kuraishi, Yufei Zhang
Summary: This article introduces a Carrier-Domain Method (CDM) for high-resolution computation of time-periodic long-wake flows, which is cost-effective and practical. The CDM utilizes a moving computational domain and high-resolution moving mesh to compute long-wake flows, providing a more cost-effective approach compared to fixed meshes. The results of the study demonstrate the effectiveness of CDM in high-resolution computation of time-periodic long-wake flows.
COMPUTATIONAL MECHANICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Takuya Terahara, Kenji Takizawa, Tayfun E. Tezduyar
Summary: We introduce a T-splines computational method and its implementation that allows for connecting structures of different parametric dimensions with continuity and smoothness. We derive the basis functions for connecting structures with 2D and 1D parametric dimensions, involving proper selection of a scale factor for the knot vector of the 1D structure. The method can be extended to achieve higher-order continuity when needed.
COMPUTATIONAL MECHANICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Takuya Terahara, Kenji Takizawa, Reha Avsar, Tayfun E. E. Tezduyar
Summary: In this article, the authors present the T-splines computational method for spacecraft parachute structural mechanics computations. The method allows for connecting structures with different parametric dimensions and ensures continuity and smoothness. The effectiveness of the method is demonstrated through computations involving both membrane and shell models of the parachute canopy fabric.
COMPUTATIONAL MECHANICS
(2023)
Article
Engineering, Multidisciplinary
Tayfun E. Tezduyar, Kenji Takizawa
Summary: The DSD/SST method is a moving-mesh method used for computational analysis of flows with moving boundaries and interfaces. It combines different stabilization components, such as SUPG and PSPG methods, to enable fluid analysis. Special methods, such as ST-IGA, were also introduced. These methods allow for the solution of challenging fluid flow problems.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Applied
Kenji Takizawa, Yuto Otoguro, Tayfun E. Tezduyar
Summary: The stabilization parameters of certain methods involve two local length scales - advection and diffusion length scales. The advection length scale is always in the flow direction, while the diffusion length scale is typically dependent on the element geometry. However, there is a justification for making the diffusion length scale also direction-dependent to account for spatial variation of the solution. To achieve this, a direction-dependent diffusion length scale calculated from the strain-rate tensor is introduced.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2023)
Review
Mechanics
Yuri Bazilevs, Kenji Takizawa, Tayfun E. Tezduyar, Artem Korobenko, Takashi Kuraishi, Yuto Otoguro
Summary: The superior accuracy isogeometric analysis (IGA) has brought higher fidelity to computational aerodynamics in fluid and solid mechanics. The IGA achieves increased accuracy in flow solution, problem geometry representation, and representation of solid surface motion in a space-time framework. IGA is part of a set of methods that have proven effective in computational aerodynamics, including complex-geometry aerodynamics. These methods can be categorized into core methods, accuracy-boosting methods, and application range-expanding methods. We provide an overview of these methods and showcase examples of their computations.
JOURNAL OF MECHANICS
(2023)
Article
Mathematics, Applied
Tayfun E. Tezduyar, Kenji Takizawa, Yuri Bazilevs
Summary: This paper provides an overview of flows with moving boundaries and interfaces (MBI), which include fluid-particle and fluid-structure interactions, multi-fluid flows, and free-surface flows. These problems are frequently encountered in engineering analysis and design, and pose computational challenges that require core computational methods and special methods. The paper focuses on isogeometric analysis, complex geometries, incompressible-flow Space-Time Variational Multiscale (ST-VMS) and Arbitrary Lagrangian-Eulerian VMS (ALE-VMS) methods, and special methods developed in connection with these core methods.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2024)
Article
Engineering, Mechanical
Hironori Takeda, Yusuke Asai, Shunichi Ishida, Yasutoshi Taniguchi, Takuya Terahara, Kenji Takizawa, Yohsuke Imai
Summary: Wrinkling and creasing of an elastic membrane in a shear flow can be influenced by shear rate and membrane thickness. The deformation type can be determined by mechanical and geometrical effects of the membrane thickness, based on the geometrical consistency of the capsule surface.
JOURNAL OF FLUIDS AND STRUCTURES
(2024)
Review
Mechanics
Takashi Kuraishi, Takuya Terahara, Kenji Takizawa, Tayfun E. Tezduyar
Summary: Representing boundary layers and contact accurately in computational flow analysis is challenging. The space-time topology change method allows for moving-mesh computation with contact, while maintaining high-resolution flow representation near the surfaces. Using these methods, many challenges in flow analysis with complex geometries, rotating or deforming surfaces, and multiscale flows have been addressed. This two-part article provides an overview of these methods and the specific challenges encountered in tire aerodynamics.
JOURNAL OF MECHANICS
(2022)
Article
Mathematics, Applied
Kevin J. Painter, Thomas Hillen, Jonathan R. Potts
Summary: The use of nonlocal PDE models in describing biological aggregation and movement behavior has gained significant attention. These models capture the self-organizing and spatial sorting characteristics of cell populations and provide insights into how animals perceive and respond to their surroundings. By deriving and analyzing these models, we can better understand biological movement behavior and provide a basis for explaining sociological phenomena.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2024)
Article
Mathematics, Applied
Nicola Bellomo, Massimo Egidi
Summary: This paper focuses on Herbert A. Simon's visionary theory of the Artificial World and proposes a mathematical theory to study the dynamics of organizational learning, highlighting the impact of decomposition and recombination of organizational structures on evolutionary changes.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2024)
Article
Mathematics, Applied
Tayfun E. Tezduyar, Kenji Takizawa, Yuri Bazilevs
Summary: This paper provides an overview of flows with moving boundaries and interfaces (MBI), which include fluid-particle and fluid-structure interactions, multi-fluid flows, and free-surface flows. These problems are frequently encountered in engineering analysis and design, and pose computational challenges that require core computational methods and special methods. The paper focuses on isogeometric analysis, complex geometries, incompressible-flow Space-Time Variational Multiscale (ST-VMS) and Arbitrary Lagrangian-Eulerian VMS (ALE-VMS) methods, and special methods developed in connection with these core methods.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2024)