Article
Mathematics, Applied
Elizabeth Carlson, Adam Larios
Summary: The well-posedness of the formal sensitivity equations with respect to viscosity for the 2D incompressible Navier-Stokes equations is rigorously proven in this study, showing convergence of difference quotients to the unique solution of the sensitivity equations. This proof method provides uniform bounds on difference quotients, indicating stable behavior of parameter recovery algorithms as the system evolves. Additionally, the analysis can be extended to the sensitivity of the 2D Euler equations to viscous regularization, marking a significant development in understanding the global existence and uniqueness of sensitivity equations in fluid dynamics.
JOURNAL OF NONLINEAR SCIENCE
(2021)
Article
Mechanics
Qiao Zhang, Chuanqiang Gao, Fangqi Zhou, Dangguo Yang, Weiwei Zhang
Summary: This study uses the Delayed-Detached Eddy Simulation and Discrete Frequency Response method to analyze the flow field and sound propagation law in different transonic buffeting states. It is found that low-frequency and small-amplitude shock oscillation in light buffeting states do not trigger large separated flow, while deep buffeting states produce high-frequency and large-amplitude shock oscillations resulting in large separated bubbles. Collisions between upstream traveling waves and shock wave oscillations increase the frequency and sound pressure levels of the shock waves. The main sound sources in this process are shock oscillations and the von Karman mode.
Article
Mathematics, Applied
Francesco Fanelli
Summary: The study focuses on the incompressible and fast rotation limit for the barotropic Navier-Stokes equations with Coriolis force, in the regime where the Mach number is large compared to the Rossby number. The limit dynamics is described by an incompressible Navier-Stokes type equation in vorticity formulation, with an additional unknown related to density oscillations. The convergence proof relies on compensated compactness argument and sharp decay estimates for solutions to a heat equation with fast diffusion in time.
PHYSICA D-NONLINEAR PHENOMENA
(2021)
Article
Multidisciplinary Sciences
M. C. Lopes Filho, H. J. Nussenzveig Lopes
Summary: In this work, the authors proved that physically realizable weak solutions of the incompressible two-dimensional Euler equations on a torus conserve kinetic energy. Physically realizable weak solutions refer to solutions that can be obtained as limits of vanishing viscosity. The authors extended the previous research by adding forcing to the flow.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Physics, Fluids & Plasmas
Candi Zheng, Yang Wang, Shiyi Chen
Summary: Finding extended hydrodynamics equations that can be applied from the dense gas region to the rarefied gas region is a difficult task. Accurate constitutive relations for stress and heat flux are crucial for success. Data-driven models offer a new approach to learning these relations, but the choice of derivatives in these models is arbitrary and lacks a physical explanation.
Article
Mathematics, Applied
D. Yakoubi
Summary: The viscosity-splitting (VS) scheme is used to solve the incompressible time-dependent Navier-Stokes equations by decoupling them into two sub-problems. This method splits the nonlinearity and incompressibility into separate steps, making each subproblem easier to solve. The Incremental viscosity-splitting (IVS) scheme improves on this method by incorporating the gradient of the pressure in the first step and modifying the Stokes equations in the second step for a more accurate prediction of the intermediate velocity. Experimental tests will be used to demonstrate the effectiveness of the suggested strategy.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Acoustics
Stefan Jacob, Emelie Trigell, Mihai Mihaescu, Mats Abom
Summary: This paper presents a numerical solution for acoustic wave scattering, which can describe sound propagation through complex geometries. By using linearized equations and a rotating frame of reference, rotational effects in sound transmission can be accounted for. The implementation of this approach is simple and computationally efficient. The results have implications for noise control in high-performance turbo-machinery used in automotive or aviation applications.
JOURNAL OF SOUND AND VIBRATION
(2023)
Article
Mathematics
Minling Li, Zheng-an Yao, Rongfeng Yu
Summary: In this study, we focus on the barotropic compressible Navier-Stokes equations with density-dependent viscosities and investigate their behavior in vacuum. It is shown that classical solutions in bounded domains will blow up under certain conditions. A new viscosity condition is introduced for the first time in this paper.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
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
Chemistry, Physical
Dario Vincenzi
Summary: Research shows that internal friction does not change the critical Weissenberg number for the coil-stretch transition of polymers, but it does steepen the slope of the extension probability distribution, making the transition more pronounced.
Article
Engineering, Multidisciplinary
R. Chabiniok, J. Hron, A. Jarolimova, J. Malek, K. R. Rajagopal, K. Rajagopal, H. Svihlova, K. Tuma
Summary: This study aims to understand the flow characteristics of three-dimensional incompressible Navier-Stokes fluid in tubes with a sinusoidal extension. The research is significant for its implications on blood flow through the aortic root, and reveals variations in flow attributes under different slip conditions.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2022)
Article
Mathematics, Applied
Xian Liao, Christian Zillinger
Summary: In this article, we studied the two-dimensional Navier-Stokes equations with variable viscosity depending on the vertical position. Our main finding is the establishment of linear enhanced dissipation near the non-affine stationary states replacing Couette flow. These shear flows can grow exponentially. Furthermore, unlike the case with constant viscosity, decreasing viscosity leads to stronger enhanced dissipation, while increasing viscosity leads to weaker dissipation.
Article
Mathematics, Applied
Jianxia He, Zhenhua Guo
Summary: In this paper, the Cauchy problem of the three-dimensional inhomogeneous incompressible Navier-Stokes equations with degenerate viscosity is investigated. For the case μ(ρ) = ρ, the global existence of strong solution for small initial data satisfying the compatibility condition is proved. Furthermore, the large time algebraic decay rates of the velocity are also obtained. The innovation of this article is that it does not require a positive lower bound for viscosity.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(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
Xueying Zhang, Yangjiong Wu
Summary: This paper proposes a high resolution strategy for the localized method of approximate particular solutions (LMAPS). The strategy aims to improve the accuracy and stability of numerical calculation by selecting upwind interpolation templates. Numerical results demonstrate that the proposed high-resolution LMAPS is effective and accurate, especially for solving the Navier-Stokes equations with high Reynolds number.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2024)