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Статті в журналах з теми "Navier Stoke"

Автор: Grafiati

Опубліковано: 11 березня 2023

Оновлено: 1 квітня 2023

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1

Cai, Jiaxi, Yihan Wang, and Shuonan Yu. "The Recent Progress and the State-of-art Applications of Navier Stokes Equation." Highlights in Science, Engineering and Technology 12 (August 26, 2022): 114–20. http://dx.doi.org/10.54097/hset.v12i.1413.

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Анотація:

Navier Stoke equation plays an important role in physics field to describe the movement of fluid. In description of movement of fluid, turbulent flow is difficult to describe because it cannot be predicted precisely for movement of every particle. In this paper, we present the basic information of Navier Stoke equation, history of developing Navier Stoke equation as well as solving method. In addition, the state-of-art applications in fluid mechanics are also demonstrated. Moreover, the limitation of Navier Stoke equation and its future prospect are proposed accordingly. These results shed light on guiding further exploration focusing on the fluid mechanics.

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2

Huan, Diem Dang. "Stability of stochastic 2D Navier-Stokes equations with memory and Poisson jumps." Open Journal of Mathematical Sciences 4, no. 1 (November 30, 2020): 417–29. http://dx.doi.org/10.30538/oms2020.0131.

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The objective of this paper is to study the stability of the weak solutions of stochastic 2D Navier-Stokes equations with memory and Poisson jumps. The asymptotic stability of the stochastic Navier-Stoke equation as a semilinear stochastic evolution equation in Hilbert spaces is obtained in both mean square and almost sure senses. Our results can extend and improve some existing ones.

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3

Yanti, Rahma. "Pengaruh Posisi Bukaan terhadap Penghawaan Alami pada Rumah Balai Padang." Gorontalo Journal of Infrastructure and Science Engineering 2, no. 1 (April 1, 2019): 10. http://dx.doi.org/10.32662/gojise.v2i1.525.

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Penelitian ini bertujuan untuk mengetahui efek dari posisi dari bukaan yang ada di rumah Balai Padang. Metode yang digunakan adalah eksperimental dengan menggunakan bantuan software CFD (computational Fluid Dimension) berdasarkan persamaan Navier-Stoke, menggunakan K-Epsilon RNG. Eksperimen dilakukan dengan validasi hasil pengukuran lapangan This study aims to investigate the effect of position openings in Balai Padang house. The numerical methodology is based on solution of the Navier-Stokes equations, using K-epsilon RNG. Numerical results are validated with available field measurement data.

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4

Almady, Wasif. "Analytical Solution for Boltzmann Collision Operator for the1-D Diffusion equation." International Journal for Research in Applied Science and Engineering Technology 9, no. 9 (September 30, 2021): 1514–17. http://dx.doi.org/10.22214/ijraset.2021.38189.

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Abstract: In this paper, we have presented the analytical solution of the collision operator for the Boltzmann equation of onedimensional diffusion equation using the analytical solution of the one-dimensional Navier Stoke diffusion equation. Keywords: Boltzmann equation; analytical collision operator; one-dimensional diffusion equation.

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5

Lévy, T., and E. Sanchez-Palencia. "Einstein-like approximation for homogenization with small concentration. II—Navier-Stoke equation." Nonlinear Analysis: Theory, Methods & Applications 9, no. 11 (November 1985): 1255–68. http://dx.doi.org/10.1016/0362-546x(85)90034-3.

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6

Zhu, Bao Li, Hui Pen Wu, and Tian Hang Xiao. "Study of Aerodynamic Interactions of Dual Flapping Airfoils in Tandem Configurations." Applied Mechanics and Materials 160 (March 2012): 301–6. http://dx.doi.org/10.4028/www.scientific.net/amm.160.301.

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The unsteady viscous flow fields of dual flapping airfoils in tandem configurations are simulated by a Navier-Stokes Solver based on dynamic deformable hybrid meshes. Aerodynamic interactions of three motion models are studied including flapping fore airfoil with fixed aft airfoil, two airfoils flapping in phase and out-of-phase. The results indicate that the aft airfoil in the wake of the flapping fore airfoil has great influence on the aerodynamic performance. When the fore airfoil flaps with a fixed aft airfoil, the thrust generation and thrust propulsive efficiency were enhanced by 65% and 44% respectively, compared to that of single flapping airfoil. When the two airfoils stoke in phase, the thrust generation is twice over that of single flapping airfoil. However the out-of-phase stroking has relatively much lower thrust.

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7

Basuki, Imam, and Fredy Susanto. "Aliran Fluida Laminer Pada Pipa Non Horizontal." JEECAE (Journal of Electrical, Electronics, Control, and Automotive Engineering) 4, no. 2 (December 3, 2019): 301–5. http://dx.doi.org/10.32486/jeecae.v4i2.435.

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aliran fluida dalam pipa nonhorizontal merupakan aliran dalam koordinat silindrikal merupakan aliran yang berkembang secara penuh dalam arah subu z. dengan menerapkan prinsip-prinsip hokum kekekalan masa dan momentum, serta berpendekatan pada teorema gauss serta menentukan kondisi batas teoritisnya, maka aplikasi persamaan navier stoke menghasilkan gambaran nilai laju arah aliran fluida berkembang penuh dalam pipa, profile aliran berupa profil aliran hiperbolik dalam pipa alir, dan laju rata-rata volume fluida yang memiliki kekuatan laju dalam nilai kuadrat 4 nilai jari-jari pipa alirnya (a^4 ).

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8

Ibthisham, A. Mohd, Srithar Rajoo, Amer Nordin Darus, Mazlan Abdul Wahid, Mohsin Mohd Sies, and Aminuddin Saat. "Simulation of Corrected Mass Flow and Non-Adiabatic Efficiency on a Turbocharger." Applied Mechanics and Materials 388 (August 2013): 23–28. http://dx.doi.org/10.4028/www.scientific.net/amm.388.23.

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The aim of this project is to evaluate turbine’s performance based on its actual condition. Holset H3B nozzles turbine geometry was used as simulation model. Turbine’s actual working condition was simulated using finite volume method (FVM). Three-dimensional Navier Stoke equations with heat convection loss via turbine volute are solved. The parameters studied are corrected mass flow and turbine’s efficiency at different heat transfer coefficients. Temperature difference within turbine’s volute is the major factor that deteriorates turbine’s efficiency. It is found that the higher the heat transfer coefficient, the lower turbine’s efficiency will be.

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9

Tasri. "Simple Improvement of Momentum Interpolation Equation for Navier-Stoke Equation Solver on Unstructured Grid." Journal of Mathematics and Statistics 6, no. 3 (August 1, 2010): 265–70. http://dx.doi.org/10.3844/jmssp.2010.265.270.

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10

MORINISHI, Koji. "A Preliminary Study of the Boltzmann/Navier-Stoke Hybrid Method for Micro Flow Simulation." Proceedings of The Computational Mechanics Conference 2004.17 (2004): 81–82. http://dx.doi.org/10.1299/jsmecmd.2004.17.81.

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11

Merder, T., M. Warzecha, and P. Warzecha. "Large-Eddy Simulations of a Flow Characteristics in a Multi-Strand Continuous Casting Tundish / Badania Numeryczne Charakterystyk Przepływu W Wielo-Wylewowej Kadzi Posredniej Metodą Wielkich Wirów (Les)." Archives of Metallurgy and Materials 60, no. 4 (December 1, 2015): 2923–26. http://dx.doi.org/10.1515/amm-2015-0466.

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In order to increase the efficiency and quality of the steel-making process a numerous studies are conducted at the various stages of the process, including continuous casting of steel. Researchers still search for new models and improve existing one, so that the specific of the process is accuratelly reproduced. One way to increase the accuracy of numerical simulation, is to apply the LES (Large Eddy Simulation) method to simulate steelmaking processes. The article presents the results of numerical analysis on the flow characteristics (RTD curves) of liquid steel in the tundish facility for the continuous casting of steel. Numerical simulations have been performed using RANS (Reynoldsaveraged Navier-Stoke) and LES methods, and those results have been verified in industrial conditions.

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12

Ondara, Koko, Ulung Jantama Wisha, and Serli Marlinda Panjaitan. "Particle Tracking Model Approach for Analyzing Crude Oil Spill (Palm Fatty Acid Distillate) in Bayur Bay Based on Navier Stokes Discrete." Buletin Oseanografi Marina 10, no. 1 (January 7, 2021): 67–74. http://dx.doi.org/10.14710/buloma.v10i1.29036.

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Анотація:

Oil spilled in the marine ecosystem may be induced by some sources which alter over time and location. Oil leakage from offshore oil drilling, underwater oil pipeline leakage, etc., are the possible source of oil spill pollution. Marine pollution generated by oil spilling occurred in Padang City in 2017. Palm Fatty Acid Distillate (PFAD) spilled within Bayur Bay Harbor due to a leaking storage tank. As much as 50 tons of PFAD overflowed and commenced to pollute Bayur coastal bay. This study aimed to determine the distribution pattern of oil spills throughout the Bayur Bay based on a hydrodynamical model. We employed some oceanographic data and PFAD characteristics obtained directly from survey results. We simulated the particle tracking model for 30 days since the PFAD spilled within the port. The model developed applied the Least Square method to analyze tidal data and a flexible mesh as a model basis, while the governing equation used is Navier Stoke discrete. During a month of simulation, the dominant particles' distribution is still spinning around the Bayur Bay due to the weak current characteristics with the magnitude ranging from 0.02-0.06 m/s. The lighter PFAD particle mass tended to move faster throughout the bay and settled in the coastal area. It will pollute the coastal system even though it is going to be decomposed chemically in the sediment.

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13

Rahmayanti, Rahmayanti. "PENGARUH WINDOW TO WALL RATIO TERHADAP KENYAMANAN FISIOLOGIS DENGAN MENGGUNAKAN CFD ANSYS 14.0." Gorontalo Journal of Infrastructure and Science Engineering 3, no. 1 (April 1, 2020): 37. http://dx.doi.org/10.32662/gojise.v3i1.905.

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The use of air conditioning energy (AC) as an effort to remove heat in buildings reaches 30% of the total energy needed in the building. To reduce the use of energy in buildings by using natural ventilation because the system does not use mechanics. Field research has been carried out with the result that the openings at Balai Padang are unable to make occupants' comfort. Therefore, the existing openings will be given treatment by wider the existing openings which are 20%, 30%, and 40%. This study purpose to investigate the effect of WWR on histologic comfort. The numerical methodology is based on the solution of the Navier-Stokes equations, using K-epsilon RNG. Numerical results are validated with available field measurement data. The results obtained that by increasing the percentage of openings, the wind speed is also highPenggunaan energi air conditioning (AC) sebagai upaya penghapus panas di dalam bangunan mencapai 30% dari total energi yang dibutuhkan di dalam bangunan. Upaya yang dilakukan untuk mengurangi penggunaan energi di dalam bangunan yakni dengan menggunakan penghawaan alami sebagai penghapus panas karena sistemnya yang tidak menggunakan mekanis. Penelitian lapangan telah dilakukan dengan hasil bahwa bukaan yang ada di Balai Padang tidak mampu mencukupi kebutuhan kecepatan angin yang diperlukan untuk mendinginkan fisiologis penghuni. Oleh karena itu, bukaan yang ada akan diberikan perlakuan dengan memperbesar bukaan yang ada yakni 20%, 30% dan 40%. Penelitian ini bertujuan untuk mengetahui efek dari WWR terhadap kenyamanan fisiologis penghuni. Metode yang digunakan adalah eksperimental dengan menggunakan bantuan software CFD (computational Fluid Dimension) berdasarkan persamaan Navier-Stoke, menggunakan K-Epsilon RNG. Eksperimen dilakukan dengan validasi hasil pengukuran lapangan. Hasil yang didapatkan bahwa dengan menambah prosentase bukaan, kecepatan angin juga semakin besar.

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14

Fadhel, Ihssan A. "Simulation of Newtonian axisymmetric pipe flow by using a Taylor Galerkin/pressure correction finite element method." BASRA JOURNAL OF SCIENCE 38, no. 2 (April 1, 2020): 198–222. http://dx.doi.org/10.29072/basjs.202024.

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Анотація:

this study, a time stepping Taylor Galerkin/pressure correction finite element scheme is employed to treat incompressible Newtonian flows. In this context, Navier-Stoke partial differential equations have been used to describe the motion of the fluid. The equations consist of a time-dependent continuity equation for conservation of mass and time-dependent conservation of momentum equations. Examples considered include a start-up of Poiseuille, flow in a axisymmetric rectangular channel for the Newtonian fluid. This test is conducted by taking a circular section of the pipe. The critical level of number is investigated under the effect of various parameters. Moreover, the effect of viscosity variation and the boundary maximum axial velocity that imposed at the inlet upon the solution is studied as well. In this manner, the findings reveal that, there is a significant effect from viscosity variation and value on the level of number such that the extremely limit of number that can be reached was around

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15

Sangotayo, E. O., and J. O. Ogidiga. "Effect of the Richardson Number on Flow and Heat Transfer in a Cylinder Filled with Cu-Water Nano-fluid at Different Nanoparticle Concentrations." Journal of Applied Sciences and Environmental Management 26, no. 9 (September 30, 2022): 1488–506. http://dx.doi.org/10.4314/jasem.v26i9.7.

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Fluid circulation and thermal exchange properties via integrated natural and artificial convection within a container have attracted considerable interest due to its many industrial uses. This present work concentrates on determining the effect of the Richardson number on flow and heat transfer in a cylinder filled with Cu-Water nanofluid at different nanoparticle concentrations. The governing equations: continuity and Navier Stoke fields were discretized using the finite difference approach and simulated in C++ programming language. In this work, the Richardson parameter ranged from 2.6*104 to 2.8*104, while the concentration of Cu nanoparticles ranged from 1% to 10%, and the results are presented as Nusselt number, vorticity, and stream function profiles. The results reveal that the maximum Richardson value is 2.76 x 104 at the nanoparticle volume of 0.04, resulting in a considerable increase in the convective heat transfer rate. Furthermore, as the Richardson parameters increase, the Nusselt number in the nanofluid increases exponentially while the local drag coefficient decreases. The stream function, longitudinal velocity and circulation increase as the Richardson parameters grow. The technical design for air turbulence prediction involves an understanding of the Richardson-driven connection as a mix of wind speed and convective stability variables.

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16

Khanh, Nguyen Hung, Lanh Le Thanh, and Thoi Le Nam. "Numerical Investigation on Characteristics of Fluid Flow Over Cavity in a Parallel Channel at Low Reynolds Numbers." International Journal of Research in Vocational Studies (IJRVOCAS) 2, no. 2 (August 17, 2022): 53–70. http://dx.doi.org/10.53893/ijrvocas.v2i2.66.

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The database management output system is interesting and available in the numerical analysis of fluid flow, especially for a fluid flowing past a cavity inside a channel. The aim of the current study is to investigate numerical simulations characteristic of fluid flowing over a cavity in a parallel channel at low Reynolds numbers and to predict reduced energy. Computer Fluid Dynamic (CFD) is utilized to solve two-dimensional low Reynolds Navier-Stoke equations with support from Gambit software, which incorporates a simulation modelling suite in the meshing model. The numerical simulations were carried out by fluid such as water for the Reynolds numbers of 50 and 1000 and for cavity aspect ratio, W/H, of 1/3, 1/2, 1, 2, and 3. The normal mean velocity input is unity. This investigation indicated that changing cavities aspect ratio influences vortex flow significantly. Besides, the study found that the aspect ratio of cavities and Reynolds numbers influence total pressure and temperature output significantly and are important for most fluid dynamic problems. Finally, the optimal reduced pressure in a channel and optimal design cavities geometries yield better results.

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17

Firdhaus, Ahmad, I. Ketut Suastika, Kiryanto Kiryanto, and Samuel Samuel. "Benchmark Study of FINETM/Marine CFD Code for the Calculation of Ship Resistance." Kapal: Jurnal Ilmu Pengetahuan dan Teknologi Kelautan 18, no. 2 (July 15, 2021): 111–18. http://dx.doi.org/10.14710/kapal.v18i2.39727.

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Benchmarking can be used to test CFD programs for selecting turbulence models, grid dependency studies, testing different numerical schemes and source codes, and testing different boundary conditions. CFD simulation in this study uses FINE™/Marine 7.2-1 software. The solver process at NUMECA uses the ISIS-CFD flow solver developed by EMN, which uses the incompressible unsteady Reynolds-average Navier stoke equation (RANSE). The solver is based on the finite volume method, and Turbulence models use SST k-ω models. The free surface flow around a model surface ship (DTMB 5415) advancing in calm water under steady conditions is numerically simulated. The geometry of the DTMB 5415 ship hull was provided in igs file format. The 1996 International Towing Tank Conference has recommended the DTMB 5415 combatant as a benchmark case for CFD computations of ship resistance and propulsion. The results compare well with the available experimental data. They allow an understanding of the differences that can be expected from vicious and potential flow methods due to their different mathematical formulations. It is demonstrated that the complementary application of these methods allows good predictions of the total ship resistance.

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18

Wang, Zhi-jian, Jian-she Zheng, Lu-lu Li, and Shuai Luo. "Research on Three-Dimensional Unsteady Turbulent Flow in Multistage Centrifugal Pump and Performance Prediction Based on CFD." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/589161.

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The three-dimensional flow physical model of any stage of the 20BZ4 multistage centrifugal pump is built which includes inlet region, impeller flow region, guide-vane flow region and exit region. The three-dimensional unsteady turbulent flow numerical model is created based on Navier-Stoke solver and standardk-εturbulent equations. The method of multireference frame (MRF) and SIMPLE algorithm are used to simulate the flow in multistage centrifugal pump based on FLUENT software. The distributions of relative velocity, absolute velocity, static pressure, and total pressure in guide vanes and impellers under design condition are analyzed. The simulation results show that the flow in impeller is mostly uniform, without eddy, backflow, and separation flow, and jet-wake phenomenon appears only along individual blades. There is secondary flow at blade end and exit of guide vane. Due to the different blade numbers of guide vane and impeller, the total pressure distribution is asymmetric. This paper also simulates the flow under different working conditions to predict the hydraulic performances of centrifugal pump and external characteristics including flow-lift, flow-shaft power, and flow-efficiency are attained. The simulation results are compared with the experimental results, and because of the mechanical losses and volume loss ignored, there is a little difference between them.

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19

Dou, Zhi, Zhifang Zhou, Jinguo Wang, and Jin Liu. "Pore-Scale Modeling of Mixing-Induced Reaction Transport through a Single Self-Affine Fracture." Geofluids 2018 (June 24, 2018): 1–10. http://dx.doi.org/10.1155/2018/9095143.

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This pore-scale modeling study in single self-affine fractures showed that the heterogeneous flow field had a significant influence on the mixing-induced reaction transport. We generated the single self-affine fracture by the successive random additions (SRA) technique. The pore-scale model was developed by coupling the Navier-Stoke equation (NSE) and advection-diffusion equation with reaction (ADER). Eddies were captured in the self-affine fracture due to the increasing Reynolds number and the sudden expansion of aperture. The flux-weighted breakthrough curves (BTCs) of reaction product showed the typical non-Fickian characteristics (i.e., “early arrival” and “heavy tail”). It was found that the reactant was involved in eddies and then reacted inside the eddy-controlled domain. Consequently, eddies played a significant role in delaying the mass exchange process between the eddy-controlled domain and the main flow channel, which resulted in the “heavy tail” in BTCs. As the Reynolds number increased, the breakthrough time increased while the concentration peaks of BTCs decreased. Furthermore, the dilution index presenting the exponential of the Shannon entropy of a concentration probability distribution was used to quantify the degree of reactant mixing. The results showed that the quantification of dilution for nonreaction transport was in good agreement with the outcomes of mixing-induced reaction transport. The high Reynolds number and Peclet number had a negative influence on the mixing process at the early time whereas they led to the enhanced mixing process at the late time.

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20

Rannacher, Rolf. "Numerical analysis of the Navier-Stokes equations." Applications of Mathematics 38, no. 4 (1993): 361–80. http://dx.doi.org/10.21136/am.1993.104560.

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21

Zheng, Lingxiao, Tyson L. Hedrick, and Rajat Mittal. "A multi-fidelity modelling approach for evaluation and optimization of wing stroke aerodynamics in flapping flight." Journal of Fluid Mechanics 721 (March 13, 2013): 118–54. http://dx.doi.org/10.1017/jfm.2013.46.

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AbstractThe aerodynamics of hovering flight in a hawkmoth (Manduca sexta) are examined using a computational modelling approach which combines a low-fidelity blade-element model with a high-fidelity Navier–Stokes-based flow solver. The focus of the study is on understanding the optimality of the hawkmoth-inpired wingstrokes with respect to lift generation and power consumption. The approach employs a tight coupling between the computational models and experiments; the Navier–Stokes model is validated against experiments, and the blade-element model is calibrated with the data from the Navier–Stokes modelling. In the first part of the study, blade-element and Navier–Stokes modelling are used concurrently to assess the predictive capabilities of the blade-element model. Comparisons between the two modelling approaches also shed insights into specific flow features and mechanisms that are lacking in the lower-fidelity model. Subsequently, we use blade-element modelling to explore a large kinematic parameter space of the flapping wing, and Navier–Stokes modelling is used to assess the performance of the wing-stroke identified as optimal by the blade-element parameter survey. This multi-fidelity optimization study indicates that even within a parameter space constrained by the animal’s natural flapping amplitude and frequency, it is relatively easy to synthesize a wing stroke that exceeds the aerodynamic performance of the hawkmoth wing stroke. Within the prescribed constraints, the optimal wing stroke closely approximates the condition of normal hover, and the implications of these findings on hawkmoth flight capabilities as well as on the issue of biomimetic versus bioinspired design of flapping wing micro-aerial vehicles, are discussed.

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22

Choi, Hyoung-Gwon, Jung-Yul Yoo, and Sung-Woo Kang. "Parallel Preconditioner for the Domain Decomposition Method of the Discretized Navier-Stokes Equation." Transactions of the Korean Society of Mechanical Engineers B 27, no. 6 (June 1, 2003): 753–65. http://dx.doi.org/10.3795/ksme-b.2003.27.6.753.

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23

Ha, Tae-Min, Don NamGung, and Yong-Sik Cho. "Directional Wave Generation in the Navier-Stokes Equations Using the Internal Wave Maker." Journal of Korea Water Resources Association 45, no. 6 (June 30, 2012): 545–55. http://dx.doi.org/10.3741/jkwra.2012.45.6.545.

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24

Akysh, A. Sh. "The Cauchy problem for the Navier-Stokes equations." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 98, no. 2 (June 30, 2020): 15–23. http://dx.doi.org/10.31489/2020m2/15-23.

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25

Zhou, Junli, Cheng Ye, Yan Hu, Hassan Hemida, Guoqiang Zhang, and Wei Yang. "Development of a model for single-sided, wind-driven natural ventilation in buildings." Building Services Engineering Research and Technology 38, no. 4 (March 14, 2017): 381–99. http://dx.doi.org/10.1177/0143624417699658.

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Анотація:

Natural ventilation is a simple and energy-efficient method to adjust the indoor environment. This study aims to develop a model for predicting the total flow rate of single-sided natural ventilation. It is motivated by the fact that the wind-driven ventilation itself is commonly considered to consist two components – a mean component and a fluctuating component. Pulsating flow rate, mean and broadband ventilation rate are discussed and considered in the model due to fluctuating wind velocity driven by the fluctuating pressures and unsteady flows around the opening. The new model shows that the total flow rate is majorly caused by pulsating flow when the area of opening is small, but it is mainly caused by mean flow in the case of large opening. Opening ratio can be taken as a boundary to distinguish the small opening area and the larger one from the case analyses in this study. Reynolds Averaged Navier-Stoke model, large eddy simulation, and other correlations are utilized to validate the developed model. The results of current method agree reasonably well with those of transient simulation. Finally, a simplified version of the model is developed which is useful for predicting the total flow rate of natural ventilation in buildings. Practical application: The model can be applied to predict the total flow rate of single-sided natural ventilation in buildings due to wind pressure. The model shows that the total flow rate is majorly caused by the pulsating flow when the area of opening is small, but it is mainly caused by the mean flow in the case of large opening. An opening ratio of 3% can be taken as a boundary to distinguish the small opening area and the large one from the cases analysed in this study.

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26

Lich, Tran Gia, Le Kim Luat, and Han Quoc Trinh. "Calculation of the pressure on the valves of a sluice." Vietnam Journal of Mechanics 19, no. 3 (September 30, 1997): 25–34. http://dx.doi.org/10.15625/0866-7136/10057.

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This paper is devoted to a numerical method for calculating the pressure on the vertical two-dimensional valve basing on Navier-Stokes equations. Numerical solutions at interior points are established by splitting Navie-Stokes unsteady two-dimensional equations into two unsteady one-dimensional equations. An implicit scheme is obtained and the solution for these equations is established by the double sweep method. The values at the boundary points are calculated by the method of characteristics.

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27

Ha, Tae-Min, Hyung-Jun Kim, and Yong-Sik Cho. "Numerical Simulation of Solitary Wave Run-up with an Internal Wave-Maker of Navier-Stokes Equations Model." Journal of Korea Water Resources Association 43, no. 9 (September 30, 2010): 801–11. http://dx.doi.org/10.3741/jkwra.2010.43.9.801.

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28

Seo, J. H., and D. J. Kang. "NAVIER-STOKES SIMULATION OF A VISCOUS MICRO PUMP WITH A SPIRAL CHANNEL." Journal of computational fluids engineering 16, no. 1 (March 31, 2011): 90–95. http://dx.doi.org/10.6112/kscfe.2011.16.1.090.

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29

Cliffe, K. A., T. J. Garratt, and A. Spence. "A modified Cayley transform for the discretized Navier-Stokes equations." Applications of Mathematics 38, no. 4 (1993): 281–88. http://dx.doi.org/10.21136/am.1993.104556.

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30

Flandoli, Franco, and Marco Romito. "Probabilistic analysis of singularities for the 3D Navier-Stokes equations." Mathematica Bohemica 127, no. 2 (2002): 211–18. http://dx.doi.org/10.21136/mb.2002.134166.

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31

Hong, Sung-Ho, Sang-Ik Son, and Kyung-Woong Kim. "A Comparative Study of the Navier-Stokes Equation & the Reynolds Equation in Spool Valve Analysis." Journal of the Korean Society of Tribologists and Lubrication Engineers 28, no. 5 (October 31, 2012): 218–32. http://dx.doi.org/10.9725/kstle-2012.28.5.218.

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32

Acevedo Tapia, P., C. Amrouche, C. Conca, and A. Ghosh. "Stokes and Navier-Stokes equations with Navier boundary conditions." Journal of Differential Equations 285 (June 2021): 258–320. http://dx.doi.org/10.1016/j.jde.2021.02.045.

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33

Acevedo, Paul, Chérif Amrouche, Carlos Conca, and Amrita Ghosh. "Stokes and Navier–Stokes equations with Navier boundary condition." Comptes Rendus Mathematique 357, no. 2 (February 2019): 115–19. http://dx.doi.org/10.1016/j.crma.2018.12.002.

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34

Brenner, Howard. "Navier–Stokes revisited." Physica A: Statistical Mechanics and its Applications 349, no. 1-2 (April 2005): 60–132. http://dx.doi.org/10.1016/j.physa.2004.10.034.

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35

Brenner, Howard. "Beyond Navier–Stokes." International Journal of Engineering Science 54 (May 2012): 67–98. http://dx.doi.org/10.1016/j.ijengsci.2012.01.006.

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36

Bela Cruzeiro, Ana. "Navier-Stokes and stochastic Navier-Stokes equations via Lagrange multipliers." Journal of Geometric Mechanics 11, no. 4 (2019): 553–60. http://dx.doi.org/10.3934/jgm.2019027.

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37

Kim, G. H., and S. O. Park. "IMPLEMENTATION OF IMMERSED BOUNDARY METHOD TO INCOMPRESSIBLE NAVIER-STOKES SOLVER USING SIMPLE ALGORITHM." Journal of computational fluids engineering 17, no. 1 (March 31, 2012): 44–53. http://dx.doi.org/10.6112/kscfe.2012.17.1.044.

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38

Amrouche, Chérif, and Ahmed Rejaiba. "Navier-Stokes equations with Navier boundary condition." Mathematical Methods in the Applied Sciences 39, no. 17 (February 16, 2015): 5091–112. http://dx.doi.org/10.1002/mma.3338.

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39

Lee, M. K., and J. S. Kim. "NUMERICAL ANALYSIS OF THE FLOW AROUND A ROTARY OSCILLATING CIRCULAR CYLINDER USING UNSTEADY TWO DIMENSIONAL NAVIER-STOKES EQUATION." Journal of computational fluids engineering 16, no. 3 (September 30, 2011): 8–14. http://dx.doi.org/10.6112/kscfe.2011.16.3.008.

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40

Cho, M. W., T. H. Yang, and O. J. Kwon. "A FEASIBILITY STUDY OF A NAVIER-STOKES FLOW SOLVER USING A KINETIC BGK SCHEME IN TRANSITIONAL REGIME." Journal of computational fluids engineering 20, no. 3 (September 30, 2015): 54–61. http://dx.doi.org/10.6112/kscfe.2015.20.3.54.

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41

Baek, C., M. Kim, S. Choi, S. Lee, and C. W. Kim. "AN UNSTRUCTURED STEADY COMPRESSIBLE NAVIER-STOKES SOLVER WITH IMPLICIT BOUNDARY CONDITION METHOD." Journal of computational fluids engineering 21, no. 1 (March 31, 2016): 10–18. http://dx.doi.org/10.6112/kscfe.2016.21.1.010.

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42

Anoshchenko, O., S. Iegorov, and E. Khruslov. "Global Weak Solutions of the Navier-Stokes / Fokker-Planck / Poisson Linked Equations." Zurnal matematiceskoj fiziki, analiza, geometrii 10, no. 3 (September 25, 2014): 267–99. http://dx.doi.org/10.15407/mag10.03.267.

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43

Hong, Sung-Ho, Sang-Ik Son, and Kyung-Woong Kim. "Comparative Study of the Navier-Stokes Equation & the Reynolds Equation in Spool Valve Analysis Considering Cavitation." Journal of the Korean Society of Tribologists and Lubrication Engineers 29, no. 5 (October 31, 2013): 275–85. http://dx.doi.org/10.9725/kstle.2013.29.5.275.

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44

Maw, Yu Yu, and Min Thaw Tun. "SENSITIVITY ANALYSIS OF ANGLE, LENGTH AND BRIM HEIGHT OF THE DIFFUSER FOR THE SMALL DIFFUSER AUGMENTED WIND TURBIN." ASEAN Engineering Journal 11, no. 4 (December 13, 2021): 280–91. http://dx.doi.org/10.11113/aej.v11.18102.

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Анотація:

This paper presents the performance of the diffuser augmented wind turbine (DAWT) with the various diffuser shapes using the numerical investigations. DAWT is also a type of wind turbine and the diffuser shapes, the nozzle shapes and the cylindrical shapes are commonly inserted around the horizontal axis wind turbine (HAWT) to become the more efficient wind turbine. The aim of this study is to find the more efficient design of the diffuser for the horizontal axis wind turbine using the numerical investigations. In this research, the converging and diverging diffuser shape is inserted and the airfoil design is calculated by using the Blade Elementary Momentum Theory. The airfoil type NACA 4412 is chosen because it is suitable for the low wind speed area and easy to produce. The turbulent model k-ω is combined with the Navier Stoke equation to solve the 3-dimensional steady flow simulation of the diffuser augmented wind turbine using the Computational Fluid Dynamics (CFD) simulations. The numerical investigation is used to compare and predict the power coefficient of the DAWT with various shapes. The baseline design of the diffuser (L = 170 mm, H = 57 mm and α = 11̊) is firstly investigated. To predict the power coefficient of the various diffuser shapes, the range of the length of the diffuser is (L/D = 0.5 to 1.5), the range of the brim height of the diffuser (H/D = 0.1 to 0.35) and the range of the angle of the diffuser (α = 5̊ to 15̊ ) are also investigated. The parameters of the diffuser shapes are assigned by using the Central Composite Design Face Centered Method. The response surface method is also used to predict the most efficient diffuser design. The performance of the horizontal axis wind turbine, that of the diffuser augmented wind turbine and that of the diffuser augmented wind turbine with various shapes of diffuser are compared. The performance of new diffuser augmented wind turbine (IND_009) is 50% and 55% higher than the baseline diffuser augmented wind turbine and the horizontal axis wind turbine at rated velocity. The flow visualization of the HAWT, DAWTs are also discussed.

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45

Ju, Qiangchang, and Jianjun Xu. "Zero-Mach limit of the compressible Navier–Stokes–Korteweg equations." Journal of Mathematical Physics 63, no. 11 (November 1, 2022): 111503. http://dx.doi.org/10.1063/5.0124119.

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Анотація:

We consider the Cauchy problem for the compressible Navier–Stokes–Korteweg system in three dimensions. Under the assumption of the global existence of strong solutions to incompressible Navier–Stokes equations, we demonstrate that the compressible Navier–Stokes–Korteweg system admits a global unique strong solution without smallness restrictions on initial data when the Mach number is sufficiently small. Furthermore, we derive the uniform convergence of strong solutions for compressible Navier–Stokes–Korteweg equations toward those for incompressible Navier–Stokes equations as long as the solution of the limiting system exists.

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46

Xi, Ke, and Chao Yan. "CFD Transonic Trajectory Predictions of Three-Store Ripple Release Using Chimera Method." Applied Mechanics and Materials 513-517 (February 2014): 4490–93. http://dx.doi.org/10.4028/www.scientific.net/amm.513-517.4490.

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Анотація:

The complicated unsteady flows with moving boundary were simulated numerically by coupling solving unsteady compressible Navier-Stokes equations and 6DOF rigid-body dynamics equations. The Chimera grid technology was used to handle the relative motion. The three-store ripple release of the wing-store configuration was simulated using this method. The computational results are in good agreement with data from other literature, showing that the method used has a strong applicability to complex multi-body separation problem.

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47

Seok, Woochan, Sang Bong Lee, and Shin Hyung Rhee. "Computational simulation of turbulent flows around a marine propeller by solving the partially averaged Navier–Stokes equation." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 18 (May 9, 2019): 6357–66. http://dx.doi.org/10.1177/0954406219848021.

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Анотація:

This study concerns the characteristics of the partially averaged Navier–Stokes method for local flow analysis around a rotating propeller. Partially averaged Navier–Stokes, resolving crucial large-scale structures of turbulent flow at a given computational grid resolution, is a bridging turbulence closure model between the Reynolds-averaged Navier–Stokes equation and the direct numerical simulation. A detailed comparison between partially averaged Navier–Stokes and Reynolds-averaged Navier–Stokes models is made to achieve a better understanding of partially averaged Navier–Stokes characteristics for predicting the coherent structures in turbulent flow. The two-equation k-ω shear stress transport model and the seven-equation Reynolds stress model are selected for Reynolds-averaged Navier–Stokes computations. The problem of interest is the flow around a rotating KP505 propeller in open water conditions at an advance ratio of 0.7. Near the leading edge, the partially averaged Navier–Stokes results are similar to those of Reynolds stress model in terms of the vortical structures. Vorticity predicted by different turbulence models, however, shows significant differences. For a more detailed analysis, the velocity gradient constituting the vorticity is identified at the leading edge. It is proven that partially averaged Navier–Stokes is able to capture the anisotropic characteristics of the flow at the leading edge, where both the geometric and flow characteristics change abruptly.

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48

Cholewa, Jan W., and Tomasz Dlotko. "Fractional Navier-Stokes equations." Discrete and Continuous Dynamical Systems - Series B 22, no. 5 (April 2017): 29. http://dx.doi.org/10.3934/dcdsb.2017149.

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49

Ramm, Alexander G. "The Navier--Stokes Problem." Synthesis Lectures on Mathematics and Statistics 13, no. 3 (April 5, 2021): 1–77. http://dx.doi.org/10.2200/s01087ed1v05y202104mas042.

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50

Ramm, Alexander G. "Navier-Stokes equations paradox." Reports on Mathematical Physics 88, no. 1 (August 2021): 41–45. http://dx.doi.org/10.1016/s0034-4877(21)00054-9.

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