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
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, Applied
Yanghai Yu, Xiaolei Yang, Xing Wu
Summary: In this paper, the Cauchy problem for the tri-dimensional compressible Navier-Stokes-Korteweg system is considered. The global solutions to the tri-dimensional Navier-Stokes-Korteweg equations are established with a specific choice on the Korteweg tensor in the whole space. These solutions are applicable to a class of large initial data whose L-2 norm can be arbitrarily large.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Yanghai Yu, Xing Wu
Summary: This paper investigates the Cauchy problem for the two-dimensional Navier-Stokes-Korteweg system with nonvacuum and general pressure laws, establishing the global well-posedness of strong solutions for general initial data in the framework of Sobolev spaces.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Engineering, Multidisciplinary
Saikat Mukherjee, Hector Gomez
Summary: In this paper, a numerical algorithm is proposed to solve the Navier-Stokes-Korteweg equations, which can predict cavitation inception without assumptions about mass transfer. The proposed numerical scheme uses a modified bulk free energy and a Taylor-Galerkin discretization. It is capable of simulating high-speed flows with large pressure gradients, and is demonstrated to be accurate, stable, and robust.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Applied
Kaile Chen, Yunyun Liang, Nengqiu Zhang
Summary: In this article, we investigate the three-dimensional compressible Navier-Stokes-Korteweg equations with the effect of external potential force. By assuming the smallness of both the external potential force and the initial perturbation, we prove the global existence and regularity of strong solutions for the Navier-Stokes-Korteweg equations.
Article
Mathematics, Applied
Hui Fang, Yihan Fan, Yanping Zhou
Summary: In this paper, the problem of energy equality in the two and three dimensional compressible Navier-Stokes-Korteweg equations with general pressure law is investigated. By using commutator estimation to handle the nonlinear terms, the sufficient conditions for the regularity of weak solutions to conserve energy are obtained.
Article
Mathematics, Applied
Yuming Qin, Jianlin Zhang, Yang Wang, Xing Su
Summary: This paper investigates the non-isothermal one-dimensional model of capillary compressible fluids derived by Slemrod (1984) and Dunn and Serrin (1985). The global existence, uniqueness, and exponential stability of strong solutions in H-+(i) (i = 1, 2, 4) for the one-dimensional Navier-Stokes equations with capillarity are established, implying the existence and exponential stability of the nonlinear C-0-semigroups S(t) on H-+(i) (i = 1, 2, 4).
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2021)
Article
Polymer Science
Lu Chen, Tianzhengxiong Deng, Helezi Zhou, Zhigao Huang, Xiongqi Peng, Huamin Zhou
Summary: This paper presents a three-dimensional simulation method for a one-step compression-stamping process, which can conduct thermoplastic compression molding and continuous fiber reinforced thermoplastic composite stamping forming simultaneously. By using new computational models and a fluid structure interaction framework, the simulation method can accurately replicate the actual molding process.
Article
Engineering, Multidisciplinary
Tianyi Hu, Yu Leng, Hector Gomez
Summary: This paper proposes a new method to impose boundary conditions naturally in the weak form of higher-order PDEs. By weighting the boundary conditions and using multiple integrations by parts, accurate and efficient imposition of boundary conditions on complex geometries is achieved.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Minling Li, Zheng-an Yao, Rongfeng Yu
Summary: In this study, the multi-dimensional barotropic compressible Navier-Stokes-Korteweg equations with degenerate coefficients of viscosities and capillary in bounded domains were explored. It was found that any classical solutions to the initial-boundary-value problem will blow up in finite time when the initial density contains an isolated mass group. Additionally, it was shown that the weak solution obtained by Bresch et al. (2003) cannot be improved to a classical one in the presence of an isolated mass group initially.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Tong Tang, Xu Wei, Zhi Ling
Summary: In this paper, the blow-up phenomena of classical solutions to the compressible Navier-Stokes-Korteweg system with degenerate viscosity in arbitrary dimensions are studied. The upper and lower decay rates of the internal energy are obtained based on previous work. Furthermore, the results of blow-up phenomena do not require specific initial data conditions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Juan Wang, Changguo Xiao, Yinghui Zhang
Summary: In this study, the optimal time decay rates of the solution and its spatial derivatives from one-order to the highest-order for the 3D compressible Navier-Stokes-Korteweg system are proved. The main novelty lies in obtaining optimal decay rates of the highest-order spatial derivative of the density and the high-frequency part of the highest-order spatial derivative of the velocity by carefully exploiting the regularity effect of the Korteweg term and making full use of low-frequency and high-frequency decomposition.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics
Takayuki Kobayashi, Masashi Misawa, Kazuyuki Tsuda
Summary: This paper studies the asymptotic profile of diffusion wave terms of solutions to the compressible Navier-Stokes-Korteweg system, finding that there are essentially different behaviors in space-time L2 between the diffusion wave parts for density and the potential flow part of momentum. The decay of the potential flow part is slower than that of the Stokes flow part in momentum when measured by L2 in space.
Article
Mathematics
Zihao Song, Jiang Xu
Summary: This passage discusses a system of equations in Rd (d > 3) that describes the evolution of isothermal, viscous, and compressible fluids of Korteweg type, which can be used as a phase transition model. When the sound speed is zero, it is found that the linearized system has a purely parabolic structure, allowing for the establishment of global-in-time existence and Gevrey analyticity of strong solutions in hybrid Besov spaces of Lp-type. The proof mainly relies on new nonlinear Besov (-Gevrey) estimates for product and composition of functions. & COPY; 2023 Elsevier Inc. All rights reserved.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Interdisciplinary Applications
Takashi Kuraishi, Zhaojing Xu, Kenji Takizawa, Tayfun E. Tezduyar, Satoshi Yamasaki
Summary: This study presents a high-resolution space-time isogeometric analysis method for car and tire aerodynamics, which accurately captures the tire geometry, road contact, and tire deformation and rotation. The method combines various techniques and methods to achieve a detailed representation of the flow near the tire and reduce computational cost and data storage burden.
COMPUTATIONAL MECHANICS
(2022)
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)
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)