Mathematical and Experimental Simulation of Operating Modes of Capillary Emitter of Electrostatic Colloidal Microthruster by S. V. Redko, E. B. Chubenko, V. P. Bondarenko, I. V. Nikiforov, M. S. Krakov

“…For the system of Navier – Stokes equations, the projection method proposed by Chorin is applied. …”
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Nanoconfined Water in Shales and Its Impact on Real Gas Flow by Yudan Li, Shaohua Gu, Cheng Dai

“…Incorporating modified boundary conditions into the Navier-Stokes equations, gas transport model through single organic/inorganic pore is derived. …”
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Finite Element Analysis of Fluid Flow through the Screen Embedded between Parallel Plates with High Reynolds Numbers by Abid A. Memon, Hammad Alotaibi, M. Asif Memon, Kaleemullah Bhatti, Gul M. Shaikh, Ilyas Khan, A. A. Mousa

“…The two-dimensional incompressible Navier Stokes equations are worked out making use of the popular software COMSOL MultiPhysics version 5.4 which implements the Galerkin’s least square scheme to discretize the governing set of equations into algebraic form. …”
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Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model by Beuchler, Sven, Endtmayer, Bernhard, Lankeit, Johannes, Wick, Thomas

“…Therein, the stationary Navier–Stokes equations are coupled with a stationary heat equation. …”
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Some features of implementation of design model of high-pressure centrifugal compressor stage with inlet guide vanes by V. V. Karabanova, A. D. Vanyashov, V. L. Yusha

“…The flow study is performed using the Navier-Stokes equations, closed by the Shear Stress Transport (SST) turbulence model. …”
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Smooth imploding solutions for 3D compressible fluids by Tristan Buckmaster, Gonzalo Cao-Labora, Javier Gómez-Serrano

“…In addition, we provide simplified proofs of linear stability [67] and nonlinear stability [69], which allow us to construct asymptotically self-similar imploding solutions to the compressible Navier-Stokes equations with density independent viscosity for the case $\gamma =\frac 75$ . …”
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The analysis of the influence of the turbulence model selection on the parameters of interaction of a supersonic jet with an obstacle by R. A. Peshkov, A. S. Shmetkova, O. V. Ispravnikova, Ju. L. Suskina

“…Differential equations describing the motion of a compressible viscous heatconducting gas (Navier-Stokes equations) are presented, and a method for averaging them by Reynolds is described. …”
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The Effect of Fracture Surface Roughness and Mechanical Aperture on the Onset of Nonlinear Flow Behaviors in 3D Self-Affine Rough Fractures by Kangsheng Xue, Xiaobo Liu, Xufeng Yan, Xiaolou Chi

“…Comparing the permeability obtained by the Navier–Stokes equation with the cube law under different hydraulic gradients, we found that their deviation increased with the increase of hydraulic gradients. …”
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On the motion of a viscous liquid with a free boundary by V. L. Sennitskii

“…To formulate the problem, the Navier—Stokes equation, the continuity equation, and the equation of conditions at both the solid and free boundaries of the liquid were used. …”
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Permeability Properties of Jointed Rock with Periodic Partially Filled Fractures by Fei Ye, Jun-Chao Duan, Wen-Xi Fu, Xing-Yu Yuan

“…In this model, the clear fluid in fractures is governed by the Navier-Stokes equation, and the fluid both in the porous medium and rock matrix are subjected to the Brinkman-Extended Darcy equation. …”
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Distributed Approximating Functional Approach to Burgers’ Equation using Element Differential Quadrature Method by M Vaghefi, H Rahideh, MR Golbaher Haghighi, AK Manshad

“…This equation is similar to, but simpler than, the Navier-Stokes equation in fluid dynamics. To verify this advantage through some comparison studies, an exact series solution are also obtained. …”
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Numerical Simulations of the Impact and Spreading of a Particulate Drop on a Solid Substrate by Hyun Jun Jeong, Wook Ryol Hwang, Chongyoup Kim

“…We present two-dimensional numerical simulations of the impact and spreading of a droplet containing a number of small particles on a flat solid surface, just after hitting the solid surface, to understand particle effects on spreading dynamics of a particle-laden droplet for the application to the industrial inkjet printing process. The Navier-Stokes equation is solved by a finite-element-based computational scheme that employs the level-set method for the accurate interface description between the drop fluid and air and a fictitious domain method for suspended particles to account for full hydrodynamic interaction. …”
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Distributed Approximating Functional Approach to Burgers’ Equation using Element Differential Quadrature Method by M Vaghefi, H Rahideh, MR Golbaher Haghighi, AK Manshad

“…This equation is similar to, but simpler than, the Navier-Stokes equation in fluid dynamics. To verify this advantage through some comparison studies, an exact series solution are also obtained. …”
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Numerical Modeling of the Influence of Solar Activity on the Global Circulation in the Earth’s Mesosphere and Lower Thermosphere by Igor Mingalev, Victor Mingalev

“…Moreover, in the model calculations, not only the horizontal components but also the vertical component of the neutral wind velocity is obtained by means of a numerical solution of a generalized Navier-Stokes equation for compressible gas, so the hydrostatic equation is not applied. …”
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Numerical Simulation on Interface Evolution and Impact of Flooding Flow by J. Hu, Z. Q. Lu, X. Y. Kan, S. L. Sun

“…A numerical model based on Navier-Stokes equation is developed to simulate the interface evolution of flooding flows. …”
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Numerical Simulation of the Nonlinear Flow Properties in Self-Affine Aperture-Based Fractures by Xin Zhou, Jianlong Sheng, Ruili Lu, Zuyang Ye, Wang Luo

“…By solving the N–S (Navier–Stokes) equation directly, the relationships between the Forchheimer-flow characteristics, fractal dimension, and standard deviation of the aperture have been obtained. …”
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A Multiscale Model for Virus Capsid Dynamics by Changjun Chen, Rishu Saxena, Guo-Wei Wei

“…We show that the classical Navier-Stokes equation for the fluid dynamics and Newton's equation for the molecular dynamics can be derived from the least action principle. …”
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Numerical study of bioheat transfer in a vascular bed with counter-flow mechanisms by K.R. Sreegowrav, R. Indira, Sushma M. Puranik, S. Jagadeesha, S.J. Vishwanatha, K. Ganesh Kumar

“…The bioheat transport equation, combined with the Navier-Stokes equation, governs the thermal and fluid behavior. …”
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Modeling the Hydrodynamic Pressure Field and Wake Field Characteristics of an Underwater Vehicle and Studying Their Correlation by Peihao Li, Hui Deng, Bingrui Xu, Weixue Xia, Wenbin Yi

“…In this paper, a numerical method is established based on the Reynolds-averaged Navier–Stokes equation. Following grid convergence verification for seven kinds of grids, the differences between the hydrodynamic pressure field and wake field are investigated using the gridding method and turbulence model. …”
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Unstructured Grid Solutions for Incompressible Laminar Flow over a Circular Cylinder Using a Particular Finite Volume-Finite Element Method by Mahdi Yousefifard, Parviz Ghadimi, Rahim Zamanian

“…A numerical modeling of a 2D Navier-Stokes equation by a particular vertex centered control volume framework on an unstructured grid is presented in this paper. …”
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