Article
Physics, Mathematical
Masahiro Suzuki, Katherine Zhiyuan Zhang
Summary: In this paper, we investigate the compressible Navier-Stokes equation in a perturbed half-space with an outflow boundary condition and the supersonic condition. We demonstrate the unique existence of stationary solutions for the perturbed half-space, which exhibit multidirectional flow and are independent of the tangential directions. Additionally, we prove the asymptotic stability of these stationary solutions.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(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
Mathematics
Vassilios N. Laskos, Thomas Kotsopoulos, Dimitrios Karpouzos, Vassilios P. Fragos
Summary: This paper studies the incompressible laminar isothermal flow of a Newtonian fluid around a surface-mounted rib in a three-dimensional numerical experiment. The dimensionless Navier-Stokes equations are numerically solved using the Galerkin finite element method for Reynolds numbers ranging from 1 to 800. The transition from steady to unsteady state and the determination of the critical Reynolds number are investigated. The results show that the flow is three-dimensional even at a Reynolds number of 10, and the critical Reynolds number is 600, below which the steady-state equations can be used for calculations.
Article
Mathematics, Applied
Yanqing Wang, Yongfu Wang, Yulin Ye
Summary: This paper discusses the continuation criteria to the 3D isentropic compressible Navier-Stokes equations in Lorentz spaces. It proves that under certain conditions, there won't be blowup occurrences at a specific time in this system.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics
Yeping Li, Zhen Luo
Summary: This paper investigates the large time behavior of the three-dimensional full compressible Navier-Stokes-Korteweg equations. The planar rarefaction wave is constructed and its asymptotic stability is proven.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Keiichi Watanabe
Summary: This article studies the stability of a stationary solution to the three-dimensional Navier-Stokes equations in a bounded domain, where surface tension effects are taken into account. It is proved that this stability result can be obtained by the positivity of the second variation of the energy functional associated with the equation that determines an equilibrium figure. The unique global solution is constructed in the L-p-in-time and L-q-in-space setting with (p, q) is an element of (2, infinity) x (3, infinity), satisfying 2/p + 3/q < 1, and the solution converges exponentially to the equilibrium.
ADVANCES IN NONLINEAR ANALYSIS
(2023)
Article
Mathematics
Anthony Suen
Summary: The study addresses the global-in-time existence, stability, and long time behavior of weak solutions of the three-dimensional compressible Navier-Stokes equations with a potential force, demonstrating the alpha-dependence of different smoothing rates for weak solutions near t = 0. Long time convergence of weak solutions in various norms is obtained, with a comparison of instantaneous states of corresponding fluid particles in two different solutions using the Lagrangian framework. The research provides qualitative insights into the long time behavior of weak solutions and their continuous dependence on initial data and steady states.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Wai-Tong Louis Fan, Michael Jolly, Ali Pakzad
Summary: This study investigates the incompressible 3D Navier-Stokes equations subject to shear induced by noisy movement of the boundary. The effect of noise is quantified by upper bounds on the first two moments of the dissipation rate, with the expected value estimate consistent with the Kolmogorov dissipation law. The boundary movement is modeled by an Ornstein-Uhlenbeck process, and there is a potential for over-dissipation if the Ornstein-Uhlenbeck process is replaced by the Wiener process.
Article
Multidisciplinary Sciences
K. Ohkitani, R. Vanon
Summary: In this study, we propose a systematic method to construct forward self-similar solutions to the Navier-Stokes equations in order to characterize the late stage of decaying turbulent flows. We utilize the vorticity curl as the dependent variable and treat the nonlinear term as a perturbation, allowing us to quantitatively estimate its strength.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Mathematics, Applied
Xiaocui Li, Xu You
Summary: This paper presents a detailed numerical analysis of the mixed finite element method for fractional Navier-Stokes equations, including stability analysis and convergence analysis, with numerical examples demonstrating the effectiveness of the proposed method.
JOURNAL OF COMPUTATIONAL MATHEMATICS
(2021)
Article
Mathematics, Applied
Hongyun Peng, Xiaoping Zhai
Summary: This paper investigates the global existence and convergence rates of solutions to the three-dimensional compressible Navier-Stokes equations without heat conductivity. It also points out that the existence of global small solutions in two dimensions is still an open problem. In this paper, positive results are obtained for both two and three dimensions by restricting the initial data to the Besov spaces.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
(2023)
Article
Computer Science, Interdisciplinary Applications
Mustafa E. Danis, Jue Yan
Summary: This study proposes a new formula for the nonlinear viscous numerical flux and extends it to the compressible Navier-Stokes equations using the direct discontinuous Galerkin method with interface correction (DDGIC). The new method simplifies the implementation and enables accurate calculation of physical quantities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Yeping LI, Zhen Luo, Jiahong Wu
Summary: This paper investigates the stability and precise large-time behavior of perturbations near the planar rarefaction wave in the three-dimensional isentropic compressible Navier-Stokes-Poisson equations. The results are new and consider the effects of the self-consistent electrostatic potential and the decay rate.
COMMUNICATIONS IN MATHEMATICAL SCIENCES
(2022)
Article
Computer Science, Interdisciplinary Applications
F. Golse, F. Hecht, O. Pironneau, D. Smets, P. -H. Tournier
Summary: This article presents a method for studying the temperature in a gas subjected to electromagnetic radiations using the Radiative Transfer equations and Navier-Stokes equations. The method employs an H-matrix compression scheme for numerical implementation, which is efficient and accurate.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Jiawei Gao, Jian Li
Summary: In this study, the steady Navier-Stokes equations are solved using three different space iteration methods. The methods, including simple, Oseen, and Newton iterative methods, are evaluated for their stability, convergence, CPU time, and numerical convergence rate. The numerical results agree well with theoretical findings, showing that the Newton method converges faster for large viscosity, while the Oseen method is more suitable for equations with small viscosity.
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS
(2022)
