Unsteady Reynolds averaged Navier-Stokes: toward accurate predictions in fuel-bundles and T-junctions

International Nuclear Information System (INIS)

Merzari, E.; Ninokata, H.; Baglietto, E.

2008-01-01

Traditional steady-state simulation and turbulence modelling are not always reliable. Even in simple flows, the results can be not accurate when particular conditions occur. Examples are buoyancy, flow oscillations, and turbulent mixing. Often, unsteady simulations are necessary, but they tend to be computationally not affordable. The Unsteady Reynolds Averaged Navier-Stokes (URANS) approach holds promise to be less computational expensive than Large Eddy Simulation (LES) or Direct Numerical Simulation (DNS), reaching a considerable degree of accuracy. Moreover, URANS methodologies do not need complex boundary formulations for the inlet and the outlet like LES or DNS. The Test cases for this methodology will be Fuel Bundles and T-junctions. Tight-Fuel Rod-Bundles present large scale coherent structures than cannot be taken into account by a simple steady-state simulation. T-junctions where a hot fluid and a cold fluid mix present temperature fluctuations and therefore thermal fatigue. For both cases the capacity of the methodology to reproduce the flow field are assessed and it is evaluated that URANS holds promise to be the industrial standard in nuclear engineering applications that do not involve buoyancy. The codes employed are STAR-CD 3.26 and 4.06. (author)

Reynolds-averaged Navier-Stokes based ice accretion for aircraft wings

Science.gov (United States)

Lashkajani, Kazem Hasanzadeh

This thesis addresses one of the current issues in flight safety towards increasing icing simulation capabilities for prediction of complex 2D and 3D glaze ice shapes over aircraft surfaces. During the 1980's and 1990's, the field of aero-icing was established to support design and certification of aircraft flying in icing conditions. The multidisciplinary technologies used in such codes were: aerodynamics (panel method), droplet trajectory calculations (Lagrangian framework), thermodynamic module (Messinger model) and geometry module (ice accretion). These are embedded in a quasi-steady module to simulate the time-dependent ice accretion process (multi-step procedure). The objectives of the present research are to upgrade the aerodynamic module from Laplace to Reynolds-Average Navier-Stokes equations solver. The advantages are many. First, the physical model allows accounting for viscous effects in the aerodynamic module. Second, the solution of the aero-icing module directly provides the means for characterizing the aerodynamic effects of icing, such as loss of lift and increased drag. Third, the use of a finite volume approach to solving the Partial Differential Equations allows rigorous mesh and time convergence analysis. Finally, the approaches developed in 2D can be easily transposed to 3D problems. The research was performed in three major steps, each providing insights into the overall numerical approaches. The most important realization comes from the need to develop specific mesh generation algorithms to ensure feasible solutions in very complex multi-step aero-icing calculations. The contributions are presented in chronological order of their realization. First, a new framework for RANS based two-dimensional ice accretion code, CANICE2D-NS, is developed. A multi-block RANS code from U. of Liverpool (named PMB) is providing the aerodynamic field using the Spalart-Allmaras turbulence model. The ICEM-CFD commercial tool is used for the iced airfoil

Performance of Reynolds Averaged Navier-Stokes Models in Predicting Separated Flows: Study of the Hump Flow Model Problem

Science.gov (United States)

Cappelli, Daniele; Mansour, Nagi N.

2012-01-01

Separation can be seen in most aerodynamic flows, but accurate prediction of separated flows is still a challenging problem for computational fluid dynamics (CFD) tools. The behavior of several Reynolds Averaged Navier-Stokes (RANS) models in predicting the separated ow over a wall-mounted hump is studied. The strengths and weaknesses of the most popular RANS models (Spalart-Allmaras, k-epsilon, k-omega, k-omega-SST) are evaluated using the open source software OpenFOAM. The hump ow modeled in this work has been documented in the 2004 CFD Validation Workshop on Synthetic Jets and Turbulent Separation Control. Only the baseline case is treated; the slot flow control cases are not considered in this paper. Particular attention is given to predicting the size of the recirculation bubble, the position of the reattachment point, and the velocity profiles downstream of the hump.

Computational analysis of water entry of a circular section at constant velocity based on Reynold's averaged Navier-Stokes method

Science.gov (United States)

Uddin, M. Maruf; Fuad, Muzaddid-E.-Zaman; Rahaman, Md. Mashiur; Islam, M. Rabiul

2017-12-01

With the rapid decrease in the cost of computational infrastructure with more efficient algorithm for solving non-linear problems, Reynold's averaged Navier-Stokes (RaNS) based Computational Fluid Dynamics (CFD) has been used widely now-a-days. As a preliminary evaluation tool, CFD is used to calculate the hydrodynamic loads on offshore installations, ships, and other structures in the ocean at initial design stages. Traditionally, wedges have been studied more than circular cylinders because cylinder section has zero deadrise angle at the instant of water impact, which increases with increase of submergence. In Present study, RaNS based commercial code ANSYS Fluent is used to simulate the water entry of a circular section at constant velocity. It is seen that present computational results were compared with experiment and other numerical method.

Incompressible Navier-Stokes and parabolized Navier-Stokes solution procedures and computational techniques

Science.gov (United States)

Rubin, S. G.

1982-01-01

Recent developments with finite-difference techniques are emphasized. The quotation marks reflect the fact that any finite discretization procedure can be included in this category. Many so-called finite element collocation and galerkin methods can be reproduced by appropriate forms of the differential equations and discretization formulas. Many of the difficulties encountered in early Navier-Stokes calculations were inherent not only in the choice of the different equations (accuracy), but also in the method of solution or choice of algorithm (convergence and stability, in the manner in which the dependent variables or discretized equations are related (coupling), in the manner that boundary conditions are applied, in the manner that the coordinate mesh is specified (grid generation), and finally, in recognizing that for many high Reynolds number flows not all contributions to the Navier-Stokes equations are necessarily of equal importance (parabolization, preferred direction, pressure interaction, asymptotic and mathematical character). It is these elements that are reviewed. Several Navier-Stokes and parabolized Navier-Stokes formulations are also presented.

A systematic comparison of two-equation Reynolds-averaged Navier-Stokes turbulence models applied to shock-cloud interactions

Science.gov (United States)

Goodson, Matthew D.; Heitsch, Fabian; Eklund, Karl; Williams, Virginia A.

2017-07-01

Turbulence models attempt to account for unresolved dynamics and diffusion in hydrodynamical simulations. We develop a common framework for two-equation Reynolds-averaged Navier-Stokes turbulence models, and we implement six models in the athena code. We verify each implementation with the standard subsonic mixing layer, although the level of agreement depends on the definition of the mixing layer width. We then test the validity of each model into the supersonic regime, showing that compressibility corrections can improve agreement with experiment. For models with buoyancy effects, we also verify our implementation via the growth of the Rayleigh-Taylor instability in a stratified medium. The models are then applied to the ubiquitous astrophysical shock-cloud interaction in three dimensions. We focus on the mixing of shock and cloud material, comparing results from turbulence models to high-resolution simulations (up to 200 cells per cloud radius) and ensemble-averaged simulations. We find that the turbulence models lead to increased spreading and mixing of the cloud, although no two models predict the same result. Increased mixing is also observed in inviscid simulations at resolutions greater than 100 cells per radius, which suggests that the turbulent mixing begins to be resolved.

Identification of severe wind conditions using a Reynolds averaged Navier-Stokes solver

DEFF Research Database (Denmark)

Sørensen, Niels N.; Bechmann, Andreas; Johansen, Jeppe

2007-01-01

The present paper describes the application of a Navier-Stokes solver to predict the presence of severe flow conditions in complex terrain, capturing conditions that may be critical to the siting of wind turbines in the terrain. First it is documented that the flow solver is capable of predicting...

Reynolds-averaged Navier-Stokes investigation of high-lift low-pressure turbine blade aerodynamics at low Reynolds number

Science.gov (United States)

Arko, Bryan M.

Design trends for the low-pressure turbine (LPT) section of modern gas turbine engines include increasing the loading per airfoil, which promises a decreased airfoil count resulting in reduced manufacturing and operating costs. Accurate Reynolds-Averaged Navier-Stokes predictions of separated boundary layers and transition to turbulence are needed, as the lack of an economical and reliable computational model has contributed to this high-lift concept not reaching its full potential. Presented here for what is believed to be the first time applied to low-Re computations of high-lift linear cascade simulations is the Abe-Kondoh-Nagano (AKN) linear low-Re two-equation turbulence model which utilizes the Kolmogorov velocity scale for improved predictions of separated boundary layers. A second turbulence model investigated is the Kato-Launder modified version of the AKN, denoted MPAKN, which damps turbulent production in highly strained regions of flow. Fully Laminar solutions have also been calculated in an effort to elucidate the transitional quality of the turbulence model solutions. Time accurate simulations of three modern high-lift blades at a Reynolds number of 25,000 are compared to experimental data and higher-order computations in order to judge the accuracy of the results, where it is shown that the RANS simulations with highly refined grids can produce both quantitatively and qualitatively similar separation behavior as found in experiments. In particular, the MPAKN model is shown to predict the correct boundary layer behavior for all three blades, and evidence of transition is found through inspection of the components of the Reynolds Stress Tensor, spectral analysis, and the turbulence production parameter. Unfortunately, definitively stating that transition is occurring becomes an uncertain task, as similar evidence of the transition process is found in the Laminar predictions. This reveals that boundary layer reattachment may be a result of laminar

A new nonlinear turbulence model based on Partially-Averaged Navier-Stokes Equations

International Nuclear Information System (INIS)

Liu, J T; Wu, Y L; Cai, C; Liu, S H; Wang, L Q

2013-01-01

Partially-averaged Navier-Stokes (PANS) Model was recognized as a Reynolds-averaged Navier-Stokes (RANS) to direct numerical simulation (DNS) bridging method. PANS model was purported for any filter width-from RANS to DNS. PANS method also shared some similarities with the currently popular URANS (unsteady RANS) method. In this paper, a new PANS model was proposed, which was based on RNG k-ε turbulence model. The Standard and RNG k-ε turbulence model were both isotropic models, as well as PANS models. The sheer stress in those PANS models was solved by linear equation. The linear hypothesis was not accurate in the simulation of complex flow, such as stall phenomenon. The sheer stress here was solved by nonlinear method proposed by Ehrhard. Then, the nonlinear PANS model was set up. The pressure coefficient of the suction side of the NACA0015 hydrofoil was predicted. The result of pressure coefficient agrees well with experimental result, which proves that the nonlinear PANS model can capture the high pressure gradient flow. A low specific centrifugal pump was used to verify the capacity of the nonlinear PANS model. The comparison between the simulation results of the centrifugal pump and Particle Image Velocimetry (PIV) results proves that the nonlinear PANS model can be used in the prediction of complex flow field

An efficient nonlinear relaxation technique for the three-dimensional, Reynolds-averaged Navier-Stokes equations

Science.gov (United States)

Edwards, Jack R.; Mcrae, D. S.

1993-01-01

An efficient implicit method for the computation of steady, three-dimensional, compressible Navier-Stokes flowfields is presented. A nonlinear iteration strategy based on planar Gauss-Seidel sweeps is used to drive the solution toward a steady state, with approximate factorization errors within a crossflow plane reduced by the application of a quasi-Newton technique. A hybrid discretization approach is employed, with flux-vector splitting utilized in the streamwise direction and central differences with artificial dissipation used for the transverse fluxes. Convergence histories and comparisons with experimental data are presented for several 3-D shock-boundary layer interactions. Both laminar and turbulent cases are considered, with turbulent closure provided by a modification of the Baldwin-Barth one-equation model. For the problems considered (175,000-325,000 mesh points), the algorithm provides steady-state convergence in 900-2000 CPU seconds on a single processor of a Cray Y-MP.

Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier Stokes uncertainty

Science.gov (United States)

Ling, J.; Templeton, J.

2015-08-01

Reynolds Averaged Navier Stokes (RANS) models are widely used in industry to predict fluid flows, despite their acknowledged deficiencies. Not only do RANS models often produce inaccurate flow predictions, but there are very limited diagnostics available to assess RANS accuracy for a given flow configuration. If experimental or higher fidelity simulation results are not available for RANS validation, there is no reliable method to evaluate RANS accuracy. This paper explores the potential of utilizing machine learning algorithms to identify regions of high RANS uncertainty. Three different machine learning algorithms were evaluated: support vector machines, Adaboost decision trees, and random forests. The algorithms were trained on a database of canonical flow configurations for which validated direct numerical simulation or large eddy simulation results were available, and were used to classify RANS results on a point-by-point basis as having either high or low uncertainty, based on the breakdown of specific RANS modeling assumptions. Classifiers were developed for three different basic RANS eddy viscosity model assumptions: the isotropy of the eddy viscosity, the linearity of the Boussinesq hypothesis, and the non-negativity of the eddy viscosity. It is shown that these classifiers are able to generalize to flows substantially different from those on which they were trained. Feature selection techniques, model evaluation, and extrapolation detection are discussed in the context of turbulence modeling applications.

Retrospective cost adaptive Reynolds-averaged Navier-Stokes k-ω model for data-driven unsteady turbulent simulations

Science.gov (United States)

Li, Zhiyong; Hoagg, Jesse B.; Martin, Alexandre; Bailey, Sean C. C.

2018-03-01

This paper presents a data-driven computational model for simulating unsteady turbulent flows, where sparse measurement data is available. The model uses the retrospective cost adaptation (RCA) algorithm to automatically adjust the closure coefficients of the Reynolds-averaged Navier-Stokes (RANS) k- ω turbulence equations to improve agreement between the simulated flow and the measurements. The RCA-RANS k- ω model is verified for steady flow using a pipe-flow test case and for unsteady flow using a surface-mounted-cube test case. Measurements used for adaptation of the verification cases are obtained from baseline simulations with known closure coefficients. These verification test cases demonstrate that the RCA-RANS k- ω model can successfully adapt the closure coefficients to improve agreement between the simulated flow field and a set of sparse flow-field measurements. Furthermore, the RCA-RANS k- ω model improves agreement between the simulated flow and the baseline flow at locations at which measurements do not exist. The RCA-RANS k- ω model is also validated with experimental data from 2 test cases: steady pipe flow, and unsteady flow past a square cylinder. In both test cases, the adaptation improves agreement with experimental data in comparison to the results from a non-adaptive RANS k- ω model that uses the standard values of the k- ω closure coefficients. For the steady pipe flow, adaptation is driven by mean stream-wise velocity measurements at 24 locations along the pipe radius. The RCA-RANS k- ω model reduces the average velocity error at these locations by over 35%. For the unsteady flow over a square cylinder, adaptation is driven by time-varying surface pressure measurements at 2 locations on the square cylinder. The RCA-RANS k- ω model reduces the average surface-pressure error at these locations by 88.8%.

Design, experimental analysis, and unsteady Reynolds-averaged Navier-Stokes simulation of laboratory-scale counter-rotating vertical-axis turbines in marine environment

Science.gov (United States)

Doan, Minh; Padricelli, Claudrio; Obi, Shinnosuke; Totsuka, Yoshitaka

2017-11-01

We present the torque and power measurement of laboratory-scale counter-rotating vertical-axis hydrokinetic turbines, built around a magnetic hysteresis brake as the speed controller and a Hall-effect sensor as the rotational speed transducer. A couple of straight-three-bladed turbines were linked through a transmission of spur gears and timing pulleys and coupled to the electronic instrumentation via flexible shaft couplers. A total of 8 experiments in 2 configurations were conducted in the water channel facility (4-m long, 0.3-m wide, and 0.15-m deep). Power generation of the turbines (0.06-m rotor diameter) was measured and compared with that of single turbines of the same size. The wakes generated by these experiments were also measured by particle image velocimetry (PIV) and numerically simulated by unsteady Reynolds-averaged Navier-Stokes (URANS) simulation using OpenFOAM. Preliminary results from wake measurement indicated the mechanism of enhanced power production behind the counter-rotating configuration of vertical-axis turbines. Current address: Politecnico di Milano.

Identification of severe wind conditions using a Reynolds Averaged Navier-Stokes solver

International Nuclear Information System (INIS)

Soerensen, N N; Bechmann, A; Johansen, J; Myllerup, L; Botha, P; Vinther, S; Nielsen, B S

2007-01-01

The present paper describes the application of a Navier-Stokes solver to predict the presence of severe flow conditions in complex terrain, capturing conditions that may be critical to the siting of wind turbines in the terrain. First it is documented that the flow solver is capable of predicting the flow in the complex terrain by comparing with measurements from two meteorology masts. Next, it is illustrated how levels of turbulent kinetic energy can be used to easily identify areas with severe flow conditions, relying on a high correlation between high turbulence intensity and severe flow conditions, in the form of high wind shear and directional shear which may seriously lower the lifetime of a wind turbine

Computation of 3D steady Navier-Stokes flow with free-surface gravity waves

NARCIS (Netherlands)

Lewis, M.R.; Koren, B.; Raven, H.C.; Armfield, S.; Morgan, P.; Srinivas, K,

2003-01-01

In this paper an iterative method for the computation of stationary gravity-wave solutions is investigated, using a novel formulation of the free-surface (FS) boundary-value problem. This method requires the solution of a sequence of stationary Reynolds-Averaged Navier-Stokes subproblems employing

Computation of 3D steady Navier-Stokes flow with free-surface gravity waves

NARCIS (Netherlands)

M.R. Lewis; B. Koren (Barry); H.C. Raven

2003-01-01

textabstractIn this paper an iterative method for the computation of stationary gravity-wave solutions is investigated, using a novel formulation of the free-surface (FS) boundary-value problem. This method requires the solution of a sequence of stationary Reynolds-Averaged Navier-Stokes subproblems

Navier--Stokes relaxation to sinh--Poisson states at finite Reynolds numbers

International Nuclear Information System (INIS)

Montgomery, D.; Shan, X.; Matthaeus, W.H.

1993-01-01

A mathematical framework is proposed in which it seems possible to justify the computationally-observed relaxation of a two-dimensional Navier--Stokes fluid to a ''most probable,'' or maximum entropy, state. The relaxation occurs at large but finite Reynolds numbers, and involves substantial decay of higher-order ideal invariants such as enstrophy. A two-fluid formulation, involving interpenetrating positive and negative vorticity fluxes (continuous and square integrable) is developed, and is shown to be intimately related to the passive scalar decay problem. Increasing interpenetration of the two fluids corresponds to the decay of vorticity flux due to viscosity. It is demonstrated numerically that, in two dimensions, passive scalars decay rapidly, relative to mean-square vorticity (enstrophy). This observation provides a basis for assigning initial data to the two-fluid field variables

The incompressible non-relativistic Navier-Stokes equation from gravity

International Nuclear Information System (INIS)

Bhattacharyya, Sayantani; Minwalla, Shiraz; Wadia, Spenta R.

2009-01-01

We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a forcing function identical to the action of a background electromagnetic field on the effectively charged fluid. We demonstrate that special conformal symmetries of the parent relativistic theory descend to 'accelerated boost' symmetries of the Navier-Stokes equations, uncovering a conformal symmetry structure of these equations. Applying our scaling limit to holographically induced fluid dynamics, we find gravity dual descriptions of an arbitrary solution of the forced non-relativistic incompressible Navier-Stokes equations. In the holographic context we also find a simple forced steady state shear solution to the Navier-Stokes equations, and demonstrate that this solution turns unstable at high enough Reynolds numbers, indicating a possible eventual transition to turbulence.

Navier-Stokes

NARCIS (Netherlands)

Koren, B.

2013-01-01

De Navier-Stokes-vergelijkingen behoren tot de meest gebruikte vergelijkingen voor de berekening van gas- en vloeistofstromingen. Op de Vakantiecursus 2013 van het Platform Wiskunde Nederland vertelt Barry Koren over de Navier-Stokes-vergelijkingen, over stromingsleer en over openstaande

On Parametric Sensitivity of Reynolds-Averaged Navier-Stokes SST Turbulence Model: 2D Hypersonic Shock-Wave Boundary Layer Interactions

Science.gov (United States)

Brown, James L.

2014-01-01

Examined is sensitivity of separation extent, wall pressure and heating to variation of primary input flow parameters, such as Mach and Reynolds numbers and shock strength, for 2D and Axisymmetric Hypersonic Shock Wave Turbulent Boundary Layer interactions obtained by Navier-Stokes methods using the SST turbulence model. Baseline parametric sensitivity response is provided in part by comparison with vetted experiments, and in part through updated correlations based on free interaction theory concepts. A recent database compilation of hypersonic 2D shock-wave/turbulent boundary layer experiments extensively used in a prior related uncertainty analysis provides the foundation for this updated correlation approach, as well as for more conventional validation. The primary CFD method for this work is DPLR, one of NASA's real-gas aerothermodynamic production RANS codes. Comparisons are also made with CFL3D, one of NASA's mature perfect-gas RANS codes. Deficiencies in predicted separation response of RANS/SST solutions to parametric variations of test conditions are summarized, along with recommendations as to future turbulence approach.

Influence of the dispersive and dissipative scales alpha and beta on the energy spectrum of the Navier-Stokes alphabeta equations.

Science.gov (United States)

Chen, Xuemei; Fried, Eliot

2008-10-01

Lundgren's vortex model for the intermittent fine structure of high-Reynolds-number turbulence is applied to the Navier-Stokes alphabeta equations and specialized to the Navier-Stokes alpha equations. The Navier-Stokes alphabeta equations involve dispersive and dissipative length scales alpha and beta, respectively. Setting beta equal to alpha reduces the Navier-Stokes alphabeta equations to the Navier-Stokes alpha equations. For the Navier-Stokes alpha equations, the energy spectrum is found to obey Kolmogorov's -5/3 law in a range of wave numbers identical to that determined by Lundgren for the Navier-Stokes equations. For the Navier-Stokes alphabeta equations, Kolmogorov's -5/3 law is also recovered. However, granted that beta Navier-Stokes alphabeta equations may have the potential to resolve features smaller than those obtainable using the Navier-Stokes alpha equations.

Analysis of Influence of the Thermal Dependence of Air Thermophysical Properties on the Accuracy of Simulation of Heat Transfer in a Turbulent Flow in Case of Applying Different Methods of Averaging Navier-Stokes Equations

Directory of Open Access Journals (Sweden)

A. D. Kliukvin

2014-01-01

Full Text Available There is theoretically investigated the influence of thermal dependence of air thermophysical properties on accuracy of heat transfer problems solution in a turbulent flow when using different methods of averaging the Navier-Stokes equations.There is analyzed the practicability of using particular method of averaging the NavierStokes equations when it’s necessary to clarify the solution of heat transfer problem taking into account the variability of air thermophysical properties.It’s shown that Reynolds and Favre averaging (the most common methods of averaging the Navier-Stokes equations are not effective in this case because these methods inaccurately describe behavior of large scale turbulent structures which strongly depends on geometry of particular flow. Thus it’s necessary to use more universal methods of turbulent flow simulation which are not based on averaging of all turbulent scales.In the article it’s shown that instead of Reynold and Favre averaging it’s possible to use large eddy simulation whereby turbulent structures are divided into small-scale and large-scale ones with subsequent modelling of small-scale ones only. But this approach leads to the necessarity of increasing the computational power by 2-3 orders.For different methods of averaging the form of additional terms of averaged Navier-Stokes equations in case of accounting pulsation of thermophysical properties of the air is obtained.On the example of a submerged heated air jet the errors (which occur when neglecting the thermal dependence of air thermophysical properties on averaged flow temperature in determination of convectional and conductive components of heat flux and viscous stresses are evaluated. It’s shown that the greatest increase of solution accuracy can be obtained in case of the flows with high temperature gradients.Finally using infinite Teylor series it’s found that underestimation of convective and conductive components of heat flux and

Stabilizing the long-time behavior of the forced Navier-Stokes and damped Euler systems by large mean flow

Science.gov (United States)

Cyranka, Jacek; Mucha, Piotr B.; Titi, Edriss S.; Zgliczyński, Piotr

2018-04-01

The paper studies the issue of stability of solutions to the forced Navier-Stokes and damped Euler systems in periodic boxes. It is shown that for large, but fixed, Grashoff (Reynolds) number the turbulent behavior of all Leray-Hopf weak solutions of the three-dimensional Navier-Stokes equations, in periodic box, is suppressed, when viewed in the right frame of reference, by large enough average flow of the initial data; a phenomenon that is similar in spirit to the Landau damping. Specifically, we consider an initial data which have large enough spatial average, then by means of the Galilean transformation, and thanks to the periodic boundary conditions, the large time independent forcing term changes into a highly oscillatory force; which then allows us to employ some averaging principles to establish our result. Moreover, we also show that under the action of fast oscillatory-in-time external forces all two-dimensional regular solutions of the Navier-Stokes and the damped Euler equations converge to a unique time-periodic solution.

Application of thin-layer Navier-Stokes equations near maximum lift

Science.gov (United States)

Anderson, W. K.; Thomas, J. L.; Rumsey, C. L.

1984-01-01

The flowfield about a NACA 0012 airfoil at a Mach number of 0.3 and Reynolds number of 1 million is computed through an angle of attack range, up to 18 deg, corresponding to conditions up to and beyond the maximum lift coefficient. Results obtained using the compressible thin-layer Navier-Stokes equations are presented as well as results from the compressible Euler equations with and without a viscous coupling procedure. The applicability of each code is assessed and many thin-layer Navier-Stokes benchmark solutions are obtained which can be used for comparison with other codes intended for use at high angles of attack. Reasonable agreement of the Navier-Stokes code with experiment and the viscous-inviscid interaction code is obtained at moderate angles of attack. An unsteady solution is obtained with the thin-layer Navier-Stokes code at the highest angle of attack considered. The maximum lift coefficient is overpredicted, however, in comparison to experimental data, which is attributed to the presence of a laminar separation bubble near the leading edge not modeled in the computations. Two comparisons with experimental data are also presented at a higher Mach number.

Navier-Stokes calculations on multi-element airfoils using a chimera-based solver

Science.gov (United States)

Jasper, Donald W.; Agrawal, Shreekant; Robinson, Brian A.

1993-01-01

A study of Navier-Stokes calculations of flows about multielement airfoils using a chimera grid approach is presented. The chimera approach utilizes structured, overlapped grids which allow great flexibility of grid arrangement and simplifies grid generation. Calculations are made for two-, three-, and four-element airfoils, and modeling of the effect of gap distance between elements is demonstrated for a two element case. Solutions are obtained using the thin-layer form of the Reynolds averaged Navier-Stokes equations with turbulence closure provided by the Baldwin-Lomax algebraic model or the Baldwin-Barth one equation model. The Baldwin-Barth turbulence model is shown to provide better agreement with experimental data and to dramatically improve convergence rates for some cases. Recently developed, improved farfield boundary conditions are incorporated into the solver for greater efficiency. Computed results show good comparison with experimental data which include aerodynamic forces, surface pressures, and boundary layer velocity profiles.

Large Eddy Simulation and Reynolds-Averaged Navier-Stokes modeling of flow in a realistic pharyngeal airway model: an investigation of obstructive sleep apnea.

Science.gov (United States)

Mihaescu, Mihai; Murugappan, Shanmugam; Kalra, Maninder; Khosla, Sid; Gutmark, Ephraim

2008-07-19

Computational fluid dynamics techniques employing primarily steady Reynolds-Averaged Navier-Stokes (RANS) methodology have been recently used to characterize the transitional/turbulent flow field in human airways. The use of RANS implies that flow phenomena are averaged over time, the flow dynamics not being captured. Further, RANS uses two-equation turbulence models that are not adequate for predicting anisotropic flows, flows with high streamline curvature, or flows where separation occurs. A more accurate approach for such flow situations that occur in the human airway is Large Eddy Simulation (LES). The paper considers flow modeling in a pharyngeal airway model reconstructed from cross-sectional magnetic resonance scans of a patient with obstructive sleep apnea. The airway model is characterized by a maximum narrowing at the site of retropalatal pharynx. Two flow-modeling strategies are employed: steady RANS and the LES approach. In the RANS modeling framework both k-epsilon and k-omega turbulence models are used. The paper discusses the differences between the airflow characteristics obtained from the RANS and LES calculations. The largest discrepancies were found in the axial velocity distributions downstream of the minimum cross-sectional area. This region is characterized by flow separation and large radial velocity gradients across the developed shear layers. The largest difference in static pressure distributions on the airway walls was found between the LES and the k-epsilon data at the site of maximum narrowing in the retropalatal pharynx.

Five-dimensional truncation of the plane incompressible navier-stokes equations

Energy Technology Data Exchange (ETDEWEB)

Boldrighini, C [Camerino Univ. (Italy). Istituto di Matematica; Franceschini, V [Modena Univ. (Italy). Istituto Matematico

1979-01-01

A five-modes truncation of the Navier-Stokes equations for a two dimensional incompressible fluid on a torus is considered. A computer analysis shows that for a certain range of the Reynolds number the system exhibits a stochastic behaviour, approached through an involved sequence of bifurcations.

Unsteady Reynolds-averaged Navier-Stokes simulations of inlet distortion in the fan system of a gas-turbine aero-engine

Science.gov (United States)

Spotts, Nathan

As modern trends in commercial aircraft design move toward high-bypass-ratio fan systems of increasing diameter with shorter, nonaxisymmetric nacelle geometries, inlet distortion is becoming common in all operating regimes. The distortion may induce aerodynamic instabilities within the fan system, leading to catastrophic damage to fan blades, should the surge margin be exceeded. Even in the absence of system instability, the heterogeneity of the flow affects aerodynamic performance significantly. Therefore, an understanding of fan-distortion interaction is critical to aircraft engine system design. This thesis research elucidates the complex fluid dynamics and fan-distortion interaction by means of computational fluid dynamics (CFD) modeling of a complete engine fan system; including rotor, stator, spinner, nacelle and nozzle; under conditions typical of those encountered by commercial aircraft. The CFD simulations, based on a Reynolds-averaged Navier-Stokes (RANS) approach, were unsteady, three-dimensional, and of a full-annulus geometry. A thorough, systematic validation has been performed for configurations from a single passage of a rotor to a full-annulus system by comparing the predicted flow characteristics and aerodynamic performance to those found in literature. The original contributions of this research include the integration of a complete engine fan system, based on the NASA rotor 67 transonic stage and representative of the propulsion systems in commercial aircraft, and a benchmark case for unsteady RANS simulations of distorted flow in such a geometry under realistic operating conditions. This study is unique in that the complex flow dynamics, resulting from fan-distortion interaction, were illustrated in a practical geometry under realistic operating conditions. For example, the compressive stage is shown to influence upstream static pressure distributions and thus suppress separation of flow on the nacelle. Knowledge of such flow physics is

Large-eddy simulation/Reynolds-averaged Navier-Stokes hybrid schemes for high speed flows

Science.gov (United States)

Xiao, Xudong

Three LES/RANS hybrid schemes have been proposed for the prediction of high speed separated flows. Each method couples the k-zeta (Enstrophy) BANS model with an LES subgrid scale one-equation model by using a blending function that is coordinate system independent. Two of these functions are based on turbulence dissipation length scale and grid size, while the third one has no explicit dependence on the grid. To implement the LES/RANS hybrid schemes, a new rescaling-reintroducing method is used to generate time-dependent turbulent inflow conditions. The hybrid schemes have been tested on a Mach 2.88 flow over 25 degree compression-expansion ramp and a Mach 2.79 flow over 20 degree compression ramp. A special computation procedure has been designed to prevent the separation zone from expanding upstream to the recycle-plane. The code is parallelized using Message Passing Interface (MPI) and is optimized for running on IBM-SP3 parallel machine. The scheme was validated first for a flat plate. It was shown that the blending function has to be monotonic to prevent the RANS region from appearing in the LES region. In the 25 deg ramp case, the hybrid schemes provided better agreement with experiment in the recovery region. Grid refinement studies demonstrated the importance of using a grid independent blend function and further improvement with experiment in the recovery region. In the 20 deg ramp case, with a relatively finer grid, the hybrid scheme characterized by grid independent blending function well predicted the flow field in both the separation region and the recovery region. Therefore, with "appropriately" fine grid, current hybrid schemes are promising for the simulation of shock wave/boundary layer interaction problems.

Reynolds averaged simulation of unsteady separated flow

International Nuclear Information System (INIS)

Iaccarino, G.; Ooi, A.; Durbin, P.A.; Behnia, M.

2003-01-01

The accuracy of Reynolds averaged Navier-Stokes (RANS) turbulence models in predicting complex flows with separation is examined. The unsteady flow around square cylinder and over a wall-mounted cube are simulated and compared with experimental data. For the cube case, none of the previously published numerical predictions obtained by steady-state RANS produced a good match with experimental data. However, evidence exists that coherent vortex shedding occurs in this flow. Its presence demands unsteady RANS computation because the flow is not statistically stationary. The present study demonstrates that unsteady RANS does indeed predict periodic shedding, and leads to much better concurrence with available experimental data than has been achieved with steady computation

Evaluation of micronozzle performance through DSMC, navier-stokes and coupled dsmc/navier-stokes approaches

NARCIS (Netherlands)

Torre, F. la; Kenjeres, S.; Kleijn, C.R.; Moerel, J.L.P.A.

2009-01-01

Both the particle based Direct Simulation Monte Carlo (DSMC) method and a compressible Navier-Stokes based continuum method are used to investigate the flow inside micronozzles and to predict the performance of such devices. For the Navier-Stokes approach, both slip and no-slip boundary conditions

Homogenization of Stokes and Navier-Stokes equations

International Nuclear Information System (INIS)

Allaire, G.

1990-04-01

This thesis is devoted to homogenization of Stokes and Navier-Stokes equations with a Dirichlet boundary condition in a domain containing many tiny obstacles. Tipycally those obstacles are distributed at the modes of a periodic lattice with same small period in each axe's direction, and their size is always asymptotically smaller than the lattice's step. With the help of the energy method, and thanks to a suitable pressure's extension, we prove the convergence of the homogenization process when the lattice's step tends to zero (and thus the number of obstacles tends to infinity). For a so-called critical size of the obstacles, the homogenized problem turns out to be a Brinkman's law (i.e. Stokes or Navier-Stokes equation plus a linear zero-order term for the velocity in the momentum equation). For obstacles which have a size smaller than the critical one, the limit problem reduces to the initial Stokes or Navier-Stokes equations, while for larger sizes the homogenized problem a Darcy's law. Furthermore, those results have been extended to the case of obstacles included in a hyperplane, and we establish a simple model of fluid flows through grids, which is based on a special form of Brinkman's law [fr

Hybrid Reynolds-Averaged/Large-Eddy Simulations of a Coaxial Supersonic Free-Jet Experiment

Science.gov (United States)

Baurle, Robert A.; Edwards, Jack R.

2010-01-01

Reynolds-averaged and hybrid Reynolds-averaged/large-eddy simulations have been applied to a supersonic coaxial jet flow experiment. The experiment was designed to study compressible mixing flow phenomenon under conditions that are representative of those encountered in scramjet combustors. The experiment utilized either helium or argon as the inner jet nozzle fluid, and the outer jet nozzle fluid consisted of laboratory air. The inner and outer nozzles were designed and operated to produce nearly pressure-matched Mach 1.8 flow conditions at the jet exit. The purpose of the computational effort was to assess the state-of-the-art for each modeling approach, and to use the hybrid Reynolds-averaged/large-eddy simulations to gather insight into the deficiencies of the Reynolds-averaged closure models. The Reynolds-averaged simulations displayed a strong sensitivity to choice of turbulent Schmidt number. The initial value chosen for this parameter resulted in an over-prediction of the mixing layer spreading rate for the helium case, but the opposite trend was observed when argon was used as the injectant. A larger turbulent Schmidt number greatly improved the comparison of the results with measurements for the helium simulations, but variations in the Schmidt number did not improve the argon comparisons. The hybrid Reynolds-averaged/large-eddy simulations also over-predicted the mixing layer spreading rate for the helium case, while under-predicting the rate of mixing when argon was used as the injectant. The primary reason conjectured for the discrepancy between the hybrid simulation results and the measurements centered around issues related to the transition from a Reynolds-averaged state to one with resolved turbulent content. Improvements to the inflow conditions were suggested as a remedy to this dilemma. Second-order turbulence statistics were also compared to their modeled Reynolds-averaged counterparts to evaluate the effectiveness of common turbulence closure

Hybrid Reynolds-Averaged/Large-Eddy Simulations of a Co-Axial Supersonic Free-Jet Experiment

Science.gov (United States)

Baurle, R. A.; Edwards, J. R.

2009-01-01

Reynolds-averaged and hybrid Reynolds-averaged/large-eddy simulations have been applied to a supersonic coaxial jet flow experiment. The experiment utilized either helium or argon as the inner jet nozzle fluid, and the outer jet nozzle fluid consisted of laboratory air. The inner and outer nozzles were designed and operated to produce nearly pressure-matched Mach 1.8 flow conditions at the jet exit. The purpose of the computational effort was to assess the state-of-the-art for each modeling approach, and to use the hybrid Reynolds-averaged/large-eddy simulations to gather insight into the deficiencies of the Reynolds-averaged closure models. The Reynolds-averaged simulations displayed a strong sensitivity to choice of turbulent Schmidt number. The baseline value chosen for this parameter resulted in an over-prediction of the mixing layer spreading rate for the helium case, but the opposite trend was noted when argon was used as the injectant. A larger turbulent Schmidt number greatly improved the comparison of the results with measurements for the helium simulations, but variations in the Schmidt number did not improve the argon comparisons. The hybrid simulation results showed the same trends as the baseline Reynolds-averaged predictions. The primary reason conjectured for the discrepancy between the hybrid simulation results and the measurements centered around issues related to the transition from a Reynolds-averaged state to one with resolved turbulent content. Improvements to the inflow conditions are suggested as a remedy to this dilemma. Comparisons between resolved second-order turbulence statistics and their modeled Reynolds-averaged counterparts were also performed.

Stochastic 2-D Navier-Stokes Equation

International Nuclear Information System (INIS)

Menaldi, J.L.; Sritharan, S.S.

2002-01-01

In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier-Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions-Prodi solutions to the deterministic Navier-Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier-Stokes martingale problem where the probability space is also obtained as a part of the solution

Investigation of vortex breakdown on delta wings using Navier-Stokes equations

Science.gov (United States)

Hsu, C.-H.; Liu, C. H.

1992-01-01

An efficient finite-difference scheme solving for the three-dimensional incompressible Navier-Stokes equations is described. Numerical simulations of vortex breakdown are then carried out for a sharp-edged delta wing and a round-edged double-delta wing at high Reynolds numbers. Computed results show that several major features of vortex breakdown are qualitatively in agreement with observations made in experiments.

Pressure fluctuation prediction in pump mode using large eddy simulation and unsteady Reynolds-averaged Navier–Stokes in a pump–turbine

Directory of Open Access Journals (Sweden)

De-You Li

2016-06-01

Full Text Available For pump–turbines, most of the instabilities couple with high-level pressure fluctuations, which are harmful to pump–turbines, even the whole units. In order to understand the causes of pressure fluctuations and reduce their amplitudes, proper numerical methods should be chosen to obtain the accurate results. The method of large eddy simulation with wall-adapting local eddy-viscosity model was chosen to predict the pressure fluctuations in pump mode of a pump–turbine compared with the method of unsteady Reynolds-averaged Navier–Stokes with two-equation turbulence model shear stress transport k–ω. Partial load operating point (0.91QBEP under 15-mm guide vane opening was selected to make a comparison of performance and frequency characteristics between large eddy simulation and unsteady Reynolds-averaged Navier–Stokes based on the experimental validation. Good agreement indicates that the method of large eddy simulation could be applied in the simulation of pump–turbines. Then, a detailed comparison of variation for peak-to-peak value in the whole passage was presented. Both the methods show that the highest level pressure fluctuations occur in the vaneless space. In addition, the propagation of amplitudes of blade pass frequency, 2 times of blade pass frequency, and 3 times of blade pass frequency in the circumferential and flow directions was investigated. Although the difference exists between large eddy simulation and unsteady Reynolds-averaged Navier–Stokes, the trend of variation in different parts is almost the same. Based on the analysis, using the same mesh (8 million, large eddy simulation underestimates pressure characteristics and shows a better result compared with the experiments, while unsteady Reynolds-averaged Navier–Stokes overestimates them.

Falling paper: Navier-Stokes solutions, model of fluid forces, and center of mass elevation.

Science.gov (United States)

Pesavento, Umberto; Wang, Z Jane

2004-10-01

We investigate the problem of falling paper by solving the two dimensional Navier-Stokes equations subject to the motion of a free-falling body at Reynolds numbers around 10(3). The aerodynamic lift on a tumbling plate is found to be dominated by the product of linear and angular velocities rather than velocity squared, as appropriate for an airfoil. This coupling between translation and rotation provides a mechanism for a brief elevation of center of mass near the cusplike turning points. The Navier-Stokes solutions further provide the missing quantity in the classical theory of lift, the instantaneous circulation, and suggest a revised model for the fluid forces.

Hybrid Reynolds-Averaged/Large Eddy Simulation of a Cavity Flameholder; Assessment of Modeling Sensitivities

Science.gov (United States)

Baurle, R. A.

2015-01-01

Steady-state and scale-resolving simulations have been performed for flow in and around a model scramjet combustor flameholder. The cases simulated corresponded to those used to examine this flowfield experimentally using particle image velocimetry. A variety of turbulence models were used for the steady-state Reynolds-averaged simulations which included both linear and non-linear eddy viscosity models. The scale-resolving simulations used a hybrid Reynolds-averaged / large eddy simulation strategy that is designed to be a large eddy simulation everywhere except in the inner portion (log layer and below) of the boundary layer. Hence, this formulation can be regarded as a wall-modeled large eddy simulation. This effort was undertaken to formally assess the performance of the hybrid Reynolds-averaged / large eddy simulation modeling approach in a flowfield of interest to the scramjet research community. The numerical errors were quantified for both the steady-state and scale-resolving simulations prior to making any claims of predictive accuracy relative to the measurements. The steady-state Reynolds-averaged results showed a high degree of variability when comparing the predictions obtained from each turbulence model, with the non-linear eddy viscosity model (an explicit algebraic stress model) providing the most accurate prediction of the measured values. The hybrid Reynolds-averaged/large eddy simulation results were carefully scrutinized to ensure that even the coarsest grid had an acceptable level of resolution for large eddy simulation, and that the time-averaged statistics were acceptably accurate. The autocorrelation and its Fourier transform were the primary tools used for this assessment. The statistics extracted from the hybrid simulation strategy proved to be more accurate than the Reynolds-averaged results obtained using the linear eddy viscosity models. However, there was no predictive improvement noted over the results obtained from the explicit

Navier-Stokes and Comprehensive Analysis Performance Predictions of the NREL Phase VI Experiment

Science.gov (United States)

Duque, Earl P. N.; Burklund, Michael D.; Johnson, Wayne

2003-01-01

A vortex lattice code, CAMRAD II, and a Reynolds-Averaged Navier-Stoke code, OVERFLOW-D2, were used to predict the aerodynamic performance of a two-bladed horizontal axis wind turbine. All computations were compared with experimental data that was collected at the NASA Ames Research Center 80- by 120-Foot Wind Tunnel. Computations were performed for both axial as well as yawed operating conditions. Various stall delay models and dynamics stall models were used by the CAMRAD II code. Comparisons between the experimental data and computed aerodynamic loads show that the OVERFLOW-D2 code can accurately predict the power and spanwise loading of a wind turbine rotor.

Some strange numerical solutions of the non-stationary Navier-Stokes equations in pipes

Energy Technology Data Exchange (ETDEWEB)

Rummler, B.

2001-07-01

A general class of boundary-pressure-driven flows of incompressible Newtonian fluids in three-dimensional pipes with known steady laminar realizations is investigated. Considering the laminar velocity as a 3D-vector-function of the cross-section-circle arguments, we fix the scale for the velocity by the L{sub 2}-norm of the laminar velocity. The usual new variables are introduced to get dimension-free Navier-Stokes equations. The characteristic physical and geometrical quantities are subsumed in the energetic Reynolds number Re and a parameter {psi}, which involves the energetic ratio and the directions of the boundary-driven part and the pressure-driven part of the laminar flow. The solution of non-stationary dimension-free Navier-Stokes equations is sought in the form u=u{sub L}+u, where u{sub L} is the scaled laminar velocity and periodical conditions in center-line-direction are prescribed for u. An autonomous system (S) of ordinary differential equations for the time-dependent coefficients of the spatial Stokes eigenfunction is got by application of the Galerkin-method to the dimension-free Navier-Stokes equations for u. The finite-dimensional approximations u{sub N({lambda}}{sub )} of u are defined in the usual way. (orig.)

Analyticity estimates for the Navier-Stokes equations

DEFF Research Database (Denmark)

Herbst, I.; Skibsted, Erik

We study spatial analyticity properties of solutions of the Navier-Stokes equation and obtain new growth rate estimates for the analyticity radius. We also study stability properties of strong global solutions of the Navier-Stokes equation with data in and prove a stability result...

A Modular Approach to Model Oscillating Control Surfaces Using Navier Stokes Equations

Science.gov (United States)

Guruswamy, Guru P.; Lee, Henry

2014-01-01

The use of active controls for rotorcraft is becoming more important for modern aerospace configurations. Efforts to reduce the vibrations of helicopter blades with use of active-controls are in progress. Modeling oscillating control surfaces using the linear aerodynamics theory is well established. However, higher-fidelity methods are needed to account for nonlinear effects, such as those that occur in transonic flow. The aeroelastic responses of a wing with an oscillating control surface, computed using the transonic small perturbation (TSP) theory, have been shown to cause important transonic flow effects such as a reversal of control surface effectiveness that occurs as the shock wave crosses the hinge line. In order to account for flow complexities such as blade-vortex interactions of rotor blades higher-fidelity methods based on the Navier-Stokes equations are used. Reference 6 presents a procedure that uses the Navier-Stokes equations with moving-sheared grids and demonstrates up to 8 degrees of control-surface amplitude, using a single grid. Later, this procedure was extended to accommodate larger amplitudes, based on sliding grid zones. The sheared grid method implemented in EulerlNavier-Stokes-based aeroelastic code ENS AERO was successfully applied to active control design by industry. Recently there are several papers that present results for oscillating control surface using Reynolds Averaged Navier-Stokes (RANS) equations. References 9 and 10 report 2-D cases by filling gaps with overset grids. Reference 9 compares integrated forces with the experiment at low oscillating frequencies whereas Ref. 10 reports parametric studies but with no validation. Reference II reports results for a 3D case by modeling the gap region with a deformed grid and compares force results with the experiment only at the mid-span of flap. In Ref. II grid is deformed to match the control surface deflections at the section where the measurements are made. However, there is no

Verification of a novel innovative blade root design for wind turbines using a hybrid numerical method

DEFF Research Database (Denmark)

Zhu, Wei Jun; Shen, Wen Zhong; Sørensen, Jens Nørkær

2017-01-01

captured at the outer part of the blades, where the relative wind speed is high. To assess the impact of this novel design idea, a hybrid numerical technique, based on solving the Reynolds-averaged Navier-Stokes equations, is utilized to determine the aerodynamic performance. The in-house developed Ellip...

A rigorous derivation of the stationary compressible Reynolds equation via the Navier-Stokes equations

Czech Academy of Sciences Publication Activity Database

Ciuperca, I. S.; Feireisl, Eduard; Jai, M.; Petrov, A.

2018-01-01

Roč. 28, č. 4 (2018), s. 697-732 ISSN 0218-2025 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible fluids * stationary Navier-Stokes equations * thin films Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 2.860, year: 2016 https://www.worldscientific.com/doi/abs/10.1142/S0218202518500185

Towards an ideal preconditioner for linearized Navier-Stokes problems

Energy Technology Data Exchange (ETDEWEB)

Murphy, M.F. [Univ. of Bristol (United Kingdom)

1996-12-31

Discretizing certain linearizations of the steady-state Navier-Stokes equations gives rise to nonsymmetric linear systems with indefinite symmetric part. We show that for such systems there exists a block diagonal preconditioner which gives convergence in three GMRES steps, independent of the mesh size and viscosity parameter (Reynolds number). While this {open_quotes}ideal{close_quotes} preconditioner is too expensive to be used in practice, it provides a useful insight into the problem. We then consider various approximations to the ideal preconditioner, and describe the eigenvalues of the preconditioned systems. Finally, we compare these preconditioners numerically, and present our conclusions.

Possible and impossible solutions of the Navier-Stokes equations

International Nuclear Information System (INIS)

Irmay, S.

1998-01-01

Flow of isochoric constant-viscosity fluids obeys continuity and the Navier-Stokes equations. They are difficult to solve being nonlinear with a nonslip boundary condition at solid walls. Berker presented many solutions, but some of them, e.g. irrotational velocity, contradict the repulsion condition. Radial flow, possible between two nonparallel planes, is shown to be impossible in a cone, though an approximate solution exists. Parallel (equidistant) streamlines are possible only if rectilinear, concentric or coaxial circles, or helices of equal inclination on coaxial cylinders. Two-way flows resemble ideal and Stokes flows. The author presents some spatial jets impacting on a fixed or parallelly moving boundary. A general unsteady spatial solution near a plane boundary is expressed as power series of z, distance from the wall, which shows most boundary layer solutions to be valid only up to z 2 terms. Uniform steady-state flow at a constant piezo metric gradient in the x-direction, between nonparallel planes, has a definite solution only up to second-order terms in (y,z), due to undefined boundary condition at ∞. Acceleration averaged over time gives insight into the properties of pseudoturbulent or chaotic (turbulent) flows. Turbulent shear is redefined and Reynolds (turbulent) stresses loose their meaning

From Petrov-Einstein to Navier-Stokes

Science.gov (United States)

Lysov, Vyacheslav

The fluid/gravity correspondence relates solutions of the incompressible Navier-Stokes equation to metrics which solve the Einstein equations. We propose propose two possible approaches to establish this correspondence: perturbative expansion for shear modes and large mean curvature expansion for algebraically special metrics. We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in p+1 dimensions, there is an associated "dual" solution of the vacuum Einstein equations in p+2 dimensions. The dual geometry has an intrinsically flat time-like boundary segment whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a "near-horizon" limit in which hypersurface becomes highly accelerated. The near-horizon expansion in gravity is shown to be mathematically equivalent to the hydrodynamic expansion in fluid dynamics, and the Einstein equation reduces to the incompressible Navier-Stokes equation. It is shown that imposing a Petrov type I condition on the hypersurface geometry reduces the degrees of freedom in the extrinsic curvature to those of a fluid. Moreover, expanding around a limit in which the mean curvature of the embedding diverges, the leading-order Einstein constraint equations on hypersurface are shown to reduce to the non-linear incompressible Navier-Stokes equation for a fluid moving in hypersurface. We extend the fluid/gravity correspondence to include the magnetohydrodynamics/gravity correspondence, which translates solutions of the equations of magnetohydrodynamics (describing charged fluids) into geometries that satisfy the Einstein-Maxwell equations. We present an explicit example of this new correspondence in the context of flat Minkowski space. We show that a perturbative deformation of the Rindler wedge satisfies the Einstein-Maxwell equations provided that the parameters appearing in the expansion, which we interpret as fluid fields, satisfy the

The numerical solution of the Navier-Stokes equations for laminar incompressible flow past a paraboloid of revolution

NARCIS (Netherlands)

Veldman, A.E.P.

1973-01-01

A numerical method is presented for the solution of the Navier-Stokes equations for flow past a paraboloid of revolution. The flow field has been computed for a large range of Reynolds numbers. Results are presented for the skinfriction and the pressure together with their respective drag

Mesh Generation and Adaption for High Reynolds Number RANS Computations, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — This proposal offers to provide NASA with an automatic mesh generator for the simulation of aerodynamic flows using Reynolds-Averages Navier-Stokes (RANS) models....

Mesh Generation and Adaption for High Reynolds Number RANS Computations, Phase II

Data.gov (United States)

National Aeronautics and Space Administration — This proposal offers to provide NASA with an automatic mesh generator for the simulation of aerodynamic flows using Reynolds-Averages Navier-Stokes (RANS) models....

Boundary Shape Control of the Navier-Stokes Equations and Applications

Institute of Scientific and Technical Information of China (English)

Kaitai LI; Jian SU; Aixiang HUANG

2010-01-01

In this paper,the geometrical design for the blade's surface(s)in an impeller or for the profile of an aircraft,is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations.The objective function is the sum of a global dissipative function and the power of the fluid.The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations.The Euler-Lagrange equations of the optimal control problem are derived,which are an elliptic boundary value system of fourth order,coupled with the Navier-Stokes equations.The authors also prove the existence of the solution of the optimal control problem,the existence of the solution of the Navier-Stokes equations with mixed boundary conditions,the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the G(a)teaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary.

Strong plasma shock structures based on the Navier--Stokes equations

International Nuclear Information System (INIS)

Abe, K.

1975-01-01

The structure of a plasma collisional shock wave is examined on the basis of the Navier--Stokes equations and simultaneously on the basis of the Fokker--Planck equation. The resultant structures are compared to check the validity of the Navier--Stokes equations applied to the structures of strong shock waves. The Navier--Stokes equations give quite correct structures for weak shock waves. For the strong shock waves, the detailed structures obtained from the Navier--Stokes equations differ from the results of the Fokker--Planck equation, but the shock thicknesses of the two shock waves are in relatively close agreement

Near wake Reynolds-averaged Navier–Stokes predictions of the wake behind the MEXICO rotor in axial and yawed flow conditions

DEFF Research Database (Denmark)

Sørensen, Niels N.; Bechmann, Andreas; Réthoré, Pierre-Elouan

2014-01-01

In the present paper, Reynolds-averaged Navier–Stokes predictions of the flow field around the MEXICO rotor in yawed conditions are compared with measurements. The paper illustrates the high degree of qualitative and quantitative agreement that can be obtained for this highly unsteady flow...

Tip loss correction for actuator / Navier Stokes computations

DEFF Research Database (Denmark)

Shen, Wen Zhong; Sørensen, Jens Nørkær; Mikkelsen, Robert Flemming

2004-01-01

The new tip loss correction, initially developed for ID BEM computations [1], is now extended to 2D Actuator Disc / Navier-Stokes (AD/NS) computations and 3D Actuator Line / Navier-Stokes (AL/NS) computations. As shown in the paper, the tip loss correction is an important and necessary step...

On full-tensor permeabilities of porous media from numerical solutions of the Navier-Stokes equation

KAUST Repository

Wang, Y.; Sun, S.; Yu, B.

2013-01-01

A numerical method is proposed to compute full-tensor permeability of porous media without artificial simplification. Navier-Stokes (N-S) equation and Darcy's law are combined to design these numerical experiments. This method can successfully detect the permeability values in principle directions of the porous media and the anisotropic degrees. It is found that the same configuration of porous media may possess isotropic features at lower Reynolds numbers while manifesting anisotropic features at higher Reynolds numbers due to the nonlinearity from convection. Anisotropy becomes pronounced especially when convection is dominant. 2013 Yi Wang et al.

Global solubility of the three-dimensional Navier-Stokes equations with uniformly large initial vorticity

International Nuclear Information System (INIS)

Makhalov, A S; Nikolaenko, V P

2003-01-01

This paper is a survey of results concerning the three-dimensional Navier-Stokes and Euler equations with initial data characterized by uniformly large vorticity. The existence of regular solutions of the three-dimensional Navier-Stokes equations on an unbounded time interval is proved for large initial data both in R 3 and in bounded cylindrical domains. Moreover, the existence of smooth solutions on large finite time intervals is established for the three-dimensional Euler equations. These results are obtained without additional assumptions on the behaviour of solutions for t>0. Any smooth solution is not close to any two-dimensional manifold. Our approach is based on the computation of singular limits of rapidly oscillating operators, non-linear averaging, and a consideration of the mutual absorption of non-linear oscillations of the vorticity field. The use of resonance conditions, methods from the theory of small divisors, and non-linear averaging of almost periodic functions leads to the limit resonant Navier-Stokes equations. Global solubility of these equations is proved without any conditions on the three-dimensional initial data. The global regularity of weak solutions of three-dimensional Navier-Stokes equations with uniformly large vorticity at t=0 is proved by using the regularity of weak solutions and the strong convergence

Solutions of Navier-Stokes Equation with Coriolis Force

Directory of Open Access Journals (Sweden)

Sunggeun Lee

2017-01-01

Full Text Available We investigate the Navier-Stokes equation in the presence of Coriolis force in this article. First, the vortex equation with the Coriolis effect is discussed. It turns out that the vorticity can be generated due to a rotation coming from the Coriolis effect, Ω. In both steady state and two-dimensional flow, the vorticity vector ω gets shifted by the amount of -2Ω. Second, we consider the specific expression of the velocity vector of the Navier-Stokes equation in two dimensions. For the two-dimensional potential flow v→=∇→ϕ, the equation satisfied by ϕ is independent of Ω. The remaining Navier-Stokes equation reduces to the nonlinear partial differential equations with respect to the velocity and the corresponding exact solution is obtained. Finally, the steady convective diffusion equation is considered for the concentration c and can be solved with the help of Navier-Stokes equation for two-dimensional potential flow. The convective diffusion equation can be solved in three dimensions with a simple choice of c.

Incompressible Navier-Stokes equations. Theory and practice

Energy Technology Data Exchange (ETDEWEB)

Gjesdal, T.

1996-12-31

This paper contains notes from a seminar presented at the Dept. of Mathematics in the University of Bergen, Norway, Oct. 1996. It first introduces the theory of existence and uniqueness of solutions to the incompressible Navier-Stokes equation and defines a well-posed initial-boundary value problem. It then discusses different methods for solving numerically the Navier-Stokes equations in velocity-pressure formulation. The emphasis is on pressure correction methods. 19 refs.

Hybrid Large-Eddy/Reynolds-Averaged Simulation of a Supersonic Cavity Using VULCAN

Science.gov (United States)

Quinlan, Jesse; McDaniel, James; Baurle, Robert A.

2013-01-01

Simulations of a supersonic recessed-cavity flow are performed using a hybrid large-eddy/Reynolds-averaged simulation approach utilizing an inflow turbulence recycling procedure and hybridized inviscid flux scheme. Calorically perfect air enters a three-dimensional domain at a free stream Mach number of 2.92. Simulations are performed to assess grid sensitivity of the solution, efficacy of the turbulence recycling, and the effect of the shock sensor used with the hybridized inviscid flux scheme. Analysis of the turbulent boundary layer upstream of the rearward-facing step for each case indicates excellent agreement with theoretical predictions. Mean velocity and pressure results are compared to Reynolds-averaged simulations and experimental data for each case and indicate good agreement on the finest grid. Simulations are repeated on a coarsened grid, and results indicate strong grid density sensitivity. Simulations are performed with and without inflow turbulence recycling on the coarse grid to isolate the effect of the recycling procedure, which is demonstrably critical to capturing the relevant shear layer dynamics. Shock sensor formulations of Ducros and Larsson are found to predict mean flow statistics equally well.

Development of the Glenn-HT Computer Code to Enable Time-Filtered Navier-Stokes (TFNS) Simulations and Application to Film Cooling on a Flat Plate Through Long Cooling Tubes

Science.gov (United States)

Ameri, Ali; Shyam, Vikram; Rigby, David; Poinsatte, Philip; Thurman, Douglas; Steinthorsson, Erlendur

2014-01-01

Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations which are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminarturbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes which take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-HT code and applied to film cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30 holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and four blowing ratios of 0.5, 1.0, 1.5 and 2.0 are shown. Flow features under those conditions are also described.

Hybrid Reynolds-Averaged/Large Eddy Simulation of the Flow in a Model SCRamjet Cavity Flameholder

Science.gov (United States)

Baurle, R. A.

2016-01-01

Steady-state and scale-resolving simulations have been performed for flow in and around a model scramjet combustor flameholder. Experimental data available for this configuration include velocity statistics obtained from particle image velocimetry. Several turbulence models were used for the steady-state Reynolds-averaged simulations which included both linear and non-linear eddy viscosity models. The scale-resolving simulations used a hybrid Reynolds-averaged/large eddy simulation strategy that is designed to be a large eddy simulation everywhere except in the inner portion (log layer and below) of the boundary layer. Hence, this formulation can be regarded as a wall-modeled large eddy simulation. This e ort was undertaken to not only assess the performance of the hybrid Reynolds-averaged / large eddy simulation modeling approach in a flowfield of interest to the scramjet research community, but to also begin to understand how this capability can best be used to augment standard Reynolds-averaged simulations. The numerical errors were quantified for the steady-state simulations, and at least qualitatively assessed for the scale-resolving simulations prior to making any claims of predictive accuracy relative to the measurements. The steady-state Reynolds-averaged results displayed a high degree of variability when comparing the flameholder fuel distributions obtained from each turbulence model. This prompted the consideration of applying the higher-fidelity scale-resolving simulations as a surrogate "truth" model to calibrate the Reynolds-averaged closures in a non-reacting setting prior to their use for the combusting simulations. In general, the Reynolds-averaged velocity profile predictions at the lowest fueling level matched the particle imaging measurements almost as well as was observed for the non-reacting condition. However, the velocity field predictions proved to be more sensitive to the flameholder fueling rate than was indicated in the measurements.

On full-tensor permeabilities of porous media from numerical solutions of the Navier-Stokes equation

KAUST Repository

Wang, Y.

2013-01-01

A numerical method is proposed to compute full-tensor permeability of porous media without artificial simplification. Navier-Stokes (N-S) equation and Darcy\\'s law are combined to design these numerical experiments. This method can successfully detect the permeability values in principle directions of the porous media and the anisotropic degrees. It is found that the same configuration of porous media may possess isotropic features at lower Reynolds numbers while manifesting anisotropic features at higher Reynolds numbers due to the nonlinearity from convection. Anisotropy becomes pronounced especially when convection is dominant. 2013 Yi Wang et al.

Multitasking a three-dimensional Navier-Stokes algorithm on the Cray-2

Science.gov (United States)

Swisshelm, Julie M.

1989-01-01

A three-dimensional computational aerodynamics algorithm has been multitasked for efficient parallel execution on the Cray-2. It provides a means for examining the multitasking performance of a complete CFD application code. An embedded zonal multigrid scheme is used to solve the Reynolds-averaged Navier-Stokes equations for an internal flow model problem. The explicit nature of each component of the method allows a spatial partitioning of the computational domain to achieve a well-balanced task load for MIMD computers with vector-processing capability. Experiments have been conducted with both two- and three-dimensional multitasked cases. The best speedup attained by an individual task group was 3.54 on four processors of the Cray-2, while the entire solver yielded a speedup of 2.67 on four processors for the three-dimensional case. The multiprocessing efficiency of various types of computational tasks is examined, performance on two Cray-2s with different memory access speeds is compared, and extrapolation to larger problems is discussed.

Optimal control of compressible Navier-Stokes equations

International Nuclear Information System (INIS)

Ito, K.; Ravindran, S.S.

1994-01-01

Optimal control for the viscous incompressible flows, which are governed by incompressible Navier-Stokes equations, has been the subject of extensive study in recent years, see, e.g., [AT], [GHS], [IR], and [S]. In this paper we consider the optimal control of compressible isentropic Navier-Stokes equations. We develop the weak variational formulation and discuss the existence and necessary optimality condition characterizing the optimal control. A numerical method based on the mixed-finite element method is also discussed to compute the control and numerical results are presented

Implications of Navier-Stokes turbulence theory for plasma turbulence

International Nuclear Information System (INIS)

Montgomery, David

1977-01-01

A brief discussion of Navier-Stokes turbulence theory is given with particular reference to the two dimensional case. The MHD turbulence is introduced with possible applications of techniques developed in Navier-Stokes theory. Turbulence in Vlasov plasma is also discussed from the point of view of the ''direct interaction approximation'' (DIA). (A.K.)

Exact solutions of the Navier-Stokes equations generalized for flow in porous media

Science.gov (United States)

Daly, Edoardo; Basser, Hossein; Rudman, Murray

2018-05-01

Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.

Modeling shock waves in an ideal gas: Going beyond the Navier-Stokes level

International Nuclear Information System (INIS)

Holian, B.L.; Patterson, C.W.; Mareschal, M.; Salomons, E.

1993-01-01

We model a shock wave in an ideal gas by solving a modified version of the compressible Navier-Stokes equations of hydrodynamics, where, following an earlier conjecture by Holian [Phys. Rev. A 37, 2562 (1988)], we use the temperature in the direction of shock propagation T xx , rather than the average temperature T=(T xx +T yy +T zz )/3, in the evaluation of the linear transport coefficients. The results are found to agree much better with the molecular-dynamics simulations of Salomons and Mareschal [Phys. Rev. Lett. 69, 269 (1992)] than standard Navier-Stokes theory

Self-similarity in incompressible Navier-Stokes equations.

Science.gov (United States)

Ercan, Ali; Kavvas, M Levent

2015-12-01

The self-similarity conditions of the 3-dimensional (3D) incompressible Navier-Stokes equations are obtained by utilizing one-parameter Lie group of point scaling transformations. It is found that the scaling exponents of length dimensions in i = 1, 2, 3 coordinates in 3-dimensions are not arbitrary but equal for the self-similarity of 3D incompressible Navier-Stokes equations. It is also shown that the self-similarity in this particular flow process can be achieved in different time and space scales when the viscosity of the fluid is also scaled in addition to other flow variables. In other words, the self-similarity of Navier-Stokes equations is achievable under different fluid environments in the same or different gravity conditions. Self-similarity criteria due to initial and boundary conditions are also presented. Utilizing the proposed self-similarity conditions of the 3D hydrodynamic flow process, the value of a flow variable at a specified time and space can be scaled to a corresponding value in a self-similar domain at the corresponding time and space.

Development of the Glenn Heat-Transfer (Glenn-HT) Computer Code to Enable Time-Filtered Navier-Stokes (TFNS) Simulations and Application to Film Cooling on a Flat Plate Through Long Cooling Tubes

Science.gov (United States)

Ameri, Ali; Shyam, Vikram; Rigby, David; Poinsatte, Phillip; Thurman, Douglas; Steinthorsson, Erlendur

2014-01-01

Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations that are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminar/turbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes that take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-Heat-Transfer (Glenn-HT) code and applied to film-cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30deg holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and two blowing ratios of 0.5 and 1.0 are shown. Flow features under those conditions are also described.

Development of the Glenn-Heat-Transfer (Glenn-HT) Computer Code to Enable Time-Filtered Navier Stokes (TFNS) Simulations and Application to Film Cooling on a Flat Plate Through Long Cooling Tubes

Science.gov (United States)

Ameri, Ali A.; Shyam, Vikram; Rigby, David; Poinsatte, Phillip; Thurman, Douglas; Steinthorsson, Erlendur

2014-01-01

Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations that are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminar/turbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes that take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-Heat-Transfer (Glenn-HT) code and applied to film-cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30deg holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and two blowing ratios of 0.5 and 1.0 are shown. Flow features under those conditions are also described.

Model Reduction Based on Proper Generalized Decomposition for the Stochastic Steady Incompressible Navier--Stokes Equations

KAUST Repository

Tamellini, L.; Le Maî tre, O.; Nouy, A.

2014-01-01

In this paper we consider a proper generalized decomposition method to solve the steady incompressible Navier-Stokes equations with random Reynolds number and forcing term. The aim of such a technique is to compute a low-cost reduced basis approximation of the full stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproblems, is proposed for an efficient greedy construction of a deterministic reduced basis approximation. This algorithm decouples the computation of the deterministic and stochastic components of the solution, thus allowing reuse of preexisting deterministic Navier-Stokes solvers. It has the remarkable property of only requiring the solution of m uncoupled deterministic problems for the construction of an m-dimensional reduced basis rather than M coupled problems of the full stochastic Galerkin approximation space, with m l M (up to one order of magnitudefor the problem at hand in this work). © 2014 Society for Industrial and Applied Mathematics.

Navier-Stokes prediction of a delta wing in roll with vortex breakdown

Science.gov (United States)

Chaderjian, Neal M.; Schiff, Lewis B.

1993-01-01

The three-dimensional, Reynolds-averaged, Navier-Stokes (RANS) equations are used to numerically simulate vortical flow about a 65 degree sweep delta wing. Subsonic turbulent flow computations are presented for this delta wing at 30 degrees angle of attack and static roll angles up to 42 degrees. This work is part of an on going effort to validate the RANS approach for predicting high-incidence vortical flows, with the eventual application to wing rock. The flow is unsteady and includes spiral-type vortex breakdown. The breakdown positions, mean surface pressures, rolling moments, normal forces, and streamwise center-of-pressure locations compare reasonably well with experiment. In some cases, the primary vortex suction peaks are significantly underpredicted due to grid coarseness. Nevertheless, the computations are able to predict the same nonlinear variation of rolling moment with roll angle that appeared in the experiment. This nonlinearity includes regions of local static roll instability, which is attributed to vortex breakdown.

On Critical Spaces for the Navier-Stokes Equations

Science.gov (United States)

Prüss, Jan; Wilke, Mathias

2017-10-01

The abstract theory of critical spaces developed in Prüss and Wilke (J Evol Equ, 2017. doi: 10.1007/s00028-017-0382-6), Prüss et al. (Critical spaces for quasilinear parabolic evolution equations and applications, 2017) is applied to the Navier-Stokes equations in bounded domains with Navier boundary conditions as well as no-slip conditions. Our approach unifies, simplifies and extends existing work in the L_p -L_q setting, considerably. As an essential step, it is shown that the strong and weak Stokes operators with Navier conditions admit an H^∞-calculus with H^∞-angle 0, and the real and complex interpolation spaces of these operators are identified.

Hybrid RANS/LES method for wind flow over complex terrain

DEFF Research Database (Denmark)

Bechmann, Andreas; Sørensen, Niels N.

2010-01-01

for flows at high Reynolds numbers. To reduce the computational cost of traditional LES, a hybrid method is proposed in which the near-wall eddies are modelled in a Reynolds-averaged sense. Close to walls, the flow is treated with the Reynolds-averaged Navier-Stokes (RANS) equations (unsteady RANS...... rough walls. Previous attempts of combining RANS and LES has resulted in unphysical transition regions between the two layers, but the present work improves this region by using a stochastic backscatter model. To demonstrate the ability of the proposed hybrid method, simulations are presented for wind...... the turbulent kinetic energy, whereas the new method captures the high turbulence levels well but underestimates the mean velocity. The presented results are for a relative mild configuration of complex terrain, but the proposed method can also be used for highly complex terrain where the benefits of the new...

About Navier-Stokes Equation in the Theory of Convective Heat Transfer

Science.gov (United States)

Davidzon, M. Y.

2017-10-01

A system of differential equations (Navier-Stokes, continuity, heat conductivity) is used to solve convective heat transfer problems. While solving Navier-Stokes equation, it is usually assumed that tangent stress is proportional to the velocity gradient. This assumption is valid with a small velocity gradient, for example, near an axis of the channel, but velocity gradient can be very large near the channel wall. Our paper shows that if we accept power law instead of linear law for tangential stress, then the velocity profile for creeping, laminar, and turbulent flow in the channel can be calculated without using Navier-Stokes equation. Also, in this case Navier-Stokes equation itself changes: the coefficient of dynamic viscosity changes its value from normal (in case of the creeping flow) to tending to infinity (in case of the well-developed turbulent flow).

Incompressible limit of compressible Navier-Stokes equations

International Nuclear Information System (INIS)

Bessaih, H.

1994-01-01

In this paper we study the system which describes the motion of compressible viscous fluid in a bounded domain Ω of R 3 . When we introduce a parameter λ, that is the inverse of the Mach number, we prove, under small initial data and external force (for barotropic flows), that the solution of Navier-Stokes equations is the incompressible limit of the solution of compressible Navier-Stokes equations, as the Mach number becomes small. For this, we show the existence of a solution verifying estimates independent of λ. Compactness argument allow us to pass to the limit on λ in the nonlinear terms. (author). 17 refs

Cavitation Modeling in Euler and Navier-Stokes Codes

Science.gov (United States)

Deshpande, Manish; Feng, Jinzhang; Merkle, Charles L.

1993-01-01

Many previous researchers have modeled sheet cavitation by means of a constant pressure solution in the cavity region coupled with a velocity potential formulation for the outer flow. The present paper discusses the issues involved in extending these cavitation models to Euler or Navier-Stokes codes. The approach taken is to start from a velocity potential model to ensure our results are compatible with those of previous researchers and available experimental data, and then to implement this model in both Euler and Navier-Stokes codes. The model is then augmented in the Navier-Stokes code by the inclusion of the energy equation which allows the effect of subcooling in the vicinity of the cavity interface to be modeled to take into account the experimentally observed reduction in cavity pressures that occurs in cryogenic fluids such as liquid hydrogen. Although our goal is to assess the practicality of implementing these cavitation models in existing three-dimensional, turbomachinery codes, the emphasis in the present paper will center on two-dimensional computations, most specifically isolated airfoils and cascades. Comparisons between velocity potential, Euler and Navier-Stokes implementations indicate they all produce consistent predictions. Comparisons with experimental results also indicate that the predictions are qualitatively correct and give a reasonable first estimate of sheet cavitation effects in both cryogenic and non-cryogenic fluids. The impact on CPU time and the code modifications required suggests that these models are appropriate for incorporation in current generation turbomachinery codes.

Quasineutral limit for the quantum Navier-Stokes-Poisson equation

OpenAIRE

Li, Min; Pu, Xueke; Wang, Shu

2015-01-01

In this paper, we study the quasineutral limit and asymptotic behaviors for the quantum Navier-Stokes-Possion equation. We apply a formal expansion according to Debye length and derive the neutral incompressible Navier-Stokes equation. To establish this limit mathematically rigorously, we derive uniform (in Debye length) estimates for the remainders, for well-prepared initial data. It is demonstrated that the quantum effect do play important roles in the estimates and the norm introduced depe...

Impact of the inherent separation of scales in the Navier-Stokes- alphabeta equations.

Science.gov (United States)

Kim, Tae-Yeon; Cassiani, Massimo; Albertson, John D; Dolbow, John E; Fried, Eliot; Gurtin, Morton E

2009-04-01

We study the effect of the length scales alpha and beta in the Navier-Stokes- alphabeta equations on the energy spectrum and the alignment between the vorticity and the eigenvectors of the stretching tensor in three-dimensional homogeneous and isotropic turbulent flows in a periodic cubic domain, including the limiting cases of the Navier-Stokes- alpha and Navier-Stokes equations. A significant increase in the accuracy of the energy spectrum at large wave numbers arises for betaNavier-Stokes- alphabeta equations also improve as beta decreases away from alpha . However, optimal choices for alpha and beta depend not only on the problem of interest but also on the grid resolution.

Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation.

Science.gov (United States)

Saveliev, V L; Gorokhovski, M A

2005-07-01

On the basis of the Euler equation and its symmetry properties, this paper proposes a model of stationary homogeneous developed turbulence. A regularized averaging formula for the product of two fields is obtained. An equation for the averaged turbulent velocity field is derived from the Navier-Stokes equation by renormalization-group transformation.

p-Euler equations and p-Navier-Stokes equations

Science.gov (United States)

Li, Lei; Liu, Jian-Guo

2018-04-01

We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

Discrete adjoint of fractional step Navier-Stokes solver in generalized coordinates

Science.gov (United States)

Wang, Mengze; Mons, Vincent; Zaki, Tamer

2017-11-01

Optimization and control in transitional and turbulent flows require evaluation of gradients of the flow state with respect to the problem parameters. Using adjoint approaches, these high-dimensional gradients can be evaluated with a similar computational cost as the forward Navier-Stokes simulations. The adjoint algorithm can be obtained by discretizing the continuous adjoint Navier-Stokes equations or by deriving the adjoint to the discretized Navier-Stokes equations directly. The latter algorithm is necessary when the forward-adjoint relations must be satisfied to machine precision. In this work, our forward model is the fractional step solution to the Navier-Stokes equations in generalized coordinates, proposed by Rosenfeld, Kwak & Vinokur. We derive the corresponding discrete adjoint equations. We also demonstrate the accuracy of the combined forward-adjoint model, and its application to unsteady wall-bounded flows. This work has been partially funded by the Office of Naval Research (Grant N00014-16-1-2542).

Generalized Stokes eignefunctions: a new trial basis for the solution of incompressible Navier-Stokes equations

International Nuclear Information System (INIS)

Batcho, P.F.; Karniadakis, G.E.

1994-01-01

The present study focuses on the solution of the incompressible Navier-Stokes equations in general, non-separable domains, and employs a Galerkin projection of divergence-free vector functions as a trail basis. This basis is obtained from the solution of a generalized constrained Stokes eigen-problem in the domain of interest. Faster convergence can be achieved by constructing a singular Stokes eigen-problem in which the Stokes operator is modified to include a variable coefficient which vanishes at the domain boundaries. The convergence properties of such functions are advantageous in a least squares sense and are shown to produce significantly better approximations to the solution of the Navier-Stokes equations in post-critical states where unsteadiness characterizes the flowfield. Solutions for the eigen-systems are efficiently accomplished using a combined Lanczos-Uzawa algorithm and spectral element discretizations. Results are presented for different simulations using these global spectral trial basis on non-separable and multiply-connected domains. It is confirmed that faster convergence is obtained using the singular eigen-expansions in approximating stationary Navier-Stokes solutions in general domains. It is also shown that 100-mode expansions of time-dependent solutions based on the singular Stokes eigenfunctions are sufficient to accurately predict the dynamics of flows in such domains, including Hopf bifurcations, intermittency, and details of flow structures

Robust Navier-Stokes method for predicting unsteady flowfield and aerodynamic characteristics of helicopter rotor

Directory of Open Access Journals (Sweden)

Qijun ZHAO

2018-02-01

Full Text Available A robust unsteady rotor flowfield solver CLORNS code is established to predict the complex unsteady aerodynamic characteristics of rotor flowfield. In order to handle the difficult problem about grid generation around rotor with complex aerodynamic shape in this CFD code, a parameterized grid generated method is established, and the moving-embedded grids are constructed by several proposed universal methods. In this work, the unsteady Reynolds-Averaged Navier-Stokes (RANS equations with Spalart-Allmaras are selected as the governing equations to predict the unsteady flowfield of helicopter rotor. The discretization of convective fluxes is accomplished by employing the second-order central difference scheme, third-order MUSCL-Roe scheme, and fifth-order WENO-Roe scheme. Aimed at simulating the unsteady aerodynamic characteristics of helicopter rotor, the dual-time scheme with implicit LU-SGS scheme is employed to accomplish the temporal discretization. In order to improve the computational efficiency of hole-cells and donor elements searching of the moving-embedded grid technology, the “disturbance diffraction method” and “minimum distance scheme of donor elements method” are established in this work. To improve the computational efficiency, Message Passing Interface (MPI parallel method based on subdivision of grid, local preconditioning method and Full Approximation Storage (FAS multi-grid method are combined in this code. By comparison of the numerical results simulated by CLORNS code with test data, it is illustrated that the present code could simulate the aerodynamic loads and aerodynamic noise characteristics of helicopter rotor accurately. Keywords: Aerodynamic characteristics, Helicopter rotor, Moving-embedded grid, Navier-Stokes equations, Upwind schemes

The Variation of Slat Noise with Mach and Reynolds Numbers

Science.gov (United States)

Lockard, David P.; Choudhari, Meelan M.

2011-01-01

The slat noise from the 30P30N high-lift system has been computed using a computational fluid dynamics code in conjunction with a Ffowcs Williams-Hawkings solver. By varying the Mach number from 0.13 to 0.25, the noise was found to vary roughly with the 5th power of the speed. Slight changes in the behavior with directivity angle could easily account for the different speed dependencies reported in the literature. Varying the Reynolds number from 1.4 to 2.4 million resulted in almost no differences, and primarily served to demonstrate the repeatability of the results. However, changing the underlying hybrid Reynolds-averaged-Navier-Stokes/Large-Eddy-Simulation turbulence model significantly altered the mean flow because of changes in the flap separation. However, the general trends observed in both the acoustics and near-field fluctuations were similar for both models.

Length scales for the Navier-Stokes equations on a rotating sphere

International Nuclear Information System (INIS)

Kyrychko, Yuliya N.; Bartuccelli, Michele V.

2004-01-01

In this Letter we obtain the dissipative length scale for the Navier-Stokes equations on a two-dimensional rotating sphere S 2 . This system is a fundamental model of the large scale atmospheric dynamics. Using the equations of motion in their vorticity form, we construct the ladder inequalities from which a set of time-averaged length scales is obtained

Reproductive solutions for the g-Navier-Stokes and g-Kelvin-Voight equations

Directory of Open Access Journals (Sweden)

Luis Friz

2016-01-01

Full Text Available This article presents the existence of reproductive solutions of g-Navier-Stokes and g-Kelvin-Voight equations. In this way, for weak solutions, we reach basically the same result as for classic Navier-Stokes equations.

On the control of the chaotic attractors of the 2-d Navier-Stokes equations.

Science.gov (United States)

Smaoui, Nejib; Zribi, Mohamed

2017-03-01

The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, R e . Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.

A composite velocity procedure for the compressible Navier-Stokes equations

Science.gov (United States)

Khosla, P. K.; Rubin, S. G.

1982-01-01

A new boundary-layer relaxation procedure is presented. In the spirit of the theory of matched asymptotic expansions, a multiplicative composite of the appropriate velocity representations for the inviscid and viscous regions is prescribed. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli relation for the pressure, while the continuity equation reduces to the familiar compressible potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary-layers; although, the full Navier-Stokes equations are considered here. Laminar flow calculations for the subsonic flow over an axisymmetric boattail simulator geometry are presented for a variety of Reynolds and Mach numbers. A strongly implicit solution method is applied for the coupled velocity components.

Application of an upwind Navier-Stokes code to two-dimensional transonic airfoil flow

International Nuclear Information System (INIS)

Rumsey, C.L.; Thomas, J.L.; Anderson, W.K.; Taylor, S.L.

1987-01-01

An upwind-biased implicit approximate factorization Navier-Stokes algorithm is applied to a variety of steady transonic airfoil cases, using the NACA 0012, RAE 2822, and Jones supercritical airfoils. The thin-layer form of the compressible Navier-Stokes equations is used. Both the CYBER 205 and CRAY 2 supercomputers are utilized, with average computational speeds of about 18 and 16 microsec/gridpoint/iteration, respectively. Lift curves, drag polars, and variations in drag coefficient with Mach number are determined for the NACA 0012 and Jones supercritical airfoils. Also, several cases are computed for comparison with experiment. The effect of grid density and grid extent on a typical turbulent airfoil solution is shown. An algebraic eddy-viscosity turbulence model is used for all of the computations. 10 references

An analytical solution of the Navier-Stokes equation for internal flows

International Nuclear Information System (INIS)

Lyberg, Mats D; Tryggeson, Henrik

2007-01-01

This paper derives a solution to the Navier-Stokes equation by considering vorticity generated at system boundaries. The result is an explicit expression for the velocity. The Navier-Stokes equation is reformulated as a divergence and integrated, giving a tensor equation that splits into a symmetric and a skew-symmetric part. One equation gives an algebraic system of quadratic equations involving velocity components. A system of nonlinear partial differential equations is reduced to algebra. The velocity is then explicitly calculated and shown to depend on boundary conditions only. This removes the need to solve the Navier-Stokes equation by a 3D numerical computation, replacing it by computation of 2D surface integrals over the boundary. (fast track communication)

Incompressible limit of the degenerate quantum compressible Navier-Stokes equations with general initial data

Science.gov (United States)

Kwon, Young-Sam; Li, Fucai

2018-03-01

In this paper we study the incompressible limit of the degenerate quantum compressible Navier-Stokes equations in a periodic domain T3 and the whole space R3 with general initial data. In the periodic case, by applying the refined relative entropy method and carrying out the detailed analysis on the oscillations of velocity, we prove rigorously that the gradient part of the weak solutions (velocity) of the degenerate quantum compressible Navier-Stokes equations converge to the strong solution of the incompressible Navier-Stokes equations. Our results improve considerably the ones obtained by Yang, Ju and Yang [25] where only the well-prepared initial data case is considered. While for the whole space case, thanks to the Strichartz's estimates of linear wave equations, we can obtain the convergence of the weak solutions of the degenerate quantum compressible Navier-Stokes equations to the strong solution of the incompressible Navier-Stokes/Euler equations with a linear damping term. Moreover, the convergence rates are also given.

On Coupled System of Navier-Stokes Equations and Temperature

African Journals Online (AJOL)

Dr. Anthony Peter

ABSTRACT. This paper deals with the coupled system of Navier-Stokes equations and temperature (Thermohydraulics) in a strip in the class of spatially non-decaying (infinite-energy) solutions belonging to the properly chosen uniformly local Sobolev spaces. The global well-posedness and dissipativity of the Navier- ...

A Discussion of Low Reynolds Number Flow for the Two-Dimensional Benchmark Test Case

DEFF Research Database (Denmark)

Weng, Miaocheng; Nielsen, Peter V.; Liu, Li

The use of CFD in ventilation research has arrived to a high level, but there are some conditions in the general CFD procedure which do not apply to all situations in the ventilation research. An example of this isthe turbulence models in Reynolds-averaged Navier-Stokes equations, i.e. (RANS...

On convergence of trajectory attractors of the 3D Navier-Stokes-α model as α approaches 0

International Nuclear Information System (INIS)

Vishik, M I; Chepyzhov, V V; Titi, E S

2007-01-01

We study the relations between the long-time dynamics of the Navier-Stokes-α model and the exact 3D Navier-Stokes system. We prove that bounded sets of solutions of the Navier-Stokes-α model converge to the trajectory attractor A 0 of the 3D Navier-Stokes system as the time approaches infinity and α approaches zero. In particular, we show that the trajectory attractor A α of the Navier-Stokes-α model converges to the trajectory attractor A 0 of the 3D Navier-Stokes system as α→0+. We also construct the minimal limit A min (subset or equal A 0 ) of the trajectory attractor A α as α→0+ and prove that the set A min is connected and strictly invariant. Bibliography: 35 titles.

Solutions to three-dimensional Navier-Stokes equations for incompressible fluids

Directory of Open Access Journals (Sweden)

Jorma Jormakka

2010-07-01

Full Text Available This article gives explicit solutions to the space-periodic Navier-Stokes problem with non-periodic pressure. These type of solutions are not unique and by using such solutions one can construct a periodic, smooth, divergence-free initial vector field allowing a space-periodic and time-bounded external force such that there exists a smooth solution to the 3-dimensional Navier-Stokes equations for incompressible fluid with those initial conditions, but the solution cannot be continued to the whole space.

Convergence acceleration of Navier-Stokes equation using adaptive wavelet method

International Nuclear Information System (INIS)

Kang, Hyung Min; Ghafoor, Imran; Lee, Do Hyung

2010-01-01

An efficient adaptive wavelet method is proposed for the enhancement of computational efficiency of the Navier-Stokes equations. The method is based on sparse point representation (SPR), which uses the wavelet decomposition and thresholding to obtain a sparsely distributed dataset. The threshold mechanism is modified in order to maintain the spatial accuracy of a conventional Navier-Stokes solver by adapting the threshold value to the order of spatial truncation error. The computational grid can be dynamically adapted to a transient solution to reflect local changes in the solution. The flux evaluation is then carried out only at the points of the adapted dataset, which reduces the computational effort and memory requirements. A stabilization technique is also implemented to avoid the additional numerical errors introduced by the threshold procedure. The numerical results of the adaptive wavelet method are compared with a conventional solver to validate the enhancement in computational efficiency of Navier-Stokes equations without the degeneration of the numerical accuracy of a conventional solver

Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions

Directory of Open Access Journals (Sweden)

Yuan Li

2013-01-01

Full Text Available This paper presents two-level iteration penalty finite element methods to approximate the solution of the Navier-Stokes equations with friction boundary conditions. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh size H in combining with solving a Stokes, Oseen, or linearized Navier-Stokes type variational inequality problem for Stokes, Oseen, or Newton iteration on a fine mesh with mesh size h. The error estimate obtained in this paper shows that if H, h, and ε can be chosen appropriately, then these two-level iteration penalty methods are of the same convergence orders as the usual one-level iteration penalty method.

A Study of Low-Reynolds Number Effects in Backward-Facing Step Flow Using Large Eddy Simulations

DEFF Research Database (Denmark)

Davidson, Lars; Nielsen, Peter V.

The flow in ventilated rooms is often not fully turbulent, but in some regions the flow can be laminar. Problems have been encountered when simulating this type of flow using RANS (Reynolds Averaged Navier-Stokes) methods. Restivo carried out experiment on the flow after a backward-facing step...

Approximate controllability of the Navier-Stokes system in unbounded domains

International Nuclear Information System (INIS)

Shorygin, P O

2003-01-01

The question of the approximate controllability for the 2- and the 3-dimensional Navier-Stokes system defined in the exterior of a bounded domain ω or in the entire space is studied. It is shown that one can find boundary controls or locally distributed controls (having support in a prescribed bounded domain) defined on the right-hand side of the system such that in prescribed time the solution of the Navier-Stokes system becomes arbitrarily close to an arbitrary prescribed divergence-free vector field

Moment realizability and the validity of the Navier - Stokes equations for rarefied gas dynamics

International Nuclear Information System (INIS)

Levermore, C.D.; Morokoff, W.J.; Nadiga, B.T.

1998-01-01

We present criteria for monitoring the validity of the Navier - Stokes approximation during the simulation of a rarefied gas. Our approach is based on an underlying kinetic formulation through which one can construct nondimensional non-negative definite matrices from moments of the molecular distribution. We then identify one such 3x3 matrix that can be evaluated intrinsically in the Navier - Stokes approximation. Our criteria are based on deviations of the eigenvalues of this matrix from their equilibrium value of unity. Not being tied to a particular benchmark problem, the resulting criteria are portable and may be applied to any Navier - Stokes simulation. We study its utility here by comparing stationary planar shock profiles computed using the Navier - Stokes equations with those computed using Monte Carlo simulations. copyright 1998 American Institute of Physics

Navier-Stokes Simulation of a Heavy Lift Slowed-Rotor Compound Helicopter Configuration

Science.gov (United States)

Allan, Brian G.; Jenkins, Luther N.; Yao, Chung-Sheng; Bartram, Scott M.; Hallissy, Jim B.; Harris, Jerome; Noonan, Kevin W.; Wong, Oliver D.; Jones, Henry E.; Malovrh, Brendon D.;

Analysis of regularized Navier-Stokes equations, 2

Science.gov (United States)

Ou, Yuh-Roung; Sritharan, S. S.

1989-01-01

A practically important regularization of the Navier-Stokes equations was analyzed. As a continuation of the previous work, the structure of the attractors characterizing the solutins was studied. Local as well as global invariant manifolds were found. Regularity properties of these manifolds are analyzed.

Analysis of compressible light dynamic stall flow at transitional Reynolds numbers

DEFF Research Database (Denmark)

Dyken, R.D. Van; Ekaterinaris, John A.; Chandrasekhara, M.S.

1996-01-01

Numerical and experimental results of steady and light dynamic stall flow over an oscillating NACA 0012 airfoil at a freestream Mach number of 0.3 and Reynolds number of 0.54 x 10(6) are compared, The experimental observation that dynamic stall is induced from the bursting of a laminar separation...... point is specified suitably and a simple transition length model is incorporated to determine the extent of the laminar separation bubble. The thin-layer approximations of compressible, Reynolds-averaged, Navier-Stokes equations are used for the numerical solution, with an implicit, upwind-biased, third...

Navier-Stokes-Fourier Equations A Rational Asymptotic Modelling Point of View

CERN Document Server

Zeytounian, Radyadour Kh

2012-01-01

This research monograph deals with a modeling theory of the system of Navier-Stokes-Fourier equations for a Newtonian fluid governing a compressible viscous and heat conducting flows. The main objective is threefold. First , to 'deconstruct' this Navier-Stokes-Fourier system in order to unify the puzzle of the various partial simplified approximate models used in Newtonian Classical Fluid Dynamics and this, first facet, have obviously a challenging approach and a very important pedagogic impact on the university education. The second facet of the main objective is to outline a rational consistent asymptotic/mathematical theory of the of  fluid flows modeling on the basis of a typical Navier-Stokes-Fourier  initial and boundary value problem. The third facet is devoted to an illustration of our rational asymptotic/mathematical modeling theory for various technological and geophysical stiff  problems from: aerodynamics, thermal and thermocapillary convections and also meteofluid dynamics.

A stable penalty method for the compressible Navier-Stokes equations: I. Open boundary conditions

DEFF Research Database (Denmark)

Hesthaven, Jan; Gottlieb, D.

1996-01-01

The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization...

Study of Tip-loss Using an Inverse 3D Navier-Stokes Method

DEFF Research Database (Denmark)

Mikkelsen, Robert; Sørensen, Jens Nørkær; Shen, Wen Zhong

2003-01-01

the 3D Navier-Stokes equations combined with the actuator line technique where blade loading is applied using an inverse method. The numerical simulations shows that the method captures the tip-correction when comparing with the theories of Prandtl and Goldstein, however, the accuracy of the obtained...... results reveal that further refinements still is needed. Keywords: Tip-loss; Actuator line; 3D Navier-Stokes methods....

On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation

International Nuclear Information System (INIS)

Kawashima, S.; Matsumara, A.; Nishida, T.

1979-01-01

The compressible and heat-conductive Navier-Stokes equation obtained as the second approximation of the formal Chapman-Enskog expansion is investigated on its relations to the original nonlinear Boltzmann equation and also to the incompressible Navier-Stokes equation. The solutions of the Boltzmann equation and the incompressible Navier-Stokes equation for small initial data are proved to be asymptotically equivalent (mod decay rate tsup(-5/4)) as t → + infinitely to that of the compressible Navier-Stokes equation for the corresponding initial data. (orig.) 891 HJ/orig. 892 MKO

Hydrodynamic potentials for the micropolar Navier-Stokes problem

International Nuclear Information System (INIS)

Martynenko, M.D.; Dimian, M.

1995-01-01

An integral representation of linear and angular velocities and pressure for the description of linear stationary flows of micropolar viscous liquid media is obtained, and on its basis hydrodynamic potentials for the micropolar Navier-Stokes problem are introduced

Integral transformation of the Navier-Stokes equations for laminar flow in channels of arbitrary two-dimensional geometry; Transformacao integral das equacoes de Navier-Stokes para escoamento laminar em canais de geometria bidimensional arbitraria

Energy Technology Data Exchange (ETDEWEB)

Perez Guerrero, Jesus Salvador

1995-12-31

Laminar developing flow in channels of arbitrary geometry was studied by solving the Navier-Stokes equations in the stream function-only formulation through the Generalized Integral Transform Technique (GITT). The stream function is expanded in an infinite system based on eigenfunctions obtained by considering solely the diffusive terms of the original formulation. The Navier-Stokes equations are transformed into an infinite system of ordinary differential equations, by using the transformation and inversion formulae. For computational purposes, the infinite series is truncated, according to an automatic error control procedure. The ordinary differential is solved through well-established scientific subroutines from widely available mathematical libraries. The classical problem of developing flow between parallel-plates is analysed first, as for both uniform and irrotational inlet conditions. The effect of truncating the duct length in the accuracy of the obtained solution is studied. A convergence analysis of the results obtained by the GITT is performed and compared with results obtained by finite difference and finite element methods, for different values of Reynolds number. The problem of flow over a backward-facing step then follows. Comparisons with experimental results in the literature indicate an excellent agreement. The numerical co-validation was established for a test case, and perfect agreement is reached against results considered as benchmarks in the recent literature. The results were shown to be physically more reasonable than others obtained by purely numerical methods, in particular for situations where three-dimensional effects are identified. Finally, a test problem for an irregular by shoped duct was studied and compared against results found in the literature, with good agreement and excellent convergence rates for the stream function field along the whole channel, for different values of Reynolds number. (author) 78 refs., 24 figs., 14 tabs.

Integral transformation of the Navier-Stokes equations for laminar flow in channels of arbitrary two-dimensional geometry; Transformacao integral das equacoes de Navier-Stokes para escoamento laminar em canais de geometria bidimensional arbitraria

Energy Technology Data Exchange (ETDEWEB)

Perez Guerrero, Jesus Salvador

1996-12-31

Laminar developing flow in channels of arbitrary geometry was studied by solving the Navier-Stokes equations in the stream function-only formulation through the Generalized Integral Transform Technique (GITT). The stream function is expanded in an infinite system based on eigenfunctions obtained by considering solely the diffusive terms of the original formulation. The Navier-Stokes equations are transformed into an infinite system of ordinary differential equations, by using the transformation and inversion formulae. For computational purposes, the infinite series is truncated, according to an automatic error control procedure. The ordinary differential is solved through well-established scientific subroutines from widely available mathematical libraries. The classical problem of developing flow between parallel-plates is analysed first, as for both uniform and irrotational inlet conditions. The effect of truncating the duct length in the accuracy of the obtained solution is studied. A convergence analysis of the results obtained by the GITT is performed and compared with results obtained by finite difference and finite element methods, for different values of Reynolds number. The problem of flow over a backward-facing step then follows. Comparisons with experimental results in the literature indicate an excellent agreement. The numerical co-validation was established for a test case, and perfect agreement is reached against results considered as benchmarks in the recent literature. The results were shown to be physically more reasonable than others obtained by purely numerical methods, in particular for situations where three-dimensional effects are identified. Finally, a test problem for an irregular by shoped duct was studied and compared against results found in the literature, with good agreement and excellent convergence rates for the stream function field along the whole channel, for different values of Reynolds number. (author) 78 refs., 24 figs., 14 tabs.

Multigrid solution of the Navier-Stokes equations at low speeds with large temperature variations

International Nuclear Information System (INIS)

Sockol, Peter M.

2003-01-01

Multigrid methods for the Navier-Stokes equations at low speeds and large temperature variations are investigated. The compressible equations with time-derivative preconditioning and preconditioned flux-difference splitting of the inviscid terms are used. Three implicit smoothers have been incorporated into a common multigrid procedure. Both full coarsening and semi-coarsening with directional fine-grid defect correction have been studied. The resulting methods have been tested on four 2D laminar problems over a range of Reynolds numbers on both uniform and highly stretched grids. Two of the three methods show efficient and robust performance over the entire range of conditions. In addition, none of the methods has any difficulty with the large temperature variations

Chaos Synchronization in Navier-Stokes Turbulence

Science.gov (United States)

Lalescu, Cristian; Meneveau, Charles; Eyink, Gregory

2013-03-01

Chaos synchronization (CS) has been studied for some time now (Pecora & Carroll 1990), for systems with only a few degrees of freedom as well as for systems described by partial differential equations (Boccaletti et al 2002). CS in general is said to be present in coupled dynamical systems when a specific property of each system has the same time evolution for all, even though the evolution itself is chaotic. The Navier-Stokes (NS) equations describe the velocity for a wide range of fluids, and their solutions are usually called turbulent if fluctuation amplitudes decrease as a power of their wavenumber. There have been some studies of CS for continuous systems (Kocarev et al 1997), but CS for NS turbulence seems not to have been investigated so far. We focus on the synchronization of the small scales of a turbulent flow for which the time history of large scales is prescribed. Our DNS results show that high-wavenumbers in turbulence are fully slaved to modes with wavenumbers up to a critical fraction of the Kolmogorov dissipation wavenumber. The motivation for our work is to study deeply sub-Kolmogorov scales in fully developed turbulence (Schumacher 2007), which we found to be recoverable even at very high Reynolds number from simulations with moderate resolutions. This work is supported by the National Science Foundation's CDI-II program, project CMMI-0941530

Investigation of vortex breakdown on a delta wing using Euler and Navier-Stokes equations

Science.gov (United States)

Agrawal, S.; Barnett, R. M.; Robinson, B. A.

1991-01-01

A numerical investigation of leading edge vortex breakdown in a delta wing at high angles of attack is presented. The analysis was restricted to low speed flows on a flat plate wing with sharp leading edges. Both Euler and Navier-Stokes equations were used and the results were compared with experimental data. Predictions of vortex breakdown progression with angle of attack with both Euler and Navier-Stokes equations are shown to be consistent with the experimental data. However, the Navier-Stokes predictions show significant improvements in breakdown location at angles of attack where the vortex breakdown approaches the wing apex. The predicted trajectories of the primary vortex are in very good agreement with the test data, the laminar solutions providing the overall best comparison. The Euler shows a small displacement of the primary vortex, relative to experiment, due to the lack of secondary vortices. The turbulent Navier-Stokes, in general, fall between the Euler and laminar solutions.

Discretizations in isogeometric analysis of Navier-Stokes flow

DEFF Research Database (Denmark)

Nielsen, Peter Nørtoft; Gersborg, Allan Roulund; Gravesen, Jens

2011-01-01

This paper deals with isogeometric analysis of 2-dimensional, steady state, incompressible Navier-Stokes flow subjected to Dirichlet boundary conditions. We present a detailed description of the numerical method used to solve the boundary value problem. Numerical inf-sup stability tests...

Sigma-convergence of stationary Navier-Stokes type equations

Directory of Open Access Journals (Sweden)

Gabriel Nguetseng

2009-06-01

Full Text Available In the framework of homogenization theory, the Sigma-convergence method is carried out on stationary Navier-Stokes type equations on a fixed domain. Our main tools are the two-scale convergence concept and the so-called homogenization algebras.

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2017-01-01

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy

Development Of A Navier-Stokes Computer Code

Science.gov (United States)

Yoon, Seokkwan; Kwak, Dochan

1993-01-01

Report discusses aspects of development of CENS3D computer code, solving three-dimensional Navier-Stokes equations of compressible, viscous, unsteady flow. Implements implicit finite-difference or finite-volume numerical-integration scheme, called "lower-upper symmetric-Gauss-Seidel" (LU-SGS), offering potential for very low computer time per iteration and for fast convergence.

Time evolution of the eddy viscosity in two-dimensional navier-stokes flow

Science.gov (United States)

Chaves; Gama

2000-02-01

The time evolution of the eddy viscosity associated with an unforced two-dimensional incompressible Navier-Stokes flow is analyzed by direct numerical simulation. The initial condition is such that the eddy viscosity is isotropic and negative. It is shown by concrete examples that the Navier-Stokes dynamics stabilizes negative eddy viscosity effects. In other words, this dynamics moves monotonically the initial negative eddy viscosity to positive values before relaxation due to viscous term occurs.

Augmented Lagrangian methods to solve Navier-Stokes equations for a Bingham fluid flow

International Nuclear Information System (INIS)

Boscardin, Laetitia

1999-01-01

The objective of this research thesis is to develop one or more methods for the numerical resolution of equations of movement obtained for a Bingham fluid. The resolution of Navier-Stokes equations is processed by splitting elliptic and hyperbolic operators (Galerkin transport). In this purpose, the author first studied the Stokes problem, and then addressed issues of stability and consistency of the global scheme. The variational formulation of the Stokes problem can be expressed under the form of a minimisation problem under the constraint of non linear and non differentiable functions. Then, the author proposes a discretization of the Stokes problem based on a hybrid finite element method. Then he extends the demonstrations of stability and consistency of the Galerkin-transport scheme which have been established for a Newtonian fluid, to the case of a Bingham fluid. A relaxation algorithm and a Newton-GMRES algorithm are developed to solve the problem, and their convergence is studied. To ensure this convergence, some constraints must be verified. In order to do so, a specific speed element has been developed [fr

A stable penalty method for the compressible Navier-Stokes equations: II: One-dimensional domain decomposition schemes

DEFF Research Database (Denmark)

Hesthaven, Jan

1997-01-01

This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions and as a res......This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions...... and as a result the patching of subdomains is local in space. The scheme is studied in detail for Burgers's equation and developed for the compressible Navier-Stokes equations in general curvilinear coordinates. The versatility of the proposed scheme for the compressible Navier-Stokes equations is illustrated...

A Liouville Problem for the Stationary Fractional Navier-Stokes-Poisson System

Science.gov (United States)

Wang, Y.; Xiao, J.

2017-06-01

This paper deals with a Liouville problem for the stationary fractional Navier-Stokes-Poisson system whose special case k=0 covers the compressible and incompressible time-independent fractional Navier-Stokes systems in R^{N≥2} . An essential difficulty raises from the fractional Laplacian, which is a non-local operator and thus makes the local analysis unsuitable. To overcome the difficulty, we utilize a recently-introduced extension-method in Wang and Xiao (Commun Contemp Math 18(6):1650019, 2016) which develops Caffarelli-Silvestre's technique in Caffarelli and Silvestre (Commun Partial Diff Equ 32:1245-1260, 2007).

Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations

International Nuclear Information System (INIS)

Dascaliuc, Radu; Thomann, Enrique; Waymire, Edward C.; Michalowski, Nicholas

2015-01-01

The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturally arise as a result of this investigation

Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations.

Science.gov (United States)

Dascaliuc, Radu; Michalowski, Nicholas; Thomann, Enrique; Waymire, Edward C

2015-07-01

The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturally arise as a result of this investigation.

Eulerian derivations of non-inertial Navier-Stokes equations

CSIR Research Space (South Africa)

Combrinck, MA

2014-09-01

Full Text Available The paper presents an Eulerian derivation of the non-inertial Navier-Stokes equations as an alternative to the Lagrangian fluid parcel approach. This work expands on the work of Kageyama and Hyodo [1] who derived the incompressible momentum equation...

Homogenization of the evolutionary Navier-Stokes system

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Namlyeyeva, Yuliya; Nečasová, Šárka

2016-01-01

Roč. 149, č. 1 (2016), s. 251-274 ISSN 0025-2611 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes system Subject RIV: BA - General Mathematics Impact factor: 0.607, year: 2016 http://link.springer.com/article/10.1007%2Fs00229-015-0778-y

Lagrange–Galerkin methods for the incompressible Navier-Stokes equations: a review

Directory of Open Access Journals (Sweden)

Bermejo Rodolfo

2016-09-01

Full Text Available We review in this paper the development of Lagrange-Galerkin (LG methods to integrate the incompressible Navier-Stokes equations (NSEs for engineering applications. These methods were introduced in the computational fluid dynamics community in the early eighties of the past century, and at that time they were considered good methods for both their theoretical stability properties and the way of dealing with the nonlinear terms of the equations; however, the numerical experience gained with the application of LG methods to different problems has identified drawbacks of them, such as the calculation of specific integrals that arise in their formulation and the calculation of the ow trajectories, which somehow have hampered the applicability of LG methods. In this paper, we focus on these issues and summarize the convergence results of LG methods; furthermore, we shall briefly introduce a new stabilized LG method suitable for high Reynolds numbers.

Navier-Stokes Computations of a Wing-Flap Model With Blowing Normal to the Flap Surface

Science.gov (United States)

Boyd, D. Douglas, Jr.

2005-01-01

A computational study of a generic wing with a half span flap shows the mean flow effects of several blown flap configurations. The effort compares and contrasts the thin-layer, Reynolds averaged, Navier-Stokes solutions of a baseline wing-flap configuration with configurations that have blowing normal to the flap surface through small slits near the flap side edge. Vorticity contours reveal a dual vortex structure at the flap side edge for all cases. The dual vortex merges into a single vortex at approximately the mid-flap chord location. Upper surface blowing reduces the strength of the merged vortex and moves the vortex away from the upper edge. Lower surface blowing thickens the lower shear layer and weakens the merged vortex, but not as much as upper surface blowing. Side surface blowing forces the lower surface vortex farther outboard of the flap edge by effectively increasing the aerodynamic span of the flap. It is seen that there is no global aerodynamic penalty or benefit from the particular blowing configurations examined.

A six-mode truncation of the Navier-Stokes equations on a two-dimensional torus: a numerical study

International Nuclear Information System (INIS)

Angelo, P.M.; Riela, G.

1981-01-01

We study a model obtained from a six-mode truncation of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus. We find that at low values of the Reynolds number R the dynamics is characterized by fixed points and, at large values of R, by two stable periodic orbits; at intermediate values of R two infinite sequences of bifurcations of periodic orbits into periodic orbits of doubled period lead to two regions of ''turbulent'' or ''chaotic'' behaviour. The turbulent regions end up for values of R for which stable periodic orbits appear. (author)

Symmetric approximations of the Navier-Stokes equations

International Nuclear Information System (INIS)

Kobel'kov, G M

2002-01-01

A new method for the symmetric approximation of the non-stationary Navier-Stokes equations by a Cauchy-Kovalevskaya-type system is proposed. Properties of the modified problem are studied. In particular, the convergence as ε→0 of the solutions of the modified problem to the solutions of the original problem on an infinite interval is established

On analytical solution of the Navier-Stokes equations

International Nuclear Information System (INIS)

Scheffel, J.

2001-04-01

An analytical method for solving the dissipative, nonlinear and non-stationary Navier-Stokes equations is presented. Velocity and pressure is expanded in power series of cartesian coordinates and time. The method is applied to 2-D incompressible gravitational flow in a bounded, rectangular domain

Inertial algorithms for the stationary Navier-Stokes equations

NARCIS (Netherlands)

Hou, Yanren; Mattheij, R.M.M.

2003-01-01

Several kind of new numerical schemes for the stationary Navier-Stokes equations based on the virtue of Inertial Manifold and Approximate Inertial Manifold, which we call them inertial algorithms in this paper, together with their error estimations are presented. All these algorithms are constructed

Navier-Stokes Computations of Sabot Discard Using Chimera Scheme

National Research Council Canada - National Science Library

Ferry, E

1997-01-01

.... Numerical flow field computations have been made for various orientations and locations of sabots using an unsteady, zonal Navier-Stokes code and the Chimera composite grid discretization technique at M = 4.0 and alpha = 0...

Navier-Stokes dynamics on a differential one-form

Science.gov (United States)

Story, Troy L.

2006-11-01

After transforming the Navier-Stokes dynamic equation into a characteristic differential one-form on an odd-dimensional differentiable manifold, exterior calculus is used to construct a pair of differential equations and tangent vector(vortex vector) characteristic of Hamiltonian geometry. A solution to the Navier-Stokes dynamic equation is then obtained by solving this pair of equations for the position x^k and the conjugate to the position bk as functions of time. The solution bk is shown to be divergence-free by contracting the differential 3-form corresponding to the divergence of the gradient of the velocity with a triple of tangent vectors, implying constraints on two of the tangent vectors for the system. Analysis of the solution bk shows it is bounded since it remains finite as | x^k | ->,, and is physically reasonable since the square of the gradient of the principal function is bounded. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian is obtained.

KNOW-BLADE task-4 report: Navier-Stokes aeroelasticity

DEFF Research Database (Denmark)

Politis, E.S.; Nikolaou, I.G.; Chaviaropoulos, P.K.

2004-01-01

wind turbine blade have been combined with 2D and 3D unsteady Navier-Stokes solvers. The relative disadvantage of the quasi-3D approach (where the elastic solver is coupled with a 2D Navier-Stokes solver) isits inability to model induced flow. The lack of a validation test case did not allow...... the computations for the full blade, 2D computations for the so-called “typical section” have been carried out. The 2D aeroelastic tools resulted in similar aerodynamic damping values. Qualitative agreement was better for the lead-lagmode. The presence of roughness tapes has a small, rather negligible impact...... on aeroelastic stability as depicted by the results of both aeroelastic tools. On the other hand, in conformity to the inability of the adopted computational model to successfullypredict the corresponding test cases under work package 2 of the project, the aeroelastic tools are not capable to predict the correct...

Spatial Fourier modes controlling Navier-Stokes flow

International Nuclear Information System (INIS)

Treve, Y.M.

1982-01-01

As shown by Foias and Prodi in the limit of infinite times the solutions of the two-dimensional Navier-Stokes equations depend only on a finite number of modes, a number for which rigorous estimates can be obtained. A survey of these results is given together with further developments, notably in connection with the numerical approximation to the exact solutions. (Auth.)

Unstructured Navier-Stokes Analysis of Full TCA Configuration

Science.gov (United States)

Frink, Neal T.; Pirzadeh, Shahyar Z.

1999-01-01

This paper presents an Unstructured Navier-Stokes Analysis of Full TCA (Technology Concept Airplane) Configuration. The topics include: 1) Motivation; 2) Milestone and approach; 3) Overview of the unstructured-grid system; 4) Results on full TCA W/B/N/D/E configuration; 5) Concluding remarks; and 6) Future directions.

Anomalous scaling of a passive vector advected by the Navier-Stokes velocity field

International Nuclear Information System (INIS)

Jurcisinova, E; Jurcisin, M; Remecky, R

2009-01-01

Using the field theoretic renormalization group and the operator-product expansion, the model of a passive vector field (a weak magnetic field in the framework of the kinematic MHD) advected by the velocity field which is governed by the stochastic Navier-Stokes equation with the Gaussian random stirring force δ-correlated in time and with the correlator proportional to k 4-d-2ε is investigated to the first order in ε (one-loop approximation). It is shown that the single-time correlation functions of the advected vector field have anomalous scaling behavior and the corresponding exponents are calculated in the isotropic case, as well as in the case with the presence of large-scale anisotropy. The hierarchy of the anisotropic critical dimensions is briefly discussed and the persistence of the anisotropy inside the inertial range is demonstrated on the behavior of the skewness and hyperskewness (dimensionless ratios of correlation functions) as functions of the Reynolds number Re. It is shown that even though the present model of a passive vector field advected by the realistic velocity field is mathematically more complicated than, on one hand, the corresponding models of a passive vector field advected by 'synthetic' Gaussian velocity fields and, on the other hand, than the corresponding model of a passive scalar quantity advected by the velocity field driven by the stochastic Navier-Stokes equation, the final one-loop approximate asymptotic scaling behavior of the single-time correlation or structure functions of the advected fields of all models are defined by the same anomalous dimensions (up to normalization)

Simulations of transition and turbulence on the Navier-Stokes computer

International Nuclear Information System (INIS)

Krist, S.E.; Zang, T.A.

1987-01-01

The Navier-Stokes Computer (NSC) consists of multiple local memory parallel processors interconnected in a hypercube network. Efficient implementation of algorithms on the NSC thus requires the effective utilization of both the coarse and fine grain paralelism inherent in the architectural design. The basic approach to implementing an algorithm on the NSC is presented herein. The particular finite-difference algorithm considered was developed for performing transition and turbulence simulations by direct solution of the time-dependent incompressible Navier-Stokes equations. The suitability of this algorithm for performing simulations of the isotropic turbulence problem is verified from computations performed on a Cray 2. Projected timing results for the algorithm on the NSC itself are presented for both the isotropic turbulence and laminar turbulent transition problems. 7 references

Navier-Stokes Calculations of Helicopter Fuselage Flowfield and Loads

DEFF Research Database (Denmark)

M, Costes; Filippone, Antonino; N, Kroll

1999-01-01

This paper describes the theoretically basedactivities conducted during the first year of theBrite/Euram Helifuse Porgramme. These activitiesmainly consisted of the numerical prediction ofhelicopter fuselage flowfields with existing Navier-Stokes solvers on a number of pre-selectedcases, taken out...

Incompressible Navier-Stokes inverse design method based on adaptive unstructured meshes

International Nuclear Information System (INIS)

Rahmati, M.T.; Charlesworth, D.; Zangeneh, M.

2005-01-01

An inverse method for blade design based on Navier-Stokes equations on adaptive unstructured meshes has been developed. In the method, unlike the method based on inviscid equations, the effect of viscosity is directly taken into account. In the method, the pressure (or pressure loading) is prescribed. The design method then computes the blade shape that would accomplish the target prescribed pressure distribution. The method is implemented using a cell-centered finite volume method, which solves the incompressible Navier-Stokes equations on unstructured meshes. An adaptive unstructured mesh method based on grid subdivision and local adaptive mesh method is utilized for increasing the accuracy. (author)

Drifting solutions with elliptic symmetry for the compressible Navier-Stokes equations with density-dependent viscosity

International Nuclear Information System (INIS)

An, Hongli; Yuen, Manwai

2014-01-01

In this paper, we investigate the analytical solutions of the compressible Navier-Stokes equations with dependent-density viscosity. By using the characteristic method, we successfully obtain a class of drifting solutions with elliptic symmetry for the Navier-Stokes model wherein the velocity components are governed by a generalized Emden dynamical system. In particular, when the viscosity variables are taken the same as Yuen [M. W. Yuen, “Analytical solutions to the Navier-Stokes equations,” J. Math. Phys. 49, 113102 (2008)], our solutions constitute a generalization of that obtained by Yuen. Interestingly, numerical simulations show that the analytical solutions can be used to explain the drifting phenomena of the propagation wave like Tsunamis in oceans

Sharp asymptotic estimates for vorticity solutions of the 2D Navier-Stokes equation

Directory of Open Access Journals (Sweden)

Yuncheng You

2008-12-01

Full Text Available The asymptotic dynamics of high-order temporal-spatial derivatives of the two-dimensional vorticity and velocity of an incompressible, viscous fluid flow in $mathbb{R}^2$ are studied, which is equivalent to the 2D Navier-Stokes equation. It is known that for any integrable initial vorticity, the 2D vorticity solution converges to the Oseen vortex. In this paper, sharp exterior decay estimates of the temporal-spatial derivatives of the vorticity solution are established. These estimates are then used and combined with similarity and $L^p$ compactness to show the asymptotical attraction rates of temporal-spatial derivatives of generic 2D vorticity and velocity solutions by the Oseen vortices and velocity solutions respectively. The asymptotic estimates and the asymptotic attraction rates of all the derivatives obtained in this paper are independent of low or high Reynolds numbers.

Viscous-inviscid interaction using the parabolized Navier-Stokes equations

DEFF Research Database (Denmark)

Filippone, Antonino; Sørensen, Jens Nørkær

1997-01-01

adaptive grid is used.The interaction is achieved by iterative updatingof the boundary conditions, through the wall transpiration concept. The Navier-Stokes equationsare discretized on a semi-staggered grid.Space-marching integration is performed starting from the stagnation streamline ontwo independent......A numerical model for the calculation of incompressible viscous flows past airfoils andwings has been developed. The approach is based on a strong viscous-inviscid coupling of aboundary element method with the Navier-Stokesequations in vorticity-streamfunction formulation.A semi-adaptive or fully...

An Application of CFD to Guide Forced Boundary-Layer Transition for Low-Speed Tests of a Hybrid Wing-Body Configuration

Science.gov (United States)

Luckring, James M.; Deere, Karen A.; Childs, Robert E.; Stremel, Paul M.; Long, Kurtis R.

2016-01-01

A hybrid transition trip-dot sizing and placement test technique was developed in support of recent experimental research on a hybrid wing-body configuration under study for the NASA Environmentally Responsible Aviation project. The approach combines traditional methods with Computational Fluid Dynamics. The application had three-dimensional boundary layers that were simulated with either fully turbulent or transitional flow models using established Reynolds-Averaged Navier-Stokes methods. Trip strip effectiveness was verified experimentally using infrared thermography during a low-speed wind tunnel test. Although the work was performed on one specific configuration, the process was based on fundamental flow physics and could be applicable to other configurations.

Parabolized Navier-Stokes solutions of separation and trailing-edge flows

Science.gov (United States)

Brown, J. L.

1983-01-01

A robust, iterative solution procedure is presented for the parabolized Navier-Stokes or higher order boundary layer equations as applied to subsonic viscous-inviscid interaction flows. The robustness of the present procedure is due, in part, to an improved algorithmic formulation. The present formulation is based on a reinterpretation of stability requirements for this class of algorithms and requires only second order accurate backward or central differences for all streamwise derivatives. Upstream influence is provided for through the algorithmic formulation and iterative sweeps in x. The primary contribution to robustness, however, is the boundary condition treatment, which imposes global constraints to control the convergence path. Discussed are successful calculations of subsonic, strong viscous-inviscid interactions, including separation. These results are consistent with Navier-Stokes solutions and triple deck theory.

The Navier-Stokes Equations Theory and Numerical Methods

CERN Document Server

Masuda, Kyûya; Rautmann, Reimund; Solonnikov, Vsevolod

1990-01-01

These proceedings contain original (refereed) research articles by specialists from many countries, on a wide variety of aspects of Navier-Stokes equations. Additionally, 2 survey articles intended for a general readership are included: one surveys the present state of the subject via open problems, and the other deals with the interplay between theory and numerical analysis.

Pipe Flow and Wall Turbulence Using a Modified Navier-Stokes Equation

International Nuclear Information System (INIS)

Jirkovsky, L.; Muriel, A.

2012-01-01

We use a derived incompressible modified Navier-Stokes equation to model pipe flow and wall turbulence. We reproduce the observed flattened paraboloid velocity profiles of turbulence that cannot be obtained directly using standard incompressible Navier-Stokes equation. The solutions found are in harmony with multi-valued velocity fields as a definition of turbulence. Repeating the procedure for the flow of turbulent fluid between two parallel flat plates we find similar flattened velocity profiles. We extend the analysis to the turbulent flow along a single wall and compare the results with experimental data and the established controversial von Karman logarithmic law of the wall. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations.

Science.gov (United States)

Vorobev, Anatoliy

2010-11-01

We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short time-scale (quasiacoustic) process that may not affect the slow dynamics but may significantly complicate the numerical treatment. Using the multiple-scale method we separate the physical processes occurring on different time scales and, ultimately, derive the equations with the filtered-out quasiacoustics. The derived equations represent the Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations. This approximation can be further employed as a universal theoretical model for an analysis of slow thermodynamic and hydrodynamic evolution of the multiphase systems with strongly evolving and diffusing interfacial boundaries, i.e., for the processes involving dissolution/nucleation, evaporation/condensation, solidification/melting, polymerization, etc.

About local fractional three-dimensional compressible Navier-Stokes equations in Cantor-type cylindrical co-ordinate system

Directory of Open Access Journals (Sweden)

Gao Guo-Ping

2016-01-01

Full Text Available In this article, we investigate the local fractional 3-D compressible Navier-Stokes equation via local fractional derivative. We use the Cantor-type cylindrical co-ordinate method to transfer 3-D compressible Navier-Stokes equation from the Cantorian co-ordinate system to the Cantor-type cylindrical co-ordinate system.

Navier-Stokes-like equations for traffic flow.

Science.gov (United States)

Velasco, R M; Marques, W

2005-10-01

The macroscopic traffic flow equations derived from the reduced Paveri-Fontana equation are closed starting with the maximization of the informational entropy. The homogeneous steady state taken as a reference is obtained for a specific model of the desired velocity and a kind of Chapman-Enskog method is developed to calculate the traffic pressure at the Navier-Stokes level. Numerical solution of the macroscopic traffic equations is obtained and its characteristics are analyzed.

Integral transformation of the Navier-Stokes equations for laminar flow in channels of arbitrary two-dimensional geometry

International Nuclear Information System (INIS)

Perez Guerrero, Jesus Salvador

1995-01-01

Laminar developing flow in channels of arbitrary geometry was studied by solving the Navier-Stokes equations in the stream function-only formulation through the Generalized Integral Transform Technique (GITT). The stream function is expanded in an infinite system based on eigenfunctions obtained by considering solely the diffusive terms of the original formulation. The Navier-Stokes equations are transformed into an infinite system of ordinary differential equations, by using the transformation and inversion formulae. For computational purposes, the infinite series is truncated, according to an automatic error control procedure. The ordinary differential is solved through well-established scientific subroutines from widely available mathematical libraries. The classical problem of developing flow between parallel-plates is analysed first, as for both uniform and irrotational inlet conditions. The effect of truncating the duct length in the accuracy of the obtained solution is studied. A convergence analysis of the results obtained by the GITT is performed and compared with results obtained by finite difference and finite element methods, for different values of Reynolds number. The problem of flow over a backward-facing step then follows. Comparisons with experimental results in the literature indicate an excellent agreement. The numerical co-validation was established for a test case, and perfect agreement is reached against results considered as benchmarks in the recent literature. The results were shown to be physically more reasonable than others obtained by purely numerical methods, in particular for situations where three-dimensional effects are identified. Finally, a test problem for an irregular by shoped duct was studied and compared against results found in the literature, with good agreement and excellent convergence rates for the stream function field along the whole channel, for different values of Reynolds number. (author)

Finite elements volumes methods: applications to the Navier-Stokes equations and convergence results

International Nuclear Information System (INIS)

Emonot, P.

1992-01-01

In the first chapter are described the equations modeling incompressible fluid flow and a quick presentation of finite volumes method. The second chapter is an introduction to the finite elements volumes method. The box model is described and a method adapted to Navier-Stokes problems is proposed. The third chapter shows a fault analysis of the finite elements volumes method for the Laplacian problem and some examples in one, two, three dimensional calculations. The fourth chapter is an extension of the error analysis of the method for the Navier-Stokes problem

Multigrid and defect correction for the steady Navier-Stokes equations

NARCIS (Netherlands)

Koren, B.

1990-01-01

Theoretical and experimental convergence results are presented for nonlinear multigrid and iterative defect correction applied to finite volume discretizations of the full, steady, 2D, compressible Navier-Stokes equations. Iterative defect correction is introduced for circumventing the difficulty in

Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Existence Analysis

International Nuclear Information System (INIS)

Bulicek, Miroslav; Haslinger, Jaroslav; Malek, Josef; Stebel, Jan

2009-01-01

We study a shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to an optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by a generalized stationary Navier-Stokes system with nontrivial mixed boundary conditions. In this paper we prove the existence of solutions both to the generalized Navier-Stokes system and to the shape optimization problem

Implicit methods for the Navier-Stokes equations

Science.gov (United States)

Yoon, S.; Kwak, D.

1990-01-01

Numerical solutions of the Navier-Stokes equations using explicit schemes can be obtained at the expense of efficiency. Conventional implicit methods which often achieve fast convergence rates suffer high cost per iteration. A new implicit scheme based on lower-upper factorization and symmetric Gauss-Seidel relaxation offers very low cost per iteration as well as fast convergence. High efficiency is achieved by accomplishing the complete vectorizability of the algorithm on oblique planes of sweep in three dimensions.

Modeling Vortex Generators in a Navier-Stokes Code

Science.gov (United States)

Dudek, Julianne C.

2011-01-01

A source-term model that simulates the effects of vortex generators was implemented into the Wind-US Navier-Stokes code. The source term added to the Navier-Stokes equations simulates the lift force that would result from a vane-type vortex generator in the flowfield. The implementation is user-friendly, requiring the user to specify only three quantities for each desired vortex generator: the range of grid points over which the force is to be applied and the planform area and angle of incidence of the physical vane. The model behavior was evaluated for subsonic flow in a rectangular duct with a single vane vortex generator, subsonic flow in an S-duct with 22 corotating vortex generators, and supersonic flow in a rectangular duct with a counter-rotating vortex-generator pair. The model was also used to successfully simulate microramps in supersonic flow by treating each microramp as a pair of vanes with opposite angles of incidence. The validation results indicate that the source-term vortex-generator model provides a useful tool for screening vortex-generator configurations and gives comparable results to solutions computed using gridded vanes.

Fluctuating Navier-Stokes equations for inelastic hard spheres or disks.

Science.gov (United States)

Brey, J Javier; Maynar, P; de Soria, M I García

2011-04-01

Starting from the fluctuating Boltzmann equation for smooth inelastic hard spheres or disks, closed equations for the fluctuating hydrodynamic fields to Navier-Stokes order are derived. This requires deriving constitutive relations for both the fluctuating fluxes and the correlations of the random forces. The former are identified as having the same form as the macroscopic average fluxes and involving the same transport coefficients. On the other hand, the random force terms exhibit two peculiarities as compared with their elastic limit for molecular systems. First, they are not white but have some finite relaxation time. Second, their amplitude is not determined by the macroscopic transport coefficients but involves new coefficients. ©2011 American Physical Society

Parallel computation of Euler and Navier-Stokes flows

International Nuclear Information System (INIS)

Swisshelm, J.M.; Johnson, G.M.; Kumar, S.P.

1986-01-01

A multigrid technique useful for accelerating the convergence of Euler and Navier-Stokes flow computations has been restructured to improve its performance on both SIMD and MIMD computers. The new algorithm allows both the construction of longer coarse-grid vectors and the multitasking of entire grids. Computational results are presented for the CDC Cyber 205, Cray X-MP, and Denelcor HEP I. 15 references

Smooth solutions of the Navier-Stokes equations

International Nuclear Information System (INIS)

Pokhozhaev, S I

2014-01-01

We consider smooth solutions of the Cauchy problem for the Navier-Stokes equations on the scale of smooth functions which are periodic with respect to x∈R 3 . We obtain existence theorems for global (with respect to t>0) and local solutions of the Cauchy problem. The statements of these depend on the smoothness and the norm of the initial vector function. Upper bounds for the behaviour of solutions in both classes, which depend on t, are also obtained. Bibliography: 10 titles

Spectral/hp least-squares finite element formulation for the Navier-Stokes equations

International Nuclear Information System (INIS)

Pontaza, J.P.; Reddy, J.N.

2003-01-01

We consider the application of least-squares finite element models combined with spectral/hp methods for the numerical solution of viscous flow problems. The paper presents the formulation, validation, and application of a spectral/hp algorithm to the numerical solution of the Navier-Stokes equations governing two- and three-dimensional stationary incompressible and low-speed compressible flows. The Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method. Spectral convergence of the L 2 least-squares functional and L 2 error norms is verified using smooth solutions to the two-dimensional stationary Poisson and incompressible Navier-Stokes equations. Numerical results for flow over a backward-facing step, steady flow past a circular cylinder, three-dimensional lid-driven cavity flow, and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation

Capability of State-of-the-Art Navier-Stokes Solvers for the Prediction of Helicopter Fuselage Aerodynamics

DEFF Research Database (Denmark)

N., Kroll; P., Renzoni; M., Amato

1998-01-01

The purpose of this paper is to describe the influence of different Navier-Stokes solvers and grids on the prediction of the global coefficients for a simplified geometry of a helicopter fuselage.......The purpose of this paper is to describe the influence of different Navier-Stokes solvers and grids on the prediction of the global coefficients for a simplified geometry of a helicopter fuselage....

F-16XL Hybrid Reynolds-Averaged Navier-Stokes/Large Eddy Simulation on Unstructured Grids

Science.gov (United States)

Park, Michael A.; Abdol-Hamid, Khaled S.; Elmiligui, Alaa

2015-01-01

This study continues the Cranked Arrow Wing Aerodynamics Program, International (CAWAPI) investigation with the FUN3D and USM3D flow solvers. CAWAPI was established to study the F-16XL, because it provides a unique opportunity to fuse fight test, wind tunnel test, and simulation to understand the aerodynamic features of swept wings. The high-lift performance of the cranked-arrow wing planform is critical for recent and past supersonic transport design concepts. Simulations of the low speed high angle of attack Flight Condition 25 are compared: Detached Eddy Simulation (DES), Modi ed Delayed Detached Eddy Simulation (MDDES), and the Spalart-Allmaras (SA) RANS model. Iso- surfaces of Q criterion show the development of coherent primary and secondary vortices on the upper surface of the wing that spiral, burst, and commingle. SA produces higher pressure peaks nearer to the leading-edge of the wing than flight test measurements. Mean DES and MDDES pressures better predict the flight test measurements, especially on the outer wing section. Vorticies and vortex-vortex interaction impact unsteady surface pressures. USM3D showed many sharp tones in volume points spectra near the wing apex with low broadband noise and FUN3D showed more broadband noise with weaker tones. Spectra of the volume points near the outer wing leading-edge was primarily broadband for both codes. Without unsteady flight measurements, the flight pressure environment can not be used to validate the simulations containing tonal or broadband spectra. Mean forces and moment are very similar between FUN3D models and between USM3D models. Spectra of the unsteady forces and moment are broadband with a few sharp peaks for USM3D.

Continuum Navier-Stokes modelling of water ow past fullerene molecules

DEFF Research Database (Denmark)

Walther, J. H.; Popadic, A.; Koumoutsakos, P.

We present continuum simulations of water flow past fullerene molecules. The governing Navier-Stokes equations are complemented with the Navier slip boundary condition with a slip length that is extracted from related molecular dynamics simulations. We find that several quantities of interest...... as computed by the present model are in good agreement with results from atomistic and atomistic-continuum simulations at a fraction of the computational cost. We simulate the flow past a single fullerene and an array of fullerenes and demonstrate that such nanoscale flows can be computed efficiently...

Continuum Navier-Stokes modelling of water flow past fullerene molecules

DEFF Research Database (Denmark)

Walther, J. H.; Popadic, A.; Koumoutsakos, P.

We present continuum simulations of water flow past fullerene molecules. The governing Navier-Stokes equations are complemented with the Navier slip boundary condition with a slip length that is extracted from related molecular dynamics simulations. We find that several quantities of interest...... as computed by the present model are in good agreement with results from atomistic and atomistic-continuum simulations at a fraction of the computational cost. We simulate the flow past a single fullerene and an array of fullerenes and demonstrate that such nanoscale flows can be computed efficiently...

An Equal-Order DG Method for the Incompressible Navier-Stokes Equations

KAUST Repository

Cockburn, Bernardo; Kanschat, Guido; Schö tzau, Dominik

2008-01-01

We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability

Quantification of topological changes of vorticity contours in two-dimensional Navier-Stokes flow.

Science.gov (United States)

Ohkitani, Koji; Al Sulti, Fayeza

2010-06-01

A characterization of reconnection of vorticity contours is made by direct numerical simulations of the two-dimensional Navier-Stokes flow at a relatively low Reynolds number. We identify all the critical points of the vorticity field and classify them by solving an eigenvalue problem of its Hessian matrix on the basis of critical-point theory. The numbers of hyperbolic (saddles) and elliptic (minima and maxima) points are confirmed to satisfy Euler's index theorem numerically. Time evolution of these indices is studied for a simple initial condition. Generally speaking, we have found that the indices are found to decrease in number with time. This result is discussed in connection with related works on streamline topology, in particular, the relationship between stagnation points and the dissipation. Associated elementary procedures in physical space, the merging of vortices, are studied in detail for a number of snapshots. A similar analysis is also done using the stream function.

A comparative study of the parabolized Navier-Stokes code using various grid-generation techniques

Science.gov (United States)

Kaul, U. K.; Chaussee, D. S.

1985-01-01

The parabolized Navier-Stokes (PNS) equations are used to calculate the flow-field characteristics about the hypersonic research aircraft X-24C. A comparison of the results obtained using elliptic, hyperbolic and algebraic grid generators is presented. The outer bow shock is treated as a sharp discontinuity, and the discontinuities within the shock layer are captured. Surface pressures and heat-transfer results at angles of attack of 6 deg and 20 deg, obtained using the three grid generators, are compared. The PNS equations are marched downstream over the body in both Cartesian and cylindrical base coordinate systems, and the results are compared. A robust marching procedure is demonstrated by successfully using large marching-step sizes with the implicit shock fitting procedure. A correlation is found between the marching-step size, Reynolds number and the angle of attack at fixed values of smoothing and stability coefficients for the marching scheme.

Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

International Nuclear Information System (INIS)

Ling, Julia; Kurzawski, Andrew; Templeton, Jeremy

2016-01-01

There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property. Furthermore, the Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.

Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations.

Science.gov (United States)

Miranda, Rodrigo A; Rempel, Erico L; Chian, Abraham C-L; Seehafer, Norbert; Toledo, Benjamin A; Muñoz, Pablo R

2013-09-01

We study a transition to hyperchaos in the two-dimensional incompressible Navier-Stokes equations with periodic boundary conditions and an external forcing term. Bifurcation diagrams are constructed by varying the Reynolds number, and a transition to hyperchaos (HC) is identified. Before the onset of HC, there is coexistence of two chaotic attractors and a hyperchaotic saddle. After the transition to HC, the two chaotic attractors merge with the hyperchaotic saddle, generating random switching between chaos and hyperchaos, which is responsible for intermittent bursts in the time series of energy and enstrophy. The chaotic mixing properties of the flow are characterized by detecting Lagrangian coherent structures. After the transition to HC, the flow displays complex Lagrangian patterns and an increase in the level of Lagrangian chaoticity during the bursty periods that can be predicted statistically by the hyperchaotic saddle prior to HC transition.

Does the flatness of the velocity derivative blow up at a finite Reynolds number?

International Nuclear Information System (INIS)

Sreenivasan, K.R.; Bershadskii, A.

2006-12-01

A tentative suggestion is made that the flatness of the velocity derivative could reach an infinite value at finite (though very large) Reynolds number, with possible implications for the singularities of the Navier-Stokes equations. A direct test of this suggestion requires measurements at Reynolds numbers presently outside the experimental capacity, so an alternative suggestion that can be tested at accessible Reynolds numbers is also made. (author)

Large Deviations for Stochastic Tamed 3D Navier-Stokes Equations

International Nuclear Information System (INIS)

Roeckner, Michael; Zhang, Tusheng; Zhang Xicheng

2010-01-01

In this paper, using weak convergence method, we prove a large deviation principle of Freidlin-Wentzell type for the stochastic tamed 3D Navier-Stokes equations driven by multiplicative noise, which was investigated in (Roeckner and Zhang in Probab. Theory Relat. Fields 145(1-2), 211-267, 2009).

Entropy Stable Staggered Grid Spectral Collocation for the Burgers' and Compressible Navier-Stokes Equations

Science.gov (United States)

Carpenter, Mark H.; Parsani, Matteo; Fisher, Travis C.; Nielsen, Eric J.

2015-01-01

Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for Burgers' and the compressible Navier-Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [1, 2], extends the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to a combination of tensor product Legendre-Gauss (LG) and LGL points. The new semi-discrete operators discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality for both Burgers' and the compressible Navier-Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly to implement. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinearly stability proof for the compressible Navier-Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).

Analysis of wall shear stress around a competitive swimmer using 3D Navier-Stokes equations in CFD.

Science.gov (United States)

Popa, C V; Zaidi, H; Arfaoui, A; Polidori, G; Taiar, R; Fohanno, S

2011-01-01

This paper deals with the flow dynamics around a competitive swimmer during underwater glide phases occurring at the start and at every turn. The influence of the head position, namely lifted up, aligned and lowered, on the wall shear stress and the static pressure distributions is analyzed. The problem is considered as 3D and in steady hydrodynamic state. Three velocities (1.4 m/s, 2.2 m/s and 3.1 m/s) that correspond to inter-regional, national and international swimming levels are studied. The flow around the swimmer is assumed turbulent. The Reynolds-averaged Navier-Stokes (RANS) equations are solved with the standard k-ω turbulent model by using the CFD (computational fluid dynamics) numerical method based on a volume control approach. Numerical simulations are carried out with the ANSYS FLUENT® CFD code. The results show that the wall shear stress increases with the velocity and consequently the drag force opposing the movement of the swimmer increases as well. Also, high wall shear stresses are observed in the areas where the body shape, globally rigid in form, presents complex surface geometries such as the head, shoulders, buttocks, heel and chest.

On three-dimensional incompressible Navier-Stokes fluid on cantor sets in spherical Cantor type co-ordinate system

Directory of Open Access Journals (Sweden)

Meng Zhi-Jun

2016-01-01

Full Text Available This paper addresses the systems of the incompressible Navier-Stokes equations on Cantor sets without the external force involving the fractal heat-conduction problem vial local fractional derivative. The spherical Cantor type co-ordinate method is used to transfer the incompressible Navier-Stokes equation from the Cantorian co-ordinate system into the spherical Cantor type co-ordinate system.

Stability result for Navier-Stokes equations with entropy transport

Czech Academy of Sciences Publication Activity Database

Michálek, Martin

2015-01-01

Roč. 17, č. 2 (2015), s. 279-285 ISSN 1422-6928 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : compressible Navier-Stokes system * entropy transport * effective viscous flux Subject RIV: BA - General Mathematics Impact factor: 1.023, year: 2015 http://link.springer.com/article/10.1007%2Fs00021-015-0205-x

Research on the optimal dynamical systems of three-dimensional Navier-Stokes equations based on weighted residual

Science.gov (United States)

Peng, NaiFu; Guan, Hui; Wu, ChuiJie

2016-04-01

In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.

Newton-like methods for Navier-Stokes solution

Science.gov (United States)

Qin, N.; Xu, X.; Richards, B. E.

1992-12-01

The paper reports on Newton-like methods called SFDN-alpha-GMRES and SQN-alpha-GMRES methods that have been devised and proven as powerful schemes for large nonlinear problems typical of viscous compressible Navier-Stokes solutions. They can be applied using a partially converged solution from a conventional explicit or approximate implicit method. Developments have included the efficient parallelization of the schemes on a distributed memory parallel computer. The methods are illustrated using a RISC workstation and a transputer parallel system respectively to solve a hypersonic vortical flow.

Generalized extended Navier-Stokes theory

DEFF Research Database (Denmark)

Hansen, J. S.; Daivis, Peter J.; Dyre, Jeppe C.

2013-01-01

in molecular fluids. To discuss these phenomena in detail, molecular dynamics simulations of molecular chlorine are performed for three different state points. In general, the theory captures the behavior for small wavevector and frequencies as expected. For example, in the hydrodynamic regime......The extended Navier-Stokes theory accounts for the coupling between the translational and rotational molecular degrees of freedom. In this paper, we generalize this theory to non-zero frequencies and wavevectors, which enables a new study of spatio-temporal correlation phenomena present...... and for molecular fluids with small moment of inertia like chlorine, the theory predicts that the longitudinal and transverse intrinsic angular velocity correlation functions are almost identical, which is also seen in the molecular dynamics simulations. However, the theory fails at large wavevector and frequencies...

Generalized extended Navier-Stokes theory: Multiscale spin relaxation in molecular fluids

DEFF Research Database (Denmark)

Hansen, Jesper Schmidt

2013-01-01

This paper studies the relaxation of the molecular spin angular velocity in the framework of generalized extended Navier-Stokes theory. Using molecular dynamics simulations, it is shown that for uncharged diatomic molecules the relaxation time decreases with increasing molecular moment of inertia...

Navier-Stokes-Voigt Equations with Memory in 3D Lacking Instantaneous Kinematic Viscosity

Science.gov (United States)

Di Plinio, Francesco; Giorgini, Andrea; Pata, Vittorino; Temam, Roger

2018-04-01

We consider a Navier-Stokes-Voigt fluid model where the instantaneous kinematic viscosity has been completely replaced by a memory term incorporating hereditary effects, in presence of Ekman damping. Unlike the classical Navier-Stokes-Voigt system, the energy balance involves the spatial gradient of the past history of the velocity rather than providing an instantaneous control on the high modes. In spite of this difficulty, we show that our system is dissipative in the dynamical systems sense and even possesses regular global and exponential attractors of finite fractal dimension. Such features of asymptotic well-posedness in absence of instantaneous high modes dissipation appear to be unique within the realm of dynamical systems arising from fluid models.

The Navier-Stokes equations on a bounded domain

International Nuclear Information System (INIS)

Scheffer, V.

1980-01-01

Suppose U is an open bounded subset of 3-space such that the boundary of U has Lebesgue measure zero. Then for any initial condition with finite kinetic energy we can find a global (i.e. for all time) weak solution u to the time dependent Navier-Stokes equations of incompressible fluid flow in U such that the curl of u is continuous outside a locally closed set whose 5/3 dimensional Hausdorff measure is finite. (orig.)

An efficient numerical technique for solving navier-stokes equations for rotating flows

International Nuclear Information System (INIS)

Haroon, T.; Shah, T.M.

2000-01-01

This paper simulates an industrial problem by solving compressible Navier-Stokes equations. The time-consuming tri-angularization process of a large-banded matrix, performed by memory economical Frontal Technique. This scheme successfully reduces the time for I/O operations even for as large as (40, 000 x 40, 000) matrix. Previously, this industrial problem can solved by using modified Newton's method with Gaussian elimination technique for the large matrix. In the present paper, the proposed Frontal Technique is successfully used, together with Newton's method, to solve compressible Navier-Stokes equations for rotating cylinders. By using the Frontal Technique, the method gives the solution within reasonably acceptance computational time. Results are compared with the earlier works done, and found computationally very efficient. Some features of the solution are reported here for the rotating machines. (author)

Advances in Spectral Methods for UQ in Incompressible Navier-Stokes Equations

KAUST Repository

Le Maitre, Olivier

2014-01-06

In this talk, I will present two recent contributions to the development of efficient methodologies for uncertainty propagation in the incompressible Navier-Stokes equations. The first one concerns the reduced basis approximation of stochastic steady solutions, using Proper Generalized Decompositions (PGD). An Arnoldi problem is projected to obtain a low dimensional Galerkin problem. The construction then amounts to the resolution of a sequence of uncoupled deterministic Navier-Stokes like problem and simple quadratic stochastic problems, followed by the resolution of a low-dimensional coupled quadratic stochastic problem, with a resulting complexity which has to be contrasted with the dimension of the whole Galerkin problem for classical spectral approaches. An efficient algorithm for the approximation of the stochastic pressure field is also proposed. Computations are presented for uncertain viscosity and forcing term to demonstrate the effectiveness of the reduced method. The second contribution concerns the computation of stochastic periodic solutions to the Navier-Stokes equations. The objective is to circumvent the well-known limitation of spectral methods for long-time integration. We propose to directly determine the stochastic limit-cycles through the definition of its stochastic period and an initial condition over the cycle. A modified Newton method is constructed to compute iteratively both the period and initial conditions. Owing to the periodic character of the solution, and by introducing an appropriate time-scaling, the solution can be approximated using low-degree polynomial expansions with large computational saving as a result. The methodology is illustrated for the von-Karman flow around a cylinder with stochastic inflow conditions.

Euler and Navier-Stokes equations on the hyperbolic plane.

Science.gov (United States)

Khesin, Boris; Misiolek, Gerard

2012-11-06

We show that nonuniqueness of the Leray-Hopf solutions of the Navier-Stokes equation on the hyperbolic plane (2) observed by Chan and Czubak is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on (n) whenever n ≥ 3. We also describe the corresponding general Hamiltonian framework of hydrodynamics on complete Riemannian manifolds, which includes the hyperbolic setting.

Advances in Spectral Methods for UQ in Incompressible Navier-Stokes Equations

KAUST Repository

Le Maitre, Olivier

2014-01-01

In this talk, I will present two recent contributions to the development of efficient methodologies for uncertainty propagation in the incompressible Navier-Stokes equations. The first one concerns the reduced basis approximation of stochastic steady solutions, using Proper Generalized Decompositions (PGD). An Arnoldi problem is projected to obtain a low dimensional Galerkin problem. The construction then amounts to the resolution of a sequence of uncoupled deterministic Navier-Stokes like problem and simple quadratic stochastic problems, followed by the resolution of a low-dimensional coupled quadratic stochastic problem, with a resulting complexity which has to be contrasted with the dimension of the whole Galerkin problem for classical spectral approaches. An efficient algorithm for the approximation of the stochastic pressure field is also proposed. Computations are presented for uncertain viscosity and forcing term to demonstrate the effectiveness of the reduced method. The second contribution concerns the computation of stochastic periodic solutions to the Navier-Stokes equations. The objective is to circumvent the well-known limitation of spectral methods for long-time integration. We propose to directly determine the stochastic limit-cycles through the definition of its stochastic period and an initial condition over the cycle. A modified Newton method is constructed to compute iteratively both the period and initial conditions. Owing to the periodic character of the solution, and by introducing an appropriate time-scaling, the solution can be approximated using low-degree polynomial expansions with large computational saving as a result. The methodology is illustrated for the von-Karman flow around a cylinder with stochastic inflow conditions.

Hybrid immersed boundary method for airfoils with a trailing-edge flap

DEFF Research Database (Denmark)

Zhu, Wei Jun; Behrens, Tim; Shen, Wen Zhong

2013-01-01

In this paper, a hybrid immersed boundary technique has been developed for simulating turbulent flows past airfoils with moving trailing-edge flaps. Over the main fixed part of the airfoil, the equations are solved using a standard body-fitted finite volume technique, whereas the moving trailing......-edge flap is simulated using the immersed boundary method on a curvilinear mesh. An existing in-house-developed flow solver is employed to solve the incompressible Reynolds-Averaged Navier-Stokes equations together with the k-ω turbulence model. To achieve consistent wall boundary conditions at the immersed...... boundaries the k-ωturbulence model is modified and adapted to the local conditions associated with the immersed boundary method. The obtained results show that the hybrid approach is an efficient and accurate method for solving turbulent flows past airfoils with a trailing-edge flap and that flow control...

Shock-wave structure based on the Navier-Stokes-Fourier equations

Science.gov (United States)

Uribe, F. J.; Velasco, R. M.

2018-04-01

We use the Navier-Stokes-Fourier constitutive equations to study plane shock waves in dilute gases. It is shown that the experimental information on the normalized density profiles can be fit by using the so-called soft sphere model, in which the viscosity and thermal conductivity are proportional to a power of the temperature.

Robustness of strong solutions to the compressible Navier-Stokes system

Czech Academy of Sciences Publication Activity Database

Bella, P.; Feireisl, Eduard; Jin, B.J.; Novotný, A.

2015-01-01

Roč. 362, 1-2 (2015), s. 281-303 ISSN 0025-5831 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible Navier-Stokes system * smooth solution * stability Subject RIV: BA - General Mathematics Impact factor: 1.366, year: 2015 http://link.springer.com/article/10.1007%2Fs00208-014-1119-2

A convergent numerical method for the Navier-Stokes-Fourier system

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Karper, T.; Novotný, A.

2016-01-01

Roč. 36, č. 4 (2016), s. 1477-1535 ISSN 0272-4979 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * Crouzeix-Raviart finite element method * finite volume method Subject RIV: BA - General Mathematics Impact factor: 1.703, year: 2016 http://imajna.oxfordjournals.org/content/36/4/1477

Modelling of arc jet plasma flow in transitional regime by Navier Stokes and state-to-state coupling

International Nuclear Information System (INIS)

Alexandrova, T.; Izrar, B.; Lino da Silva, M.; Dudeck, M.

2005-01-01

The combination of 2D Navier-Stokes and state-to-state approaches has been used to describe the air plasma flow in an arc-jet. The gas dynamic parameters were calculated in Navier-Stokes approximation in a steady state description without chemical reaction and vibrational exchanges. And then, the set of equations of vibrational level densities and atomic species densities was locally solved. Experimental validations have been performed

The direct Discontinuous Galerkin method for the compressible Navier-Stokes equations on arbitrary grids

Science.gov (United States)

Yang, Xiaoquan; Cheng, Jian; Liu, Tiegang; Luo, Hong

2015-11-01

The direct discontinuous Galerkin (DDG) method based on a traditional discontinuous Galerkin (DG) formulation is extended and implemented for solving the compressible Navier-Stokes equations on arbitrary grids. Compared to the widely used second Bassi-Rebay (BR2) scheme for the discretization of diffusive fluxes, the DDG method has two attractive features: first, it is simple to implement as it is directly based on the weak form, and therefore there is no need for any local or global lifting operator; second, it can deliver comparable results, if not better than BR2 scheme, in a more efficient way with much less CPU time. Two approaches to perform the DDG flux for the Navier- Stokes equations are presented in this work, one is based on conservative variables, the other is based on primitive variables. In the implementation of the DDG method for arbitrary grid, the definition of mesh size plays a critical role as the formation of viscous flux explicitly depends on the geometry. A variety of test cases are presented to demonstrate the accuracy and efficiency of the DDG method for discretizing the viscous fluxes in the compressible Navier-Stokes equations on arbitrary grids.

Local strong solutions to the stochastic compressible Navier-Stokes system

Czech Academy of Sciences Publication Activity Database

Breit, D.; Feireisl, Eduard; Hofmanová, M.

2018-01-01

Roč. 43, č. 2 (2018), s. 313-345 ISSN 0360-5302 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible fluids * local strong solutions * Navier-Stokes system Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.608, year: 2016 https://www.tandfonline.com/doi/full/10.1080/03605302.2018.1442476

Inviscid incompressible limits of the full Navier-Stokes-Fourier system

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Novotný, A.

2013-01-01

Roč. 321, č. 3 (2013), s. 605-628 ISSN 0010-3616 R&D Projects: GA ČR GA201/09/0917 Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * inviscid limit * incompressible limit Subject RIV: BA - General Mathematics Impact factor: 1.901, year: 2013 http://link.springer.com/article/10.1007%2Fs00220-013-1691-4

Regularity of the 3D Navier-Stokes equations with viewpoint of 2D flow

Science.gov (United States)

Bae, Hyeong-Ohk

2018-04-01

The regularity of 2D Navier-Stokes flow is well known. In this article we study the relationship of 3D and 2D flow, and the regularity of the 3D Naiver-Stokes equations with viewpoint of 2D equations. We consider the problem in the Cartesian and in the cylindrical coordinates.

A unified approach to determining forms for the 2D Navier-Stokes equations -- the general interpolants case

International Nuclear Information System (INIS)

Foias, C; Jolly, M S; Kravchenko, R; Titi, E S

2014-01-01

It is shown that the long-time dynamics (the global attractor) of the 2D Navier-Stokes system is embedded in the long-time dynamics of an ordinary differential equation, called a determining form, in a space of trajectories which is isomorphic to C b 1 (R;R N ) for sufficiently large N depending on the physical parameters of the Navier-Stokes equations. A unified approach is presented, based on interpolant operators constructed from various determining parameters for the Navier-Stokes equations, namely, determining nodal values, Fourier modes, finite volume elements, finite elements, and so on. There are two immediate and interesting consequences of this unified approach. The first is that the constructed determining form has a Lyapunov function, and thus its solutions converge to the set of steady states of the determining form as the time goes to infinity. The second is that these steady states of the determining form can be uniquely identified with the trajectories in the global attractor of the Navier-Stokes system. It should be added that this unified approach is general enough that it applies, in an almost straightforward manner, to a whole class of dissipative dynamical systems. Bibliography: 23 titles

An introduction to the mathematical theory of the Navier-Stokes equations

CERN Document Server

Galdi, Giovanni P

1994-01-01

Undoubtedly, the Navier-Stokes equations are of basic importance within the context of modern theory of partial differential equations. Although the range of their applicability to concrete problems has now been clearly recognised to be limited, as my dear friend and bright colleague K.R. Ra­ jagopal has showed me by several examples during the past six years, the mathematical questions that remain open are of such a fascinating and challenging nature that analysts and applied mathematicians cannot help being attracted by them and trying to contribute to their resolution. Thus, it is not a coincidence that over the past ten years more than seventy sig­ nificant research papers have appeared concerning the well-posedness of boundary and initial-boundary value problems. In this monograph I shall perform a systematic and up-to-date investiga­ tion of the fundamental properties of the Navier-Stokes equations, including existence, uniqueness, and regularity of solutions and, whenever the region of flow is unbou...

Boltzmann equation and hydrodynamics beyond Navier-Stokes.

Science.gov (United States)

Bobylev, A V

2018-04-28

We consider in this paper the problem of derivation and regularization of higher (in Knudsen number) equations of hydrodynamics. The author's approach based on successive changes of hydrodynamic variables is presented in more detail for the Burnett level. The complete theory is briefly discussed for the linearized Boltzmann equation. It is shown that the best results in this case can be obtained by using the 'diagonal' equations of hydrodynamics. Rigorous estimates of accuracy of the Navier-Stokes and Burnett approximations are also presented.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

The interior regularity of pressure associated with a weak solution to the Navier-Stokes equations with the Navier-type boundary conditions

Czech Academy of Sciences Publication Activity Database

Neustupa, Jiří; Al Baba, Hind

2018-01-01

Roč. 463, č. 1 (2018), s. 222-234 ISSN 0022-247X R&D Projects: GA ČR(CZ) GA17-01747S Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * Navier-type boundary conditions * interior regularity Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 https://www.sciencedirect.com/science/article/pii/S0022247X18302233?via%3Dihub

Estudio comparativo de flujo de fluido a través de una placa de orificio usando las ecuaciones de Stokes y de Navier-Stokes

Directory of Open Access Journals (Sweden)

Miryam Lucía Guerra-Mazo

2016-05-01

Full Text Available Presenta los resultados de la comparación entre las ecuaciones de Stokes y de Navier-Stokes para la simulación del flujo de agua líquida, a condiciones atmosféricas, a través de una placa orificio concéntrica. A partir de los datos experimentales que fueron tomados en el banco de fluidos, se evaluaron las simulaciones de ambas ecuaciones, usando el software libre Freefem++cs, que se basa en el método de los elementos finitos; las variables evaluadas son velocidad y presión en un intervalo de tiempo. Al analizar los resultados obtenidos con las simulaciones y comparar con los datos experimentales se encontró que las ecuaciones de Navier-Stokes representan mejor el sistema que la ecuación de Stokes.

Developpement of a numerical method for Navier-Stokes equations in anelastic approximation: application to Rayleigh-Taylor instabilities

International Nuclear Information System (INIS)

Hammouch, Z.

2012-01-01

The 'anelastic' approximation allows us to filter the acoustic waves thanks to an asymptotic development of the Navier-Stokes equations, so increasing the averaged time step, during the numerical simulation of hydrodynamic instabilities development. So, the anelastic equations for a two fluid mixture in case of Rayleigh-Taylor instability are established.The linear stability of Rayleigh-Taylor flow is studied, for the first time, for perfect fluids in the anelastic approximation. We define the Stokes problem resulting from Navier-Stokes equations without the non linear terms (a part of the buoyancy is considered); the ellipticity is demonstrated, the Eigenmodes and the invariance related to the pressure are detailed. The Uzawa's method is extended to the anelastic approximation and shows the decoupling speeds in 3D, the particular case k = 0 and the spurious modes of pressure. Passing to multi-domain allowed to establish the transmission conditions.The algorithms and the implementation in the existing program are validated by comparing the Uzawa's operator in Fortran and Mathematica languages, to an experiment with incompressible fluids and results from anelastic and compressible numerical simulations. The study of the influence of the initial stratification of both fluids on the development of the Rayleigh-Taylor instability is initiated. (author) [fr

Three-Dimensional Navier-Stokes Calculations Using the Modified Space-Time CESE Method

Science.gov (United States)

Chang, Chau-lyan

2007-01-01

The space-time conservation element solution element (CESE) method is modified to address the robustness issues of high-aspect-ratio, viscous, near-wall meshes. In this new approach, the dependent variable gradients are evaluated using element edges and the corresponding neighboring solution elements while keeping the original flux integration procedure intact. As such, the excellent flux conservation property is retained and the new edge-based gradients evaluation significantly improves the robustness for high-aspect ratio meshes frequently encountered in three-dimensional, Navier-Stokes calculations. The order of accuracy of the proposed method is demonstrated for oblique acoustic wave propagation, shock-wave interaction, and hypersonic flows over a blunt body. The confirmed second-order convergence along with the enhanced robustness in handling hypersonic blunt body flow calculations makes the proposed approach a very competitive CFD framework for 3D Navier-Stokes simulations.

Numerical resolution of Navier-Stokes equations coupled to the heat equation

International Nuclear Information System (INIS)

Zenouda, Jean-Claude

1970-08-01

The author proves a uniqueness theorem for the time dependent Navier-Stokes equations coupled with heat flow in the two-dimensional case. He studies stability and convergence of several finite - difference schemes to solve these equations. Numerical experiments are done in the case of a square domain. (author) [fr

Introduction to turbulence modelling: Applications of Reynolds Averaged Navier Stokes Equations (RANSE) to engineering problems

International Nuclear Information System (INIS)

Laurence, D.

1997-01-01

The k-ε model and Reynolds stress transport model are set out in a few words. Limitations of models are shown, particularly for turbulence generation in the turbulent viscosity context, and, more generally, the uncertainties and miscellaneous changes made to the dissipation equation. The performances of models are then compared, using results of the three latest ERCOFTA/IAHR workshops. It is shown that algebraic constraints which can be derived exactly by assuming asymptotic limits (rapid distortion, homogeneous shear at infinite time, 2D turbulence) have inhibited a better tuning of the models for real life flow where these limits are not encountered. A more pragmatic approach could be taken by allowing the constants to be functions of invariant parameters. But these functions, making the models non-linear, can lead to bifurcations or instability. One essential parameter is the distance to the wall, which recent models have tried to eliminate, although this parameter appears indirectly through the Poisson equation for the fluctuating pressure. A possible indirect model is the elliptic relaxation. Progress was recently achieved in near-wall low Re modelling, but these advances do not always result in benefits to industry since only the 'wall function' approaches can be used in the high Re, 3D flows that we need to study. With the knowledge gained from near-wall modelling, it might be profitable to revisit the 'wall functions' devised 20 years ago. (author)

Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations

Directory of Open Access Journals (Sweden)

Junbai Ren

2014-01-01

Full Text Available This paper is concerned with the large time behavior of the weak solutions for three-dimensional globally modified Navier-Stokes equations. With the aid of energy methods and auxiliary decay estimates together with Lp-Lq estimates of heat semigroup, we derive the optimal upper and lower decay estimates of the weak solutions for the globally modified Navier-Stokes equations as C1(1+t-3/4≤uL2≤C2(1+t-3/4,  t>1. The decay rate is optimal since it coincides with that of heat equation.

Navier-Stokes computer

International Nuclear Information System (INIS)

Hayder, M.E.

1988-01-01

A new scientific supercomputer, known as the Navier-Stokes Computer (NSC), has been designed. The NSC is a multi-purpose machine, and for applications in the field of computational fluid dynamics (CFD), this supercomputer is expected to yield a computational speed far exceeding that of the present-day super computers. This computer has a few very powerful processors (known as nodes) connected by an internodal network. There are three versions of the NSC nodes: micro-, mini- and full-node. The micro-node was developed to prove, to demonstrate and to refine the key architectural features of the NSC. Architectures of the two recent versions of the NSC nodes are presented, with the main focus on the full-node. At a clock speed of 20 MHz, the mini- and the full-node have peak computational speeds of 200 and 640 MFLOPS, respectively. The full-node is the final version for the NSC nodes and an NSC is expected to have 128 full-nodes. To test the suitability of different algorithms on the NSC architecture, an NSC simulator was developed. Some of the existing computational fluid dynamics codes were placed on this simulator to determine important and relevant issues relating to the efficient use of the NSC architecture

The interior regularity of pressure associated with a weak solution to the Navier-Stokes equations with the Navier-type boundary conditions

Czech Academy of Sciences Publication Activity Database

Neustupa, Jiří; Al Baba, Hind

2018-01-01

Roč. 463, č. 1 (2018), s. 222-234 ISSN 0022-247X R&D Projects: GA ČR(CZ) GA17-01747S Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * Navier-type boundary conditions * interior regularity Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 https://www. science direct.com/ science /article/pii/S0022247X18302233?via%3Dihub

Non-linear instability analysis of the two-dimensional Navier-Stokes equation: The Taylor-Green vortex problem

Science.gov (United States)

Sengupta, Tapan K.; Sharma, Nidhi; Sengupta, Aditi

2018-05-01

An enstrophy-based non-linear instability analysis of the Navier-Stokes equation for two-dimensional (2D) flows is presented here, using the Taylor-Green vortex (TGV) problem as an example. This problem admits a time-dependent analytical solution as the base flow, whose instability is traced here. The numerical study of the evolution of the Taylor-Green vortices shows that the flow becomes turbulent, but an explanation for this transition has not been advanced so far. The deviation of the numerical solution from the analytical solution is studied here using a high accuracy compact scheme on a non-uniform grid (NUC6), with the fourth-order Runge-Kutta method. The stream function-vorticity (ψ, ω) formulation of the governing equations is solved here in a periodic square domain with four vortices at t = 0. Simulations performed at different Reynolds numbers reveal that numerical errors in computations induce a breakdown of symmetry and simultaneous fragmentation of vortices. It is shown that the actual physical instability is triggered by the growth of disturbances and is explained by the evolution of disturbance mechanical energy and enstrophy. The disturbance evolution equations have been traced by looking at (a) disturbance mechanical energy of the Navier-Stokes equation, as described in the work of Sengupta et al., "Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003), and (b) the creation of rotationality via the enstrophy transport equation in the work of Sengupta et al., "Diffusion in inhomogeneous flows: Unique equilibrium state in an internal flow," Comput. Fluids 88, 440-451 (2013).

KNOW-BLADE task-4 report. Navier-Stokes aeroelasticity

Energy Technology Data Exchange (ETDEWEB)

Politis, E.S.; Nikolaou, I.G.; Chaviaropoulos, P.K.; Bertagnolio, F.; Soerensen, N.N.; Johansen, J.

2005-01-01

The problem of the aeroelastic stability of wind turbine blades is addressed in this report by advancing the aerodynamic modelling in the beam element type codes from the engineering-type empirical models to unsteady, 2D or 3D, Navier-Stokes solvers. In this project, structural models for the full wind turbine blade have been combined with 2D and 3D unsteady Navier-Stokes solvers. The relative disadvantage of the quasi-3D approach (where the elastic solver is coupled with a 2D Navier-Stokes solver) is its inability to model induced flow. The lack of a validation test case did not allow for quantitative comparisons with experimental data to be carried out; instead the results of the advanced aeroelastic tools are qualitatively cross-compared. All investigated methods predicted qualitatively similar results. They all resulted in positive aerodynamic damping values for the flap mode, in a decrease in damping with the increase of wind speeds and in a minimum value for the damping for wind speed around 15{approx}m/s. The eigenvalue analyses resulted in steeper distributions for this mode. The agreement in aerodynamic damping decrease with the increase of wind speed is also observed in the distributions for the lead-lag mode. In perspective, the uncoupled, linear method results in higher values of aerodynamic damping compared to the 3D aeroelastic tool. The quasi-3D tool results in lower aerodynamic damping values in the higher wind speeds and in lower damping values in the lower wind speed regime. Apart from the computations for the full blade, 2D computations for the so-called 'typical section' have been carried out. The 2D aeroelastic tools resulted in similar aerodynamic damping values. Qualitative agreement was better for the lead-lag mode. The presence of roughness tapes has a small, rather negligible impact on aeroelastic stability as depicted by the results of both aeroelastic tools. On the other hand, in conformity to the inability of the adopted

SIERRA/Aero Theory Manual Version 4.44

Energy Technology Data Exchange (ETDEWEB)

Sierra Thermal/Fluid Team

2017-04-01

SIERRA/Aero is a two and three dimensional, node-centered, edge-based finite volume code that approximates the compressible Navier-Stokes equations on unstructured meshes. It is applicable to inviscid and high Reynolds number laminar and turbulent flows. Currently, two classes of turbulence models are provided: Reynolds Averaged Navier-Stokes (RANS) and hybrid methods such as Detached Eddy Simulation (DES). Large Eddy Simulation (LES) models are currently under development. The gas may be modeled either as ideal, or as a non-equilibrium, chemically reacting mixture of ideal gases. This document describes the mathematical models contained in the code, as well as certain implementation details. First, the governing equations are presented, followed by a description of the spatial discretization. Next, the time discretization is described, and finally the boundary conditions. Throughout the document, SIERRA/ Aero is referred to simply as Aero for brevity.

SIERRA/Aero Theory Manual Version 4.46.

Energy Technology Data Exchange (ETDEWEB)

Sierra Thermal/Fluid Team

2017-09-01

SIERRA/Aero is a two and three dimensional, node-centered, edge-based finite volume code that approximates the compressible Navier-Stokes equations on unstructured meshes. It is applicable to inviscid and high Reynolds number laminar and turbulent flows. Currently, two classes of turbulence models are provided: Reynolds Averaged Navier-Stokes (RANS) and hybrid methods such as Detached Eddy Simulation (DES). Large Eddy Simulation (LES) models are currently under development. The gas may be modeled either as ideal, or as a non-equilibrium, chemically reacting mixture of ideal gases. This document describes the mathematical models contained in the code, as well as certain implementation details. First, the governing equations are presented, followed by a description of the spatial discretization. Next, the time discretization is described, and finally the boundary conditions. Throughout the document, SIERRA/ Aero is referred to simply as Aero for brevity.

Decay Properties of Axially Symmetric D-Solutions to the Steady Navier-Stokes Equations

Science.gov (United States)

Weng, Shangkun

2018-03-01

We investigate the decay properties of smooth axially symmetric D-solutions to the steady Navier-Stokes equations. The achievements of this paper are two folds. One is improved decay rates of u_{θ } and \

The Actuator Surface Model: A New Navier-Stokes Based Model for Rotor Computations

DEFF Research Database (Denmark)

Shen, Wen Zhong; Zhang, J.H.; Sørensen, Jens Nørkær

2009-01-01

This paper presents a new numerical technique for simulating two-dimensional wind turbine flow. The method, denoted as the 2D actuator surface technique, consists of a two-dimensional Navier-Stokes solver in which the pressure distribution is represented by body forces that are distributed along ....... In the last part, the actuator surface technique is applied to compute the flow past a two-bladed vertical axis wind turbine equipped with NACA 0012 airfoils. Comparisons with experimental data show an encouraging performance of the method.......This paper presents a new numerical technique for simulating two-dimensional wind turbine flow. The method, denoted as the 2D actuator surface technique, consists of a two-dimensional Navier-Stokes solver in which the pressure distribution is represented by body forces that are distributed along...

Turbomachinery Heat Transfer and Loss Modeling for 3D Navier-Stokes Codes

Science.gov (United States)

DeWitt, Kenneth; Ameri, Ali

2005-01-01

This report's contents focus on making use of NASA Glenn on-site computational facilities,to develop, validate, and apply models for use in advanced 3D Navier-Stokes Computational Fluid Dynamics (CFD) codes to enhance the capability to compute heat transfer and losses in turbomachiney.

On Stationary Navier-Stokes Flows Around a Rotating Obstacle in Two-Dimensions

Science.gov (United States)

Higaki, Mitsuo; Maekawa, Yasunori; Nakahara, Yuu

2018-05-01

We study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of the obstacle and the given exterior force are sufficiently small.

Numerics made easy: solving the Navier-Stokes equation for arbitrary channel cross-sections using Microsoft Excel.

Science.gov (United States)

Richter, Christiane; Kotz, Frederik; Giselbrecht, Stefan; Helmer, Dorothea; Rapp, Bastian E

2016-06-01

The fluid mechanics of microfluidics is distinctively simpler than the fluid mechanics of macroscopic systems. In macroscopic systems effects such as non-laminar flow, convection, gravity etc. need to be accounted for all of which can usually be neglected in microfluidic systems. Still, there exists only a very limited selection of channel cross-sections for which the Navier-Stokes equation for pressure-driven Poiseuille flow can be solved analytically. From these equations, velocity profiles as well as flow rates can be calculated. However, whenever a cross-section is not highly symmetric (rectangular, elliptical or circular) the Navier-Stokes equation can usually not be solved analytically. In all of these cases, numerical methods are required. However, in many instances it is not necessary to turn to complex numerical solver packages for deriving, e.g., the velocity profile of a more complex microfluidic channel cross-section. In this paper, a simple spreadsheet analysis tool (here: Microsoft Excel) will be used to implement a simple numerical scheme which allows solving the Navier-Stokes equation for arbitrary channel cross-sections.

A nonlinear relaxation/quasi-Newton algorithm for the compressible Navier-Stokes equations

Science.gov (United States)

Edwards, Jack R.; Mcrae, D. S.

1992-01-01

A highly efficient implicit method for the computation of steady, two-dimensional compressible Navier-Stokes flowfields is presented. The discretization of the governing equations is hybrid in nature, with flux-vector splitting utilized in the streamwise direction and central differences with flux-limited artificial dissipation used for the transverse fluxes. Line Jacobi relaxation is used to provide a suitable initial guess for a new nonlinear iteration strategy based on line Gauss-Seidel sweeps. The applicability of quasi-Newton methods as convergence accelerators for this and other line relaxation algorithms is discussed, and efficient implementations of such techniques are presented. Convergence histories and comparisons with experimental data are presented for supersonic flow over a flat plate and for several high-speed compression corner interactions. Results indicate a marked improvement in computational efficiency over more conventional upwind relaxation strategies, particularly for flowfields containing large pockets of streamwise subsonic flow.

Implementation and analysis of a Navier-Stokes algorithm on parallel computers

Science.gov (United States)

Fatoohi, Raad A.; Grosch, Chester E.

1988-01-01

The results of the implementation of a Navier-Stokes algorithm on three parallel/vector computers are presented. The object of this research is to determine how well, or poorly, a single numerical algorithm would map onto three different architectures. The algorithm is a compact difference scheme for the solution of the incompressible, two-dimensional, time-dependent Navier-Stokes equations. The computers were chosen so as to encompass a variety of architectures. They are the following: the MPP, an SIMD machine with 16K bit serial processors; Flex/32, an MIMD machine with 20 processors; and Cray/2. The implementation of the algorithm is discussed in relation to these architectures and measures of the performance on each machine are given. The basic comparison is among SIMD instruction parallelism on the MPP, MIMD process parallelism on the Flex/32, and vectorization of a serial code on the Cray/2. Simple performance models are used to describe the performance. These models highlight the bottlenecks and limiting factors for this algorithm on these architectures. Finally, conclusions are presented.

Cell-Averaged discretization for incompressible Navier-Stokes with embedded boundaries and locally refined Cartesian meshes: a high-order finite volume approach

Science.gov (United States)

Bhalla, Amneet Pal Singh; Johansen, Hans; Graves, Dan; Martin, Dan; Colella, Phillip; Applied Numerical Algorithms Group Team

2017-11-01

We present a consistent cell-averaged discretization for incompressible Navier-Stokes equations on complex domains using embedded boundaries. The embedded boundary is allowed to freely cut the locally-refined background Cartesian grid. Implicit-function representation is used for the embedded boundary, which allows us to convert the required geometric moments in the Taylor series expansion (upto arbitrary order) of polynomials into an algebraic problem in lower dimensions. The computed geometric moments are then used to construct stencils for various operators like the Laplacian, divergence, gradient, etc., by solving a least-squares system locally. We also construct the inter-level data-transfer operators like prolongation and restriction for multi grid solvers using the same least-squares system approach. This allows us to retain high-order of accuracy near coarse-fine interface and near embedded boundaries. Canonical problems like Taylor-Green vortex flow and flow past bluff bodies will be presented to demonstrate the proposed method. U.S. Department of Energy, Office of Science, ASCR (Award Number DE-AC02-05CH11231).

Mathematical geophysics an introduction to rotating fluids and the Navier-Stokes equations

CERN Document Server

Chemin, Jean-Yves; Gallagher, Isabelle; Grenier, Emmanuel

2006-01-01

Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The Navier-Stokes equations are examined in both incompressible and rapidly rotating forms.

Reliability enhancement of Navier-Stokes codes through convergence acceleration

Science.gov (United States)

Merkle, Charles L.; Dulikravich, George S.

1995-01-01

Methods for enhancing the reliability of Navier-Stokes computer codes through improving convergence characteristics are presented. The improving of these characteristics decreases the likelihood of code unreliability and user interventions in a design environment. The problem referred to as a 'stiffness' in the governing equations for propulsion-related flowfields is investigated, particularly in regard to common sources of equation stiffness that lead to convergence degradation of CFD algorithms. Von Neumann stability theory is employed as a tool to study the convergence difficulties involved. Based on the stability results, improved algorithms are devised to ensure efficient convergence in different situations. A number of test cases are considered to confirm a correlation between stability theory and numerical convergence. The examples of turbulent and reacting flow are presented, and a generalized form of the preconditioning matrix is derived to handle these problems, i.e., the problems involving additional differential equations for describing the transport of turbulent kinetic energy, dissipation rate and chemical species. Algorithms for unsteady computations are considered. The extension of the preconditioning techniques and algorithms derived for Navier-Stokes computations to three-dimensional flow problems is discussed. New methods to accelerate the convergence of iterative schemes for the numerical integration of systems of partial differential equtions are developed, with a special emphasis on the acceleration of convergence on highly clustered grids.

Application of the implicit MacCormack scheme to the parabolized Navier-Stokes equations

Science.gov (United States)

Lawrence, J. L.; Tannehill, J. C.; Chaussee, D. S.

1984-01-01

MacCormack's implicit finite-difference scheme was used to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method for solving the PNS equations does not require the inversion of block tridiagonal systems of algebraic equations and permits the original explicit MacCormack scheme to be employed in those regions where implicit treatment is not needed. The advantages and disadvantages of the present adaptation are discussed in relation to those of the conventional Beam-Warming scheme for a flat plate boundary layer test case. Comparisons are made for accuracy, stability, computer time, computer storage, and ease of implementation. The present method was also applied to a second test case of hypersonic laminar flow over a 15% compression corner. The computed results compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.

On a model for the Navier-Stokes equations using magnetization variables

Science.gov (United States)

Pooley, Benjamin C.

2018-04-01

It is known that in a classical setting, the Navier-Stokes equations can be reformulated in terms of so-called magnetization variables w that satisfy Our main focus is the proof of global well-posedness in H 1 / 2 for a new variant of (1), where Pw is replaced by w in the second nonlinear term:

Multigrid and defect correction for the steady Navier-Stokes equations : application to aerodynamics

NARCIS (Netherlands)

Koren, B.

1991-01-01

Theoretical and expcrimental convergence results are presented for nonlinear multigrid and iterative defect correction applied to finite volume discretizations of the full, steady, 2D, compressible NavierStokes equations. lterative defect correction is introduced for circumventing the difficulty in

Incomplete augmented Lagrangian preconditioner for steady incompressible Navier-Stokes equations.

Science.gov (United States)

Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun

2013-01-01

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.

Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term

International Nuclear Information System (INIS)

Johnston, Hans; Liu Jianguo

2004-01-01

We present numerical schemes for the incompressible Navier-Stokes equations based on a primitive variable formulation in which the incompressibility constraint has been replaced by a pressure Poisson equation. The pressure is treated explicitly in time, completely decoupling the computation of the momentum and kinematic equations. The result is a class of extremely efficient Navier-Stokes solvers. Full time accuracy is achieved for all flow variables. The key to the schemes is a Neumann boundary condition for the pressure Poisson equation which enforces the incompressibility condition for the velocity field. Irrespective of explicit or implicit time discretization of the viscous term in the momentum equation the explicit time discretization of the pressure term does not affect the time step constraint. Indeed, we prove unconditional stability of the new formulation for the Stokes equation with explicit treatment of the pressure term and first or second order implicit treatment of the viscous term. Systematic numerical experiments for the full Navier-Stokes equations indicate that a second order implicit time discretization of the viscous term, with the pressure and convective terms treated explicitly, is stable under the standard CFL condition. Additionally, various numerical examples are presented, including both implicit and explicit time discretizations, using spectral and finite difference spatial discretizations, demonstrating the accuracy, flexibility and efficiency of this class of schemes. In particular, a Galerkin formulation is presented requiring only C 0 elements to implement

Navier-Stokes equations by the finite element method

International Nuclear Information System (INIS)

Portella, P.E.

1984-01-01

A computer program to solve the Navier-Stokes equations by using the Finite Element Method is implemented. The solutions variables investigated are stream-function/vorticity in the steady case and velocity/pressure in the steady state and transient cases. For steady state flow the equations are solved simultaneously by the Newton-Raphson method. For the time dependent formulation, a fractional step method is employed to discretize in time and artificial viscosity is used to preclude spurious oscilations in the solution. The element used is the three node triangle. Some numerical examples are presented and comparisons are made with applications already existent. (Author) [pt

Navier-Stokes Computations With One-Equation Turbulence Model for Flows Along Concave Wall Surfaces

Science.gov (United States)

Wang, Chi R.

2005-01-01

This report presents the use of a time-marching three-dimensional compressible Navier-Stokes equation numerical solver with a one-equation turbulence model to simulate the flow fields developed along concave wall surfaces without and with a downstream extension flat wall surface. The 3-D Navier- Stokes numerical solver came from the NASA Glenn-HT code. The one-equation turbulence model was derived from the Spalart and Allmaras model. The computational approach was first calibrated with the computations of the velocity and Reynolds shear stress profiles of a steady flat plate boundary layer flow. The computational approach was then used to simulate developing boundary layer flows along concave wall surfaces without and with a downstream extension wall. The author investigated the computational results of surface friction factors, near surface velocity components, near wall temperatures, and a turbulent shear stress component in terms of turbulence modeling, computational mesh configurations, inlet turbulence level, and time iteration step. The computational results were compared with existing measurements of skin friction factors, velocity components, and shear stresses of the developing boundary layer flows. With a fine computational mesh and a one-equation model, the computational approach could predict accurately the skin friction factors, near surface velocity and temperature, and shear stress within the flows. The computed velocity components and shear stresses also showed the vortices effect on the velocity variations over a concave wall. The computed eddy viscosities at the near wall locations were also compared with the results from a two equation turbulence modeling technique. The inlet turbulence length scale was found to have little effect on the eddy viscosities at locations near the concave wall surface. The eddy viscosities, from the one-equation and two-equation modeling, were comparable at most stream-wise stations. The present one

Actuator Line/Navier-Stokes Computations for Flows past the Yawed MEXICO Rotor

DEFF Research Database (Denmark)

Shen, Wen Zhong; Sørensen, Jens Nørkær; Yang, H.

2011-01-01

In the paper the Actuator Line/Navier-Stokes model has been used to simulate flows past the yawed MEXICO rotor. The computed loads as well as the velocity field behind the yawed rotor are compared to detailed pressure and PIV measurements which were carried out in the EU funded MEXICO project...

Status for the two-dimensional Navier-Stokes solver EllipSys2D

DEFF Research Database (Denmark)

Bertagnolio, F.; Sørensen, Niels N.; Johansen, J.

2001-01-01

This report sets up an evaluation of the two-dimensional Navier-Stokes solver EllipSys2D in its present state. This code is used for blade aerodynamics simulations in the Aeroelastic Design group at Risø. Two airfoils are investigated by computing theflow at several angles of attack ranging from...

Existence of weak solutions for compressible Navier-Stokes equations with entropy transport

Czech Academy of Sciences Publication Activity Database

Maltese, D.; Michálek, Martin; Mucha, P.; Novotný, A.; Pokorný, M.; Zatorska, E.

2016-01-01

Roč. 261, č. 8 (2016), s. 4448-4485 ISSN 0022-0396 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equations Subject RIV: BA - General Mathematics Impact factor: 1.988, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022039616301656

The Navier-Stokes-Fourier system: From weak solutions to numerical analysis

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard

2015-01-01

Roč. 35, č. 3 (2015), s. 185-193 ISSN 0174-4747 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * weak solution * mixed finite-volume finite-element numerical scheme Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/anly.2015.35.issue-3/anly-2014-1300/anly-2014-1300. xml

EXPONENTIAL ERGODICITY FOR STOCHASTIC BURGERS AND 2D NAVIER-STOKES EQUATIONS

CERN Document Server

Goldys, B

2004-01-01

It is shown that transition measures of the stochastic Navier-Stokes equation in dimension 2 converge exponentially fast to the corresponding invariant measures in the distance of total variation. As a corollary we obtain the existence of spectral gap for a related semigroup obtained by a sort of ground state trasformation. Analogous results are proved for the stochastic Burgers equation.

Development of Multigrid Methods for diffusion, Advection, and the incompressible Navier-Stokes Equations

Energy Technology Data Exchange (ETDEWEB)

Gjesdal, Thor

1997-12-31

This thesis discusses the development and application of efficient numerical methods for the simulation of fluid flows, in particular the flow of incompressible fluids. The emphasis is on practical aspects of algorithm development and on application of the methods either to linear scalar model equations or to the non-linear incompressible Navier-Stokes equations. The first part deals with cell centred multigrid methods and linear correction scheme and presents papers on (1) generalization of the method to arbitrary sized grids for diffusion problems, (2) low order method for advection-diffusion problems, (3) attempt to extend the basic method to advection-diffusion problems, (4) Fourier smoothing analysis of multicolour relaxation schemes, and (5) analysis of high-order discretizations for advection terms. The second part discusses a multigrid based on pressure correction methods, non-linear full approximation scheme, and papers on (1) systematic comparison of the performance of different pressure correction smoothers and some other algorithmic variants, low to moderate Reynolds numbers, and (2) systematic study of implementation strategies for high order advection schemes, high-Re flow. An appendix contains Fortran 90 data structures for multigrid development. 160 refs., 26 figs., 22 tabs.

Multilocality and fusion rules on the generalized structure functions in two-dimensional and three-dimensional Navier-Stokes turbulence.

Science.gov (United States)

Gkioulekas, Eleftherios

2016-09-01

Using the fusion-rules hypothesis for three-dimensional and two-dimensional Navier-Stokes turbulence, we generalize a previous nonperturbative locality proof to multiple applications of the nonlinear interactions operator on generalized structure functions of velocity differences. We call this generalization of nonperturbative locality to multiple applications of the nonlinear interactions operator "multilocality." The resulting cross terms pose a new challenge requiring a new argument and the introduction of a new fusion rule that takes advantage of rotational symmetry. Our main result is that the fusion-rules hypothesis implies both locality and multilocality in both the IR and UV limits for the downscale energy cascade of three-dimensional Navier-Stokes turbulence and the downscale enstrophy cascade and inverse energy cascade of two-dimensional Navier-Stokes turbulence. We stress that these claims relate to nonperturbative locality of generalized structure functions on all orders and not the term-by-term perturbative locality of diagrammatic theories or closure models that involve only two-point correlation and response functions.

Coupling Navier-stokes and Cahn-hilliard Equations in a Two-dimensional Annular flow Configuration

KAUST Repository

Vignal, Philippe; Sarmiento, Adel; Cortes, Adriano Mauricio; Dalcin, Lisandro; Calo, Victor M.

2015-01-01

In this work, we present a novel isogeometric analysis discretization for the Navier-Stokes- Cahn-Hilliard equation, which uses divergence-conforming spaces. Basis functions generated with this method can have higher-order continuity, and allow

Nonperturbative renormalization group study of the stochastic Navier-Stokes equation.

Science.gov (United States)

Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

2012-07-01

We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4-2ε of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's -5/3 law is, thus, recovered for ε = 2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the -5/3 law emerges in the presence of a saturation in the ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.

Random Attractors for the Stochastic Navier-Stokes Equations on the 2D Unit Sphere

Science.gov (United States)

Brzeźniak, Z.; Goldys, B.; Le Gia, Q. T.

2018-03-01

In this paper we prove the existence of random attractors for the Navier-Stokes equations on 2 dimensional sphere under random forcing irregular in space and time. We also deduce the existence of an invariant measure.

Investigation of Navier-Stokes Code Verification and Design Optimization

Science.gov (United States)

Vaidyanathan, Rajkumar

2004-01-01

With rapid progress made in employing computational techniques for various complex Navier-Stokes fluid flow problems, design optimization problems traditionally based on empirical formulations and experiments are now being addressed with the aid of computational fluid dynamics (CFD). To be able to carry out an effective CFD-based optimization study, it is essential that the uncertainty and appropriate confidence limits of the CFD solutions be quantified over the chosen design space. The present dissertation investigates the issues related to code verification, surrogate model-based optimization and sensitivity evaluation. For Navier-Stokes (NS) CFD code verification a least square extrapolation (LSE) method is assessed. This method projects numerically computed NS solutions from multiple, coarser base grids onto a freer grid and improves solution accuracy by minimizing the residual of the discretized NS equations over the projected grid. In this dissertation, the finite volume (FV) formulation is focused on. The interplay between the xi concepts and the outcome of LSE, and the effects of solution gradients and singularities, nonlinear physics, and coupling of flow variables on the effectiveness of LSE are investigated. A CFD-based design optimization of a single element liquid rocket injector is conducted with surrogate models developed using response surface methodology (RSM) based on CFD solutions. The computational model consists of the NS equations, finite rate chemistry, and the k-6 turbulence closure. With the aid of these surrogate models, sensitivity and trade-off analyses are carried out for the injector design whose geometry (hydrogen flow angle, hydrogen and oxygen flow areas and oxygen post tip thickness) is optimized to attain desirable goals in performance (combustion length) and life/survivability (the maximum temperatures on the oxidizer post tip and injector face and a combustion chamber wall temperature). A preliminary multi-objective optimization

Simulation of time-dependent free-surface Navier-Stokes flows

International Nuclear Information System (INIS)

Muldowney, G.P.

1989-01-01

Two numerical methods for simulation of time-dependent free-surface Navier-Stokes flows are developed. Both techniques are based on semi-implicit time advancement of the momentum equations, integral formulation of the spatial problem at each timestep, and spectral-element discretization to solve the resulting integral equation. Central to each algorithm is a boundary-specific solution step which permits the spatial treatment in two dimensions to be performed in O(N 3 ) operations per timestep despite the presence of deforming geometry. The first approach is a domain-integral formulation involving integrals over the entire flow domain of kernel functions which arise in time-differencing the Navier-Stokes equations. The second is a particular-solution formulation which replaces domain integration with an iterative scheme to generate particular velocity and pressure fields on individual elements, followed by a patching step to produce a particular solution continuous over the full domain. Two of the most difficult aspects of viscous free-surface flow simulations, namely time-dependent geometry and nontrivial boundary conditions, are well accommodated by these integral equation techniques. In addition the methods offer spectral accuracy in space and admit arbitrarily high-order discretization in time. For large-scale computations and/or long-term time advancement the domain-integral algorithm must be executed on a supercomputer to deliver results in reasonable processing time. A detailed simulation of gas liquid flow with full resolution of the free phase boundary requires approximately five CPU hours at 80 megaflops

Preconditioned conjugate gradient methods for the Navier-Stokes equations

Science.gov (United States)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1994-01-01

A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.

Quasiconservation laws for compressible three-dimensional Navier-Stokes flow.

Science.gov (United States)

Gibbon, J D; Holm, D D

2012-10-01

We formulate the quasi-Lagrangian fluid transport dynamics of mass density ρ and the projection q=ω·∇ρ of the vorticity ω onto the density gradient, as determined by the three-dimensional compressible Navier-Stokes equations for an ideal gas, although the results apply for an arbitrary equation of state. It turns out that the quasi-Lagrangian transport of q cannot cross a level set of ρ. That is, in this formulation, level sets of ρ (isopycnals) are impermeable to the transport of the projection q.

Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations

KAUST Repository

Gomez, Hector

2010-05-01

This paper is devoted to the numerical simulation of the Navier-Stokes-Korteweg equations, a phase-field model for water/water-vapor two-phase flows. We develop a numerical formulation based on isogeometric analysis that permits straightforward treatment of the higher-order partial-differential operator that represents capillarity. We introduce a new refinement methodology that desensitizes the numerical solution to the computational mesh and achieves mesh invariant solutions. Finally, we present several numerical examples in two and three dimensions that illustrate the effectiveness and robustness of our approach. © 2010 Elsevier B.V.

Incompressible Navier-Stokes equation from Einstein-Maxwell and Gauss-Bonnet-Maxwell theories

International Nuclear Information System (INIS)

Niu Chao; Tian Yu; Wu Xiaoning; Ling Yi

2012-01-01

The dual fluid description for a general cutoff surface at radius r=r c outside the horizon in the charged AdS black brane bulk space-time is investigated, first in the Einstein-Maxwell theory. Under the non-relativistic long-wavelength expansion with parameter ε, the coupled Einstein-Maxwell equations are solved up to O(ε 2 ). The incompressible Navier-Stokes equation with external force density is obtained as the constraint equation at the cutoff surface. For non-extremal black brane, the viscosity of the dual fluid is determined by the regularity of the metric fluctuation at the horizon, whose ratio to entropy density η/s is independent of both the cutoff r c and the black brane charge. Then, we extend our discussion to the Gauss-Bonnet-Maxwell case, where the incompressible Navier-Stokes equation with external force density is also obtained at a general cutoff surface. In this case, it turns out that the ratio η/s is independent of the cutoff r c but dependent on the charge density of the black brane.

An implicit turbulence model for low-Mach Roe scheme using truncated Navier-Stokes equations

Science.gov (United States)

Li, Chung-Gang; Tsubokura, Makoto

2017-09-01

The original Roe scheme is well-known to be unsuitable in simulations of turbulence because the dissipation that develops is unsatisfactory. Simulations of turbulent channel flow for Reτ = 180 show that, with the 'low-Mach-fix for Roe' (LMRoe) proposed by Rieper [J. Comput. Phys. 230 (2011) 5263-5287], the Roe dissipation term potentially equates the simulation to an implicit large eddy simulation (ILES) at low Mach number. Thus inspired, a new implicit turbulence model for low Mach numbers is proposed that controls the Roe dissipation term appropriately. Referred to as the automatic dissipation adjustment (ADA) model, the method of solution follows procedures developed previously for the truncated Navier-Stokes (TNS) equations and, without tuning of parameters, uses the energy ratio as a criterion to automatically adjust the upwind dissipation. Turbulent channel flow at two different Reynold numbers and the Taylor-Green vortex were performed to validate the ADA model. In simulations of turbulent channel flow for Reτ = 180 at Mach number of 0.05 using the ADA model, the mean velocity and turbulence intensities are in excellent agreement with DNS results. With Reτ = 950 at Mach number of 0.1, the result is also consistent with DNS results, indicating that the ADA model is also reliable at higher Reynolds numbers. In simulations of the Taylor-Green vortex at Re = 3000, the kinetic energy is consistent with the power law of decaying turbulence with -1.2 exponents for both LMRoe with and without the ADA model. However, with the ADA model, the dissipation rate can be significantly improved near the dissipation peak region and the peak duration can be also more accurately captured. With a firm basis in TNS theory, applicability at higher Reynolds number, and ease in implementation as no extra terms are needed, the ADA model offers to become a promising tool for turbulence modeling.

Chemical nonequilibrium Navier-Stokes solutions for hypersonic flow over an ablating graphite nosetip

Science.gov (United States)

Chen, Y. K.; Henline, W. D.

1993-01-01

The general boundary conditions including mass and energy balances of chemically equilibrated or nonequilibrated gas adjacent to ablating surfaces have been derived. A computer procedure based on these conditions was developed and interfaced with the Navier-Stokes solver for predictions of the flow field, surface temperature, and surface ablation rates over re-entry space vehicles with ablating Thermal Protection Systems (TPS). The Navier-Stokes solver with general surface thermochemistry boundary conditions can predict more realistic solutions and provide useful information for the design of TPS. A test case with a proposed hypersonic test vehicle configuration and associated free stream conditions was developed. Solutions with various surface boundary conditions were obtained, and the effect of nonequilibrium gas as well as surface chemistry on surface heating and ablation rate were examined. The solutions of the GASP code with complete ablating surface conditions were compared with those of the ASC code. The direction of future work is also discussed.

Simulations of incompressible Navier Stokes equations on curved surfaces using discrete exterior calculus

Science.gov (United States)

Samtaney, Ravi; Mohamed, Mamdouh; Hirani, Anil

2015-11-01

We present examples of numerical solutions of incompressible flow on 2D curved domains. The Navier-Stokes equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. A conservative discretization of Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). The discretization is then carried out by substituting the corresponding discrete operators based on the DEC framework. By construction, the method is conservative in that both the discrete divergence and circulation are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step. Numerical examples include Taylor vortices on a sphere, Stuart vortices on a sphere, and flow past a cylinder on domains with varying curvature. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01.

Capillary-gravity waves and the Navier-Stokes equation

International Nuclear Information System (INIS)

Behroozi, F.; Podolefsky, N.

2001-01-01

Water waves are a source of great fascination for undergraduates and thus provide an excellent context for introducing some important topics in fluid dynamics. In this paper we introduce the potential theory for incompressible and inviscid flow and derive the differential equation that governs the behaviour of the velocity potential. Next we obtain the harmonic solutions of the velocity potential by a very general argument. These solutions in turn yield the equations for the velocity and displacement of a water element under the action of a harmonic wave. Finally we obtain the dispersion relation for surface waves by requiring that the harmonic solutions satisfy the Navier-Stokes equation. (author)

Adaptive Sampling for Nonlinear Dimensionality Reduction Based on Manifold Learning

DEFF Research Database (Denmark)

Franz, Thomas; Zimmermann, Ralf; Goertz, Stefan

2017-01-01

We make use of the non-intrusive dimensionality reduction method Isomap in order to emulate nonlinear parametric flow problems that are governed by the Reynolds-averaged Navier-Stokes equations. Isomap is a manifold learning approach that provides a low-dimensional embedding space that is approxi...... to detect and fill up gaps in the sampling in the embedding space. The performance of the proposed manifold filling method will be illustrated by numerical experiments, where we consider nonlinear parameter-dependent steady-state Navier-Stokes flows in the transonic regime.......We make use of the non-intrusive dimensionality reduction method Isomap in order to emulate nonlinear parametric flow problems that are governed by the Reynolds-averaged Navier-Stokes equations. Isomap is a manifold learning approach that provides a low-dimensional embedding space...

On the equivalence between particular types of Navier-Stokes and non-linear Schroedinger equations

International Nuclear Information System (INIS)

Dietrich, K.; Vautherin, D.

1985-01-01

We derive a Schroedinger equation equivalent to the Navier-Stokes equation in the special case of constant kinematic viscosities. This equation contains a non-linear term similar to that proposed by Kostin for a quantum description of friction [fr

The solutions of Navier-Stokes equations in squeezing flow between parallel plates

Czech Academy of Sciences Publication Activity Database

Petrov, A. G.; Kharlamova, Irina

2014-01-01

Roč. 48, November–December (2014), s. 40-48 ISSN 0997-7546 Grant - others:Russian Foundation for Basic Research(RU) 14-01- 00818; Russian Foundation for Basic Research(RU) 14-01-00892 Institutional support: RVO:67985874 Keywords : closed form solution * Navier-Stokes equations * squeezing flow between plates * counterflow Subject RIV: BK - Fluid Dynamics Impact factor: 1.656, year: 2014

Modified Einstein and Navier-Stokes Equations

Science.gov (United States)

Bulyzhenkov, I. É.

2018-05-01

The appearance of inertial rest mass-energy is associated with the kinematic slowing-down of time and with the vortex state of the elementary massive space with zero integral of its kinetic and potential energies. An analog of the Einstein equation is found for moving densities of a non-empty metric space in the concept of the Einstein-Infeld material field. The vector consequences of this tensor equation for a metric medium of overlapping elementary carriers of continuous mass-energies allow us to modify the Navier-Stokes equation under inertial motion of the matter of the nonlocal field in the nonrelativistic limit. The nonlocality of massenergy generates kinematic accelerations of feedback to Newtonian acceleration, which impedes asymptotic divergence of energy fluxes. Stabilization of inertial media by dynamic Bernoulli pressure corresponds to nonlocal self-organization of Einstein-Infeld non-empty space and invalidates Newtonian localization of masses in empty space.

Aeroacoustic Calculations of Wind Turbine Noise with the Actuator Line/ Navier-Stokes Technique

DEFF Research Database (Denmark)

Debertshäuser, Harald; Shen, Wen Zhong; Zhu, Wei Jun

2016-01-01

technique where the wind turbine flow is calculated by using the in-house actuator line/LES/Navier-Stokes technique and the acoustics is obtained by solving the acoustic perturbation equations. In the flow solver, the wind turbine blades are modelled by rotating lines with body forces determined according...

The meshless local Petrov-Galerkin method based on moving Kriging interpolation for solving the time fractional Navier-Stokes equations.

Science.gov (United States)

Thamareerat, N; Luadsong, A; Aschariyaphotha, N

2016-01-01

In this paper, we present a numerical scheme used to solve the nonlinear time fractional Navier-Stokes equations in two dimensions. We first employ the meshless local Petrov-Galerkin (MLPG) method based on a local weak formulation to form the system of discretized equations and then we will approximate the time fractional derivative interpreted in the sense of Caputo by a simple quadrature formula. The moving Kriging interpolation which possesses the Kronecker delta property is applied to construct shape functions. This research aims to extend and develop further the applicability of the truly MLPG method to the generalized incompressible Navier-Stokes equations. Two numerical examples are provided to illustrate the accuracy and efficiency of the proposed algorithm. Very good agreement between the numerically and analytically computed solutions can be observed in the verification. The present MLPG method has proved its efficiency and reliability for solving the two-dimensional time fractional Navier-Stokes equations arising in fluid dynamics as well as several other problems in science and engineering.

A hybridized discontinuous Galerkin framework for high-order particle-mesh operator splitting of the incompressible Navier-Stokes equations

Science.gov (United States)

Maljaars, Jakob M.; Labeur, Robert Jan; Möller, Matthias

2018-04-01

A generic particle-mesh method using a hybridized discontinuous Galerkin (HDG) framework is presented and validated for the solution of the incompressible Navier-Stokes equations. Building upon particle-in-cell concepts, the method is formulated in terms of an operator splitting technique in which Lagrangian particles are used to discretize an advection operator, and an Eulerian mesh-based HDG method is employed for the constitutive modeling to account for the inter-particle interactions. Key to the method is the variational framework provided by the HDG method. This allows to formulate the projections between the Lagrangian particle space and the Eulerian finite element space in terms of local (i.e. cellwise) ℓ2-projections efficiently. Furthermore, exploiting the HDG framework for solving the constitutive equations results in velocity fields which excellently approach the incompressibility constraint in a local sense. By advecting the particles through these velocity fields, the particle distribution remains uniform over time, obviating the need for additional quality control. The presented methodology allows for a straightforward extension to arbitrary-order spatial accuracy on general meshes. A range of numerical examples shows that optimal convergence rates are obtained in space and, given the particular time stepping strategy, second-order accuracy is obtained in time. The model capabilities are further demonstrated by presenting results for the flow over a backward facing step and for the flow around a cylinder.

Time-Filtered Navier-Stokes Approach and Emulation of Turbulence-Chemistry Interaction

Science.gov (United States)

Liu, Nan-Suey; Wey, Thomas; Shih, Tsan-Hsing

2013-01-01

This paper describes the time-filtered Navier-Stokes approach capable of capturing unsteady flow structures important for turbulent mixing and an accompanying subgrid model directly accounting for the major processes in turbulence-chemistry interaction. They have been applied to the computation of two-phase turbulent combustion occurring in a single-element lean-direct-injection combustor. Some of the preliminary results from this computational effort are presented in this paper.

Hydrodynamics at the smallest scales: a solvability criterion for Navier-Stokes equations in high dimensions.

Science.gov (United States)

Viswanathan, T M; Viswanathan, G M

2011-01-28

Strong global solvability is difficult to prove for high-dimensional hydrodynamic systems because of the complex interplay between nonlinearity and scale invariance. We define the Ladyzhenskaya-Lions exponent α(L)(n)=(2+n)/4 for Navier-Stokes equations with dissipation -(-Δ)(α) in R(n), for all n≥2. We review the proof of strong global solvability when α≥α(L)(n), given smooth initial data. If the corresponding Euler equations for n>2 were to allow uncontrolled growth of the enstrophy (1/2)∥∇u∥(L²)(2), then no globally controlled coercive quantity is currently known to exist that can regularize solutions of the Navier-Stokes equations for α<α(L)(n). The energy is critical under scale transformations only for α=α(L)(n).

Numerical Study of Natural Gas/Diesel Reactivity Controlled Compression Ignition Combustion with Large Eddy Simulation and Reynolds-Averaged Navier–Stokes Model

Directory of Open Access Journals (Sweden)

Amir-Hasan Kakaee

2018-03-01

Full Text Available In the current study, a comparative study is performed using Large Eddy Simulation (LES and Reynolds-averaged Navier–Stokes (RANS turbulence models on a natural gas/diesel Reactivity Controlled Compression Ignition (RCCI engine. The numerical results are validated against the available research work in the literature. The RNG (Re-Normalization Group k − ε and dynamic structure models are employed to model turbulent flow for RANS and LES simulations, respectively. Parameters like the premixed natural gas mass fraction, the second start of injection timing (SOI2 of diesel and the engine speed are studied to compare performance of RANS and LES models on combustion and pollutant emissions prediction. The results obtained showed that the LES and RANS model give almost similar predictions of cylinder pressure and heat release rate at lower natural gas mass fractions and late SOI2 timings. However, the LES showed improved capability to predict the natural gas auto-ignition and pollutant emissions prediction compared to RANS model especially at higher natural gas mass fractions.

On the Dynamic Programming Approach for the 3D Navier-Stokes Equations

International Nuclear Information System (INIS)

Manca, Luigi

2008-01-01

The dynamic programming approach for the control of a 3D flow governed by the stochastic Navier-Stokes equations for incompressible fluid in a bounded domain is studied. By a compactness argument, existence of solutions for the associated Hamilton-Jacobi-Bellman equation is proved. Finally, existence of an optimal control through the feedback formula and of an optimal state is discussed

Nonlinear and parallel algorithms for finite element discretizations of the incompressible Navier-Stokes equations

Science.gov (United States)

Arteaga, Santiago Egido

1998-12-01

The steady-state Navier-Stokes equations are of considerable interest because they are used to model numerous common physical phenomena. The applications encountered in practice often involve small viscosities and complicated domain geometries, and they result in challenging problems in spite of the vast attention that has been dedicated to them. In this thesis we examine methods for computing the numerical solution of the primitive variable formulation of the incompressible equations on distributed memory parallel computers. We use the Galerkin method to discretize the differential equations, although most results are stated so that they apply also to stabilized methods. We also reformulate some classical results in a single framework and discuss some issues frequently dismissed in the literature, such as the implementation of pressure space basis and non- homogeneous boundary values. We consider three nonlinear methods: Newton's method, Oseen's (or Picard) iteration, and sequences of Stokes problems. All these iterative nonlinear methods require solving a linear system at every step. Newton's method has quadratic convergence while that of the others is only linear; however, we obtain theoretical bounds showing that Oseen's iteration is more robust, and we confirm it experimentally. In addition, although Oseen's iteration usually requires more iterations than Newton's method, the linear systems it generates tend to be simpler and its overall costs (in CPU time) are lower. The Stokes problems result in linear systems which are easier to solve, but its convergence is much slower, so that it is competitive only for large viscosities. Inexact versions of these methods are studied, and we explain why the best timings are obtained using relatively modest error tolerances in solving the corresponding linear systems. We also present a new damping optimization strategy based on the quadratic nature of the Navier-Stokes equations, which improves the robustness of all the

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.

2017-05-23

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.

Navier-Stokes Dynamics by a Discrete Boltzmann Model

Science.gov (United States)

Rubinstein, Robet

2010-01-01

This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.

N3S project of fluid mechanics. High order in time methods by operator splitting. Application to Navier-Stokes equations; Projet N3S. Methode en temps d`ordre eleve par decomposition d`operateurs. Application aux equations de Navier-Stokes

Energy Technology Data Exchange (ETDEWEB)

Boukir, K

1994-06-01

This thesis deals with the extension to higher order in time of two splitting methods for the Navier-Stokes equations: the characteristics method and the projection one. The first consists in decoupling the convection operator from the Stokes one. The second decomposes this latter into a diffusion problem and a pressure-continuity one. Concerning the characteristics method, numerical and theoretical study is developed for the second order scheme together with a finite element spatial discretization. The case of a spectral spatial discretization is also treated and theoretical analysis are given respectively for second and third order schemes. For both spatial discretizations, we obtain good error estimates, unconditionally or under non stringent stability conditions, for both velocity and pressure. Numerical results illustrate the interest of the second order scheme comparing to the first order one. Extensions of the second order scheme to the K-epsilon turbulence model are proposed and tested, in the case of a finite element spatial discretization. Concerning the projection method, we define the order schemes. The theoretical study deals with stability and convergence of first and second order projection schemes, for the incompressible Navier-Stokes equations and with a finite element spatial discretization. The numerical study concerns mainly the second order scheme applied to the Navier-Stokes equations with varying density. (authors). 63 refs., figs.

New representation of Navier-Stokes equations governing self-similar homogeneous turbulence

International Nuclear Information System (INIS)

Foias, C.; Manley, O.P.; Temam, R.

1983-01-01

A new form of the Navier-Stokes equation resulting from a change of variables is presented. The new form has several advantages: It yields a new asymptotic behavior of the flow for long times and vanishingly small viscosity. In addition an interpretation of the new equation in terms of a simple random walk yields immediately not only the Kolmogorov (2/3)-power law but also an intermittency exponent well within the experimental uncertainty

Numerical simulation of the transient cavitating turbulent flows around the Clark-Y hydrofoil using modified partially averaged Navier-Stokes method

Energy Technology Data Exchange (ETDEWEB)

Huang, Renfang; Luo, Xianwu [Tsinghua University, Beijing (China); Ji, Bin [Wuhan University, Hubei (China)

2017-06-15

This paper presents the implementation and assessment of a modified Partially averaged Navier-Stokes (PANS) turbulence model which can successfully predict the transient cavitating turbulent flows. The proposed model treats the standard k-e model as the parent model, and its main distinctive features are to (1) formulate the unresolved-to-total kinetic energy ratio (f{sub k}) based on the local grid size as well as turbulence length scale, and (2) vary the f{sub k}-field both in space and time. Numerical simulation used the modified PANS model for the sheet/cloud cavitating flows around a three-dimensional Clark-Y hydrofoil. The available experimental data and calculations of the standard k-e model, the f{sub k} = 0.8 PANS model, the f{sub k} = 0.5 PANS model are also provided for comparisons. The results show that the modified PANS model accurately captures the transient cavitation features as observed in experiments, namely, the attached sheet cavity grows in the flow direction until to a maximum length and then it breaks into a highly turbulent cloud cavity with three-dimensional structures in nature. Time-averaged drag/lift coefficients together with the streamwise velocity profiles predicted by the proposed model are in good agreement with the experimental data, and improvements are shown when compared with results of the standard k-e model, the f{sub k} = 0.8 PANS model and the f{sub k} = 0.5 PANS model. Overall, the modified PANS model shows its encouraging capability of predicting the transient cavitating turbulent flows.

A Full Hydro- and Morphodynamic Description of Breaker Bar Development

DEFF Research Database (Denmark)

Jacobsen, Niels Gjøl

The present thesis considers a coupled modelling approach for hydro- and morphodynamics in the surf zone, which is based on a solution to the Reynolds Averaged Navier-Stokes (RANS) equations with a Volume of Fluid (VOF) closure for the surf tracking. The basis for the numerical approach is the su......The present thesis considers a coupled modelling approach for hydro- and morphodynamics in the surf zone, which is based on a solution to the Reynolds Averaged Navier-Stokes (RANS) equations with a Volume of Fluid (VOF) closure for the surf tracking. The basis for the numerical approach...

A rigorous justification of the Euler and Navier-Stokes equations with geometric effects

Czech Academy of Sciences Publication Activity Database

Bella, P.; Feireisl, Eduard; Lewicka, M.; Novotný, A.

2016-01-01

Roč. 48, č. 6 (2016), s. 3907-3930 ISSN 0036-1410 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : isentropic Navier-Stokes system * isentropic Euler system * inviscid limit Subject RIV: BA - General Mathematics Impact factor: 1.648, year: 2016 http://epubs.siam.org/doi/10.1137/15M1048963

On time-periodic Navier-Stokes flows with fast spatial decay in the whole space

Czech Academy of Sciences Publication Activity Database

Nakatsuka, Tomoyuki

2018-01-01

Roč. 4, č. 1 (2018), s. 51-67 ISSN 2296-9020 Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * time-periodic solution * asymptotic property Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics https://link.springer.com/article/10. 1007 %2Fs41808-018-0011-8

On time-periodic Navier-Stokes flows with fast spatial decay in the whole space

Czech Academy of Sciences Publication Activity Database

Nakatsuka, Tomoyuki

2018-01-01

Roč. 4, č. 1 (2018), s. 51-67 ISSN 2296-9020 Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * time-periodic solution * asymptotic property Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics https://link.springer.com/article/10.1007%2Fs41808-018-0011-8

Some results on the well-posedness of Euler-Voigt and Navier-Stokes-Voigt models

OpenAIRE

Berselli, Luigi C.; Bisconti, Luca

2010-01-01

We consider the Euler-Voigt equations and the Navier-Stokes-Voigt equations, which are obtained by an inviscid alpha-regularization from the corresponding equations. The main result we show is the structural stability of the system in term of the variations of both viscosity of regularization parameters.

Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.

Science.gov (United States)

Li, Q; He, Y L; Wang, Y; Tao, W Q

2007-11-01

A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

Analysis of spurious oscillation modes for the shallow water and Navier-Stokes equations

Science.gov (United States)

Walters, R.A.; Carey, G.F.

1983-01-01

The origin and nature of spurious oscillation modes that appear in mixed finite element methods are examined. In particular, the shallow water equations are considered and a modal analysis for the one-dimensional problem is developed. From the resulting dispersion relations we find that the spurious modes in elevation are associated with zero frequency and large wave number (wavelengths of the order of the nodal spacing) and consequently are zero-velocity modes. The spurious modal behavior is the result of the finite spatial discretization. By means of an artificial compressibility and limiting argument we are able to resolve the similar problem for the Navier-Stokes equations. The relationship of this simpler analysis to alternative consistency arguments is explained. This modal approach provides an explanation of the phenomenon in question and permits us to deduce the cause of the very complex behavior of spurious modes observed in numerical experiments with the shallow water equations and Navier-Stokes equations. Furthermore, this analysis is not limited to finite element formulations, but is also applicable to finite difference formulations. ?? 1983.

A frequency domain linearized Navier-Stokes equations approach to acoustic propagation in flow ducts with sharp edges.

Science.gov (United States)

Kierkegaard, Axel; Boij, Susann; Efraimsson, Gunilla

2010-02-01

Acoustic wave propagation in flow ducts is commonly modeled with time-domain non-linear Navier-Stokes equation methodologies. To reduce computational effort, investigations of a linearized approach in frequency domain are carried out. Calculations of sound wave propagation in a straight duct are presented with an orifice plate and a mean flow present. Results of transmission and reflections at the orifice are presented on a two-port scattering matrix form and are compared to measurements with good agreement. The wave propagation is modeled with a frequency domain linearized Navier-Stokes equation methodology. This methodology is found to be efficient for cases where the acoustic field does not alter the mean flow field, i.e., when whistling does not occur.

A GPU-accelerated semi-implicit fractional step method for numerical solutions of incompressible Navier-Stokes equations

Science.gov (United States)

Ha, Sanghyun; Park, Junshin; You, Donghyun

2017-11-01

Utility of the computational power of modern Graphics Processing Units (GPUs) is elaborated for solutions of incompressible Navier-Stokes equations which are integrated using a semi-implicit fractional-step method. Due to its serial and bandwidth-bound nature, the present choice of numerical methods is considered to be a good candidate for evaluating the potential of GPUs for solving Navier-Stokes equations using non-explicit time integration. An efficient algorithm is presented for GPU acceleration of the Alternating Direction Implicit (ADI) and the Fourier-transform-based direct solution method used in the semi-implicit fractional-step method. OpenMP is employed for concurrent collection of turbulence statistics on a CPU while Navier-Stokes equations are computed on a GPU. Extension to multiple NVIDIA GPUs is implemented using NVLink supported by the Pascal architecture. Performance of the present method is experimented on multiple Tesla P100 GPUs compared with a single-core Xeon E5-2650 v4 CPU in simulations of boundary-layer flow over a flat plate. Supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (Ministry of Science, ICT and Future Planning NRF-2016R1E1A2A01939553, NRF-2014R1A2A1A11049599, and Ministry of Trade, Industry and Energy 201611101000230).

Boundary Asymptotic Analysis for an Incompressible Viscous Flow: Navier Wall Laws

International Nuclear Information System (INIS)

El Jarroudi, M.; Brillard, A.

2008-01-01

We consider a new way of establishing Navier wall laws. Considering a bounded domain Ω of R N , N=2,3, surrounded by a thin layer Σ ε , along a part Γ 2 of its boundary ∂Ω, we consider a Navier-Stokes flow in Ω union ∂Ω union Σ ε with Reynolds' number of order 1/ε in Σ ε . Using Γ-convergence arguments, we describe the asymptotic behaviour of the solution of this problem and get a general Navier law involving a matrix of Borel measures having the same support contained in the interface Γ 2 . We then consider two special cases where we characterize this matrix of measures. As a further application, we consider an optimal control problem within this context

Entropy Stable Staggered Grid Discontinuous Spectral Collocation Methods of any Order for the Compressible Navier--Stokes Equations

KAUST Repository

Parsani, Matteo

2016-10-04

Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for the compressible Euler and Navier--Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [M. H. Carpenter, T. C. Fisher, E. J. Nielsen, and S. H. Frankel, SIAM J. Sci. Comput., 36 (2014), pp. B835--B867, M. Parsani, M. H. Carpenter, and E. J. Nielsen, J. Comput. Phys., 292 (2015), pp. 88--113], extends the applicable set of points from tensor product, Legendre--Gauss--Lobatto (LGL), to a combination of tensor product Legendre--Gauss (LG) and LGL points. The new semidiscrete operators discretely conserve mass, momentum, energy, and satisfy a mathematical entropy inequality for the compressible Navier--Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly from a theoretical point of view. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinear stability proof for the compressible Navier--Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).

Status and future prospects of using numerical methods to study complex flows at High Reynolds numbers

Science.gov (United States)

Maccormack, R. W.

1978-01-01

The calculation of flow fields past aircraft configuration at flight Reynolds numbers is considered. Progress in devising accurate and efficient numerical methods, in understanding and modeling the physics of turbulence, and in developing reliable and powerful computer hardware is discussed. Emphasis is placed on efficient solutions to the Navier-Stokes equations.

One problem of the Navier type for the Stokes system in planar domains

Czech Academy of Sciences Publication Activity Database

Medková, Dagmar

2016-01-01

Roč. 261, č. 10 (2016), s. 5670-5689 ISSN 0022-0396 R&D Projects: GA ČR GA16-03230S Institutional support: RVO:67985840 Keywords : Stokes system * Navier type problem * regularity of a solution Subject RIV: BA - General Mathematics Impact factor: 1.988, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022039616302121

Ergodicity for the Randomly Forced 2D Navier-Stokes Equations

International Nuclear Information System (INIS)

Kuksin, Sergei; Shirikyan, Armen

2001-01-01

We study space-periodic 2D Navier-Stokes equations perturbed by an unbounded random kick-force. It is assumed that Fourier coefficients of the kicks are independent random variables all of whose moments are bounded and that the distributions of the first N 0 coefficients (where N 0 is a sufficiently large integer) have positive densities against the Lebesgue measure. We treat the equation as a random dynamical system in the space of square integrable divergence-free vector fields. We prove that this dynamical system has a unique stationary measure and study its ergodic properties

A study of plunging breaker mechanics by PIV measurements and a Navier-Stokes solver

DEFF Research Database (Denmark)

Emarat, Narumon; Forehand, David I. M.; Christensen, Erik Damgaard

2000-01-01

The mechanics of a surf-zone plunging breaker are studied from Particle Image Velocimetry (PIV) measurements and a numerical model based on the Navier-Stokes equations, using a Volume of Fluid (VOF) method. An additional numerical model using a Boundary-Integral Method (BIM) is also used in order...

Direct and iterative algorithms for the parallel solution of the one-dimensional macroscopic Navier-Stokes equations

International Nuclear Information System (INIS)

Doster, J.M.; Sills, E.D.

1986-01-01

Current efforts are under way to develop and evaluate numerical algorithms for the parallel solution of the large sparse matrix equations associated with the finite difference representation of the macroscopic Navier-Stokes equations. Previous work has shown that these equations can be cast into smaller coupled matrix equations suitable for solution utilizing multiple computer processors operating in parallel. The individual processors themselves may exhibit parallelism through the use of vector pipelines. This wor, has concentrated on the one-dimensional drift flux form of the Navier-Stokes equations. Direct and iterative algorithms that may be suitable for implementation on parallel computer architectures are evaluated in terms of accuracy and overall execution speed. This work has application to engineering and training simulations, on-line process control systems, and engineering workstations where increased computational speeds are required

A nonperturbative approximation for the moderate Reynolds number Navier–Stokes equations

Science.gov (United States)

Roper, Marcus; Brenner, Michael P.

2009-01-01

The nonlinearity of the Navier–Stokes equations makes predicting the flow of fluid around rapidly moving small bodies highly resistant to all approaches save careful experiments or brute force computation. Here, we show how a linearization of the Navier–Stokes equations captures the drag-determining features of the flow and allows simplified or analytical computation of the drag on bodies up to Reynolds number of order 100. We illustrate the utility of this linearization in 2 practical problems that normally can only be tackled with sophisticated numerical methods: understanding flow separation in the flow around a bluff body and finding drag-minimizing shapes. PMID:19211800

Perturbation of eigenvalues of preconditioned Navier-Stokes operators

Energy Technology Data Exchange (ETDEWEB)

Elman, H.C. [Univ. of Maryland, College Park, MD (United States)

1996-12-31

We study the sensitivity of algebraic eigenvalue problems associated with matrices arising from linearization and discretization of the steady-state Navier-Stokes equations. In particular, for several choices of preconditioners applied to the system of discrete equations, we derive upper bounds on perturbations of eigenvalues as functions of the viscosity and discretization mesh size. The bounds suggest that the sensitivity of the eigenvalues is at worst linear in the inverse of the viscosity and quadratic in the inverse of the mesh size, and that scaling can be used to decrease the sensitivity in some cases. Experimental results supplement these results and confirm the relatively mild dependence on viscosity. They also indicate a dependence on the mesh size of magnitude smaller than the analysis suggests.

Formal solution of the Navier-Stokes initial- and boundary-value problem for incompressible fluids

International Nuclear Information System (INIS)

Alankus, T.

1984-01-01

A general formal solution of the integral equivalent of Navier-Stokes equation for incompressible viscous fluids is presented through a linear operator acting on the functionals of solenoidal vector fields. This solution operator is completely determined by the Green functions of Laplace and diffusion equations corresponding to the flow region

Exponential decay rate of the power spectrum for solutions of the Navier--Stokes equations

International Nuclear Information System (INIS)

Doering, C.R.; Titi, E.S.

1995-01-01

Using a method developed by Foias and Temam [J. Funct. Anal. 87, 359 (1989)], exponential decay of the spatial Fourier power spectrum for solutions of the incompressible Navier--Stokes equations is established and explicit rigorous lower bounds on a small length scale defined by the exponential decay rate are obtained

Prandtl boundary layer expansions of steady Navier-Stokes flows over a moving plate

OpenAIRE

Guo, Yan; Nguyen, Toan T.

2014-01-01

This paper concerns the validity of the Prandtl boundary layer theory in the inviscid limit for steady incompressible Navier-Stokes flows. The stationary flows, with small viscosity, are considered on $[0,L]\\times \\mathbb{R}_{+}$, assuming a no-slip boundary condition over a moving plate at $y=0$. We establish the validity of the Prandtl boundary layer expansion and its error estimates.

Error Estimate of the Ares I Vehicle Longitudinal Aerodynamic Characteristics Based on Turbulent Navier-Stokes Analysis

Science.gov (United States)

Abdol-Hamid, Khaled S.; Ghaffari, Farhad

2011-01-01

Numerical predictions of the longitudinal aerodynamic characteristics for the Ares I class of vehicles, along with the associated error estimate derived from an iterative convergence grid refinement, are presented. Computational results are based on the unstructured grid, Reynolds-averaged Navier-Stokes flow solver USM3D, with an assumption that the flow is fully turbulent over the entire vehicle. This effort was designed to complement the prior computational activities conducted over the past five years in support of the Ares I Project with the emphasis on the vehicle s last design cycle designated as the A106 configuration. Due to a lack of flight data for this particular design s outer mold line, the initial vehicle s aerodynamic predictions and the associated error estimates were first assessed and validated against the available experimental data at representative wind tunnel flow conditions pertinent to the ascent phase of the trajectory without including any propulsion effects. Subsequently, the established procedures were then applied to obtain the longitudinal aerodynamic predictions at the selected flight flow conditions. Sample computed results and the correlations with the experimental measurements are presented. In addition, the present analysis includes the relevant data to highlight the balance between the prediction accuracy against the grid size and, thus, the corresponding computer resource requirements for the computations at both wind tunnel and flight flow conditions. NOTE: Some details have been removed from selected plots and figures in compliance with the sensitive but unclassified (SBU) restrictions. However, the content still conveys the merits of the technical approach and the relevant results.

A finite element method for the numerical solution of the coupled Cahn-Hilliard and Navier-Stokes system for moving contact line problems

KAUST Repository

Bao, Kai

2012-10-01

In this paper, a semi-implicit finite element method is presented for the coupled Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition for the moving contact line problems. In our method, the system is solved in a decoupled way. For the Cahn-Hilliard equations, a convex splitting scheme is used along with a P1-P1 finite element discretization. The scheme is unconditionally stable. A linearized semi-implicit P2-P0 mixed finite element method is employed to solve the Navier-Stokes equations. With our method, the generalized Navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way. The efficiency and capacity of the present method are well demonstrated with several numerical examples. © 2012 Elsevier Inc..

A finite element method for the numerical solution of the coupled Cahn-Hilliard and Navier-Stokes system for moving contact line problems

KAUST Repository

Bao, Kai; Shi, Yi; Sun, Shuyu; Wang, Xiaoping

2012-01-01

In this paper, a semi-implicit finite element method is presented for the coupled Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition for the moving contact line problems. In our method, the system is solved in a decoupled way. For the Cahn-Hilliard equations, a convex splitting scheme is used along with a P1-P1 finite element discretization. The scheme is unconditionally stable. A linearized semi-implicit P2-P0 mixed finite element method is employed to solve the Navier-Stokes equations. With our method, the generalized Navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way. The efficiency and capacity of the present method are well demonstrated with several numerical examples. © 2012 Elsevier Inc..

Statistical solutions of the Navier endash Stokes equations on the phase space of vorticity and the inviscid limits

International Nuclear Information System (INIS)

Constantin, P.; Wu, J.

1997-01-01

Using the methods of Foias [Sem. Math. Univ. Padova 48, 219 endash 343 (1972); 49, 9 endash 123 (1973)] and Vishik endash Fursikov [Mathematical Problems of Statistical Hydromechanics (Kluwer, Dordrecht, 1988)], we prove the existence and uniqueness of both spatial and space endash time statistical solutions of the Navier endash Stokes equations on the phase space of vorticity. Here the initial vorticity is in Yudovich space and the initial measure has finite mean enstrophy. We show under further assumptions on the initial vorticity that the statistical solutions of the Navier endash Stokes equations converge weakly and the inviscid limits are the corresponding statistical solutions of the Euler equations. copyright 1997 American Institute of Physics

On a nu-continuous famaly of strong solutions to the Euler or Navier-Stokes equations with the Navier-type boundary condition

Czech Academy of Sciences Publication Activity Database

Bellout, H.; Neustupa, Jiří; Penel, P.

2010-01-01

Roč. 27, č. 4 (2010), s. 1353-1373 ISSN 1078-0947 R&D Projects: GA AV ČR IAA100190905 Institutional research plan: CEZ:AV0Z10190503 Keywords : Euler equations * Navier-Stokes equations * zero viscosity limit Subject RIV: BA - General Mathematics Impact factor: 0.986, year: 2010 http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5028

Simulation of wing-body junction flows with hybrid RANS/LES methods

International Nuclear Information System (INIS)

Fu Song; Xiao Zhixiang; Chen Haixin; Zhang Yufei; Huang Jingbo

2007-01-01

In this paper, flows past two wing-body junctions, the Rood at zero angle of attack and NASA TN D-712 at 12.5 o angle of attack, are investigated with two Reynolds-Averaged Navier-Stokes (RANS) and large eddy simulation (LES) hybrid methods. One is detached eddy simulation (DES) and the other is delayed-DES, both are based on a weakly nonlinear two-equation k-ω model. While the RANS method can predict the mean flow behaviours reasonably accurately, its performance for the turbulent kinetic energy and shear stress, as compared with available experimental data, is not satisfactory. DES, through introducing a length scale in the dissipation terms of the turbulent kinetic energy equation, delivers flow separation, a vortex or the onset of vortex breakdown too early. DDES, with its delayed effect, shows a great improvement in flow structures and turbulence characteristics, and agrees well with measurements

Parallel iterative solution of the incompressible Navier-Stokes equations with application to rotating wings

Czech Academy of Sciences Publication Activity Database

Šístek, Jakub; Cirak, F.

2015-01-01

Roč. 122, 20 November (2015), s. 165-183 ISSN 0045-7930 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : Navier-Stokes * incompressible flow * Krylov subspace methods Subject RIV: BA - General Mathematics Impact factor: 1.891, year: 2015 http://www.sciencedirect.com/science/article/pii/S0045793015003023

A Navier-Stokes phase-field crystal model for colloidal suspensions.

Science.gov (United States)

Praetorius, Simon; Voigt, Axel

2015-04-21

We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier-Stokes Phase-Field Crystal model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail and related to other dynamic density functional theory approaches with hydrodynamic interactions. The derived system is numerically solved using adaptive finite elements and is used to analyze colloidal crystallization in flowing environments demonstrating a strong coupling in both directions between the crystal shape and the flow field. We further validate the model against other computational approaches for particulate flow systems for various colloidal sedimentation problems.

Low-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence.

Science.gov (United States)

Sharma, Ati S; Moarref, Rashad; McKeon, Beverley J; Park, Jae Sung; Graham, Michael D; Willis, Ashley P

2016-02-01

We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just a few modes of the model of McKeon and Sharma [J. Fluid Mech. 658, 336 (2010)]. This model provides modes that act as a basis to decompose the velocity field, ordered by their amplitude of response to forcing arising from the interaction between scales. The model was originally derived from the Navier-Stokes equations to represent turbulent flows and has been used to explain coherent structure and to predict turbulent statistics. This establishes a surprising new link between the two distinct approaches to understanding turbulence.

Strong solutions for an incompressible Navier-Stokes/Allen-Cahn system with different densities

Science.gov (United States)

Li, Yinghua; Huang, Mingxia

2018-06-01

In this paper, we investigate a coupled Navier-Stokes/Allen-Cahn system describing a diffuse interface model for two-phase flow of viscous incompressible fluids with different densities in a bounded domain Ω \\subset R^N(N=2,3). We prove the existence and uniqueness of local strong solutions to the initial boundary value problem when the initial density function ρ _0 has a positive lower bound.

On large-time energy concentration in solutions to the Navier-Stokes equations in general domains

Czech Academy of Sciences Publication Activity Database

Skalák, Zdeněk

2011-01-01

Roč. 91, č. 9 (2011), s. 724-732 ISSN 0044-2267 R&D Projects: GA AV ČR IAA100190905 Institutional research plan: CEZ:AV0Z20600510 Keywords : Navier-Stokes equations * large-time behavior * energy concentration Subject RIV: BA - General Mathematics Impact factor: 0.863, year: 2011

Convergence of a numerical method for the compressible Navier-Stokes system on general domains

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Karper, T.; Michálek, Martin

2016-01-01

Roč. 134, č. 4 (2016), s. 667-704 ISSN 0029-599X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : numerical methods * Navier-Stokes system Subject RIV: BA - General Mathematics Impact factor: 2.152, year: 2016 http://link.springer.com/article/10.1007%2Fs00211-015-0786-6

Parallel iterative solution of the incompressible Navier-Stokes equations with application to rotating wings

Czech Academy of Sciences Publication Activity Database

Šístek, Jakub; Cirak, F.

2015-01-01

Roč. 122, 20 November (2015), s. 165-183 ISSN 0045-7930 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : Navier-Stokes * incompressible flow * Krylov subspace method s Subject RIV: BA - General Mathematics Impact factor: 1.891, year: 2015 http://www. science direct.com/ science /article/pii/S0045793015003023

Lower Bounds for Possible Singular Solutions for the Navier-Stokes and Euler Equations Revisited

Science.gov (United States)

Cortissoz, Jean C.; Montero, Julio A.

2018-03-01

In this paper we give optimal lower bounds for the blow-up rate of the \\dot{H}s( T^3) -norm, 1/2Navier-Stokes equations, and we also present an elementary proof for a lower bound on blow-up rate of the Sobolev norms of possible singular solutions to the Euler equations when s>5/2.

Convergence of a numerical method for the compressible Navier-Stokes system on general domains

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Karper, T.; Michálek, Martin

2016-01-01

Roč. 134, č. 4 (2016), s. 667-704 ISSN 0029-599X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : numerical methods * Navier - Stokes system Subject RIV: BA - General Mathematics Impact factor: 2.152, year: 2016 http://link.springer.com/article/10.1007%2Fs00211-015-0786-6

Space-time coupled spectral/hp least-squares finite element formulation for the incompressible Navier-Stokes equations

International Nuclear Information System (INIS)

Pontaza, J.P.; Reddy, J.N.

2004-01-01

We consider least-squares finite element models for the numerical solution of the non-stationary Navier-Stokes equations governing viscous incompressible fluid flows. The paper presents a formulation where the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space-time decoupled formulation where a least-squares minimization procedure is performed in space at each time step. The formulation is first presented for the linear advection-diffusion equation and then extended to the Navier-Stokes equations. The formulation has no time step stability restrictions and is spectrally accurate in both space and time. To allow the use of practical C 0 element expansions in the resulting finite element model, the Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity as an additional independent variable and the least-squares method is used to develop the finite element model of the governing equations. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix-free form. Spectral convergence of the L 2 least-squares functional and L 2 error norms in space-time is verified using a smooth solution to the two-dimensional non-stationary incompressible Navier-Stokes equations. Numerical results are presented for impulsively started lid-driven cavity flow, oscillatory lid-driven cavity flow, transient flow over a backward-facing step, and flow around a circular cylinder; the results demonstrate the predictive capability and robustness of the proposed formulation. Even though the space-time coupled formulation is emphasized, we also present the formulation and numerical results for least

Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces

Science.gov (United States)

Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.

2013-01-01

Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.

Dynamics of three-tori in a periodically forced navier-stokes flow

Science.gov (United States)

Lopez; Marques

2000-07-31

Three-tori solutions of the Navier-Stokes equations and their dynamics are elucidated by use of a global Poincare map. The flow is contained in a finite annular gap between two concentric cylinders, driven by the steady rotation and axial harmonic oscillations of the inner cylinder. The three-tori solutions undergo global bifurcations, including a new gluing bifurcation, associated with homoclinic and heteroclinic connections to unstable solutions (two-tori). These unstable two-tori act as organizing centers for the three-tori dynamics. A discrete space-time symmetry influences the dynamics.

Modeling digital pulse waveforms by solving one-dimensional Navier-stokes equations.

Science.gov (United States)

Fedotov, Aleksandr A; Akulova, Anna S; Akulov, Sergey A

2016-08-01

Mathematical modeling for composition distal arterial pulse wave in the blood vessels of the upper limbs was considered. Formation of distal arterial pulse wave is represented as a composition of forward and reflected pulse waves propagating along the arterial vessels. The formal analogy between pulse waves propagation along the human arterial system and the propagation of electrical oscillations in electrical transmission lines with distributed parameters was proposed. Dependencies of pulse wave propagation along the human arterial system were obtained by solving the one-dimensional Navier-Stokes equations for a few special cases.

Note on the fast decay property of steady Navier-Stokes flows in the whole space

Czech Academy of Sciences Publication Activity Database

Nakatsuka, Tomoyuki

2018-01-01

Roč. 38, č. 2 (2018), s. 81-89 ISSN 0174-4747 Institutional support: RVO:67985840 Keywords : stationary Navier-Stokes equation * asymptotic behavior Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics https://www.degruyter.com/view/j/anly.2018.38.issue-2/anly-2017-0016/anly-2017-0016.xml

The Oberbeck-Boussinesq approximation as a singular limit of the full Navier-Stokes-Fourier system

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Novotný, A.

2009-01-01

Roč. 11, č. 2 (2009), s. 274-302 ISSN 1422-6928 R&D Projects: GA ČR GA201/05/0164 Institutional research plan: CEZ:AV0Z10190503 Keywords : singular limit * Navier-Stokes-Fourier system * Oberbeck -Boussinesq approximation Subject RIV: BA - General Mathematics Impact factor: 1.214, year: 2009

A GPU-accelerated semi-implicit fractional-step method for numerical solutions of incompressible Navier-Stokes equations

Science.gov (United States)

Ha, Sanghyun; Park, Junshin; You, Donghyun

2018-01-01

Utility of the computational power of Graphics Processing Units (GPUs) is elaborated for solutions of incompressible Navier-Stokes equations which are integrated using a semi-implicit fractional-step method. The Alternating Direction Implicit (ADI) and the Fourier-transform-based direct solution methods used in the semi-implicit fractional-step method take advantage of multiple tridiagonal matrices whose inversion is known as the major bottleneck for acceleration on a typical multi-core machine. A novel implementation of the semi-implicit fractional-step method designed for GPU acceleration of the incompressible Navier-Stokes equations is presented. Aspects of the programing model of Compute Unified Device Architecture (CUDA), which are critical to the bandwidth-bound nature of the present method are discussed in detail. A data layout for efficient use of CUDA libraries is proposed for acceleration of tridiagonal matrix inversion and fast Fourier transform. OpenMP is employed for concurrent collection of turbulence statistics on a CPU while the Navier-Stokes equations are computed on a GPU. Performance of the present method using CUDA is assessed by comparing the speed of solving three tridiagonal matrices using ADI with the speed of solving one heptadiagonal matrix using a conjugate gradient method. An overall speedup of 20 times is achieved using a Tesla K40 GPU in comparison with a single-core Xeon E5-2660 v3 CPU in simulations of turbulent boundary-layer flow over a flat plate conducted on over 134 million grids. Enhanced performance of 48 times speedup is reached for the same problem using a Tesla P100 GPU.

N3S project of fluid mechanics. High order in time methods by operator splitting. Application to Navier-Stokes equations

International Nuclear Information System (INIS)

Boukir, K.

1994-06-01

This thesis deals with the extension to higher order in time of two splitting methods for the Navier-Stokes equations: the characteristics method and the projection one. The first consists in decoupling the convection operator from the Stokes one. The second decomposes this latter into a diffusion problem and a pressure-continuity one. Concerning the characteristics method, numerical and theoretical study is developed for the second order scheme together with a finite element spatial discretization. The case of a spectral spatial discretization is also treated and theoretical analysis are given respectively for second and third order schemes. For both spatial discretizations, we obtain good error estimates, unconditionally or under non stringent stability conditions, for both velocity and pressure. Numerical results illustrate the interest of the second order scheme comparing to the first order one. Extensions of the second order scheme to the K-epsilon turbulence model are proposed and tested, in the case of a finite element spatial discretization. Concerning the projection method, we define the order schemes. The theoretical study deals with stability and convergence of first and second order projection schemes, for the incompressible Navier-Stokes equations and with a finite element spatial discretization. The numerical study concerns mainly the second order scheme applied to the Navier-Stokes equations with varying density. (authors). 63 refs., figs

Effects of friction on forced two-dimensional Navier-Stokes turbulence.

Science.gov (United States)

Blackbourn, Luke A K; Tran, Chuong V

2011-10-01

Large-scale dissipation mechanisms have been routinely employed in numerical simulations of two-dimensional turbulence to absorb energy at large scales, presumably mimicking the quasisteady picture of Kraichnan in an unbounded fluid. Here, "side effects" of such a mechanism--mechanical friction--on the small-scale dynamics of forced two-dimensional Navier-Stokes turbulence are elaborated by both theoretical and numerical analysis. Given a positive friction coefficient α, viscous dissipation of enstrophy has been known to vanish in the inviscid limit ν→0. This effectively renders the scale-neutral friction the only mechanism responsible for enstrophy dissipation in that limit. The resulting dynamical picture is that the classical enstrophy inertial range becomes a dissipation range in which the dissipation of enstrophy by friction mainly occurs. For each α>0, there exists a critical viscosity ν(c), which depends on physical parameters, separating the regimes of predominant viscous and frictional dissipation of enstrophy. It is found that ν(c)=[η'(1/3)/(Ck(f)(2))]exp[-η'(1/3)/(Cα)], where η' is half the enstrophy injection rate, k(f) is the forcing wave number, and C is a nondimensional constant (the Kraichnan-Batchelor constant). The present results have important theoretical and practical implications. Apparently, mechanical friction is a poor choice in numerical attempts to address fundamental issues concerning the direct enstrophy transfer in two-dimensional Navier-Stokes turbulence. Furthermore, as relatively strong friction naturally occurs on the surfaces and at lateral boundaries of experimental fluids as well as at the interfaces of shallow layers in geophysical fluid models, the frictional effects discussed in this study are crucial in understanding the dynamics of these systems.

CCM Continuity Constraint Method: A finite-element computational fluid dynamics algorithm for incompressible Navier-Stokes fluid flows

Energy Technology Data Exchange (ETDEWEB)

Williams, P. T. [Univ. of Tennessee, Knoxville, TN (United States)

1993-09-01

As the field of computational fluid dynamics (CFD) continues to mature, algorithms are required to exploit the most recent advances in approximation theory, numerical mathematics, computing architectures, and hardware. Meeting this requirement is particularly challenging in incompressible fluid mechanics, where primitive-variable CFD formulations that are robust, while also accurate and efficient in three dimensions, remain an elusive goal. This dissertation asserts that one key to accomplishing this goal is recognition of the dual role assumed by the pressure, i.e., a mechanism for instantaneously enforcing conservation of mass and a force in the mechanical balance law for conservation of momentum. Proving this assertion has motivated the development of a new, primitive-variable, incompressible, CFD algorithm called the Continuity Constraint Method (CCM). The theoretical basis for the CCM consists of a finite-element spatial semi-discretization of a Galerkin weak statement, equal-order interpolation for all state-variables, a 0-implicit time-integration scheme, and a quasi-Newton iterative procedure extended by a Taylor Weak Statement (TWS) formulation for dispersion error control. Original contributions to algorithmic theory include: (a) formulation of the unsteady evolution of the divergence error, (b) investigation of the role of non-smoothness in the discretized continuity-constraint function, (c) development of a uniformly H¹ Galerkin weak statement for the Reynolds-averaged Navier-Stokes pressure Poisson equation, (d) derivation of physically and numerically well-posed boundary conditions, and (e) investigation of sparse data structures and iterative methods for solving the matrix algebra statements generated by the algorithm.

On the convergence of a fully discrete scheme of LES type to physically relevant solutions of the incompressible Navier-Stokes

Science.gov (United States)

Berselli, Luigi C.; Spirito, Stefano

2018-06-01

Obtaining reliable numerical simulations of turbulent fluids is a challenging problem in computational fluid mechanics. The large eddy simulation (LES) models are efficient tools to approximate turbulent fluids, and an important step in the validation of these models is the ability to reproduce relevant properties of the flow. In this paper, we consider a fully discrete approximation of the Navier-Stokes-Voigt model by an implicit Euler algorithm (with respect to the time variable) and a Fourier-Galerkin method (in the space variables). We prove the convergence to weak solutions of the incompressible Navier-Stokes equations satisfying the natural local entropy condition, hence selecting the so-called physically relevant solutions.

A regularity criterion for the Navier-Stokes equations based on the gradient of one velocity component

Czech Academy of Sciences Publication Activity Database

Skalák, Zdeněk

2016-01-01

Roč. 437, č. 1 (2016), s. 474-484 ISSN 0022-247X R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985874 Keywords : Navier - Stokes equations * regularity of solutions * regularity criteria Subject RIV: BK - Fluid Dynamics Impact factor: 1.064, year: 2016

Infrasonic attenuation in the upper mesosphere-lower thermosphere: a comparison between Navier-Stokes and Burnett predictions.

Science.gov (United States)

Akintunde, Akinjide; Petculescu, Andi

2014-10-01

This paper presents the results of a pilot study comparing the use of continuum and non-continuum fluid dynamics to predict infrasound attenuation in the rarefied lower thermosphere. The continuum approach is embodied by the Navier-Stokes equations, while the non-continuum method is implemented via the Burnett equations [Proc. London Math. Soc. 39, 385-430 (1935); 40, 382-435 (1936)]. In the Burnett framework, the coupling between stress tensor and heat flux affects the dispersion equation, leading to an attenuation coefficient smaller than its Navier-Stokes counterpart by amounts of order 0.1 dB/km at 0.1 Hz, 10 dB/km at 1 Hz, and 100 dB/km at 10 Hz. It has been observed that many measured thermospheric arrivals are stronger than current predictions based on continuum mechanics. In this context, the consistently smaller Burnett-based absorption is cautiously encouraging.

A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditions.

Science.gov (United States)

Li, Zhilin; Xiao, Li; Cai, Qin; Zhao, Hongkai; Luo, Ray

2015-08-15

In this paper, a new Navier-Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier-Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented.

An energy-stable method for solving the incompressible Navier-Stokes equations with non-slip boundary condition

Science.gov (United States)

Lee, Byungjoon; Min, Chohong

2018-05-01

We introduce a stable method for solving the incompressible Navier-Stokes equations with variable density and viscosity. Our method is stable in the sense that it does not increase the total energy of dynamics that is the sum of kinetic energy and potential energy. Instead of velocity, a new state variable is taken so that the kinetic energy is formulated by the L2 norm of the new variable. Navier-Stokes equations are rephrased with respect to the new variable, and a stable time discretization for the rephrased equations is presented. Taking into consideration the incompressibility in the Marker-And-Cell (MAC) grid, we present a modified Lax-Friedrich method that is L2 stable. Utilizing the discrete integration-by-parts in MAC grid and the modified Lax-Friedrich method, the time discretization is fully discretized. An explicit CFL condition for the stability of the full discretization is given and mathematically proved.

A note on local interior regularity of a suitable weak solution to the Navier--Stokes problem

Czech Academy of Sciences Publication Activity Database

Neustupa, Jiří

2013-01-01

Roč. 6, č. 5 (2013), s. 1391-1400 ISSN 1937-1632 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equations * suitable weak solution * regularity Subject RIV: BA - General Mathematics http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=8344

A convergent numerical method for the full Navier-Stokes-Fourier system in smooth physical domains

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Hošek, Radim; Michálek, Martin

2016-01-01

Roč. 54, č. 5 (2016), s. 3062-3082 ISSN 0036-1429 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * finite element method * finite volume method Subject RIV: BA - General Mathematics Impact factor: 1.978, year: 2016 http://epubs.siam.org/doi/abs/10.1137/15M1011809

The incompressible limit of the full Navier-Stokes-Fourier system on domains with rough boundaries

Czech Academy of Sciences Publication Activity Database

Bucur, D.; Feireisl, Eduard

2009-01-01

Roč. 10, č. 5 (2009), s. 3203-3229 ISSN 1468-1218 R&D Projects: GA AV ČR(CZ) IAA100190606; GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : low Mach number * Navier-Stokes-Fourier system * rough boundary Subject RIV: BA - General Mathematics Impact factor: 2.381, year: 2009

A convergent numerical method for the full Navier-Stokes-Fourier system in smooth physical domains

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Hošek, Radim; Michálek, Martin

2016-01-01

Roč. 54, č. 5 (2016), s. 3062-3082 ISSN 0036-1429 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes- Fourier system * finite element method * finite volume method Subject RIV: BA - General Mathematics Impact factor: 1.978, year: 2016 http://epubs.siam.org/doi/abs/10.1137/15M1011809

Local lubrication model for spherical particles within incompressible Navier-Stokes flows

Science.gov (United States)

Lambert, B.; Weynans, L.; Bergmann, M.

2018-03-01

The lubrication forces are short-range hydrodynamic interactions essential to describe suspension of the particles. Usually, they are underestimated in direct numerical simulations of particle-laden flows. In this paper, we propose a lubrication model for a coupled volume penalization method and discrete element method solver that estimates the unresolved hydrodynamic forces and torques in an incompressible Navier-Stokes flow. Corrections are made locally on the surface of the interacting particles without any assumption on the global particle shape. The numerical model has been validated against experimental data and performs as well as existing numerical models that are limited to spherical particles.

Local lubrication model for spherical particles within incompressible Navier-Stokes flows.

Science.gov (United States)

Lambert, B; Weynans, L; Bergmann, M

2018-03-01

The lubrication forces are short-range hydrodynamic interactions essential to describe suspension of the particles. Usually, they are underestimated in direct numerical simulations of particle-laden flows. In this paper, we propose a lubrication model for a coupled volume penalization method and discrete element method solver that estimates the unresolved hydrodynamic forces and torques in an incompressible Navier-Stokes flow. Corrections are made locally on the surface of the interacting particles without any assumption on the global particle shape. The numerical model has been validated against experimental data and performs as well as existing numerical models that are limited to spherical particles.

Non-isothermal Smoluchowski-Poisson equation as a singular limit of the Navier-Stokes-Fourier-Poisson system

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Laurençot, P.

2007-01-01

Roč. 88, - (2007), s. 325-349 ISSN 0021-7824 R&D Projects: GA ČR GA201/05/0164 Institutional research plan: CEZ:AV0Z10190503 Keywords : Navier-Stokes-Fourier- Poisson system * Smoluchowski- Poisson system * singular limit Subject RIV: BA - General Mathematics Impact factor: 1.118, year: 2007

A Spectral Multi-Domain Penalty Method for Elliptic Problems Arising From a Time-Splitting Algorithm For the Incompressible Navier-Stokes Equations

Science.gov (United States)

Diamantopoulos, Theodore; Rowe, Kristopher; Diamessis, Peter

2017-11-01

The Collocation Penalty Method (CPM) solves a PDE on the interior of a domain, while weakly enforcing boundary conditions at domain edges via penalty terms, and naturally lends itself to high-order and multi-domain discretization. Such spectral multi-domain penalty methods (SMPM) have been used to solve the Navier-Stokes equations. Bounds for penalty coefficients are typically derived using the energy method to guarantee stability for time-dependent problems. The choice of collocation points and penalty parameter can greatly affect the conditioning and accuracy of a solution. Effort has been made in recent years to relate various high-order methods on multiple elements or domains under the umbrella of the Correction Procedure via Reconstruction (CPR). Most applications of CPR have focused on solving the compressible Navier-Stokes equations using explicit time-stepping procedures. A particularly important aspect which is still missing in the context of the SMPM is a study of the Helmholtz equation arising in many popular time-splitting schemes for the incompressible Navier-Stokes equations. Stability and convergence results for the SMPM for the Helmholtz equation will be presented. Emphasis will be placed on the efficiency and accuracy of high-order methods.

Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier–Stokes simulations: A data-driven, physics-informed Bayesian approach

International Nuclear Information System (INIS)

Xiao, H.; Wu, J.-L.; Wang, J.-X.; Sun, R.; Roy, C.J.

2016-01-01

Despite their well-known limitations, Reynolds-Averaged Navier–Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering analysis, design and optimization. While the predictive capability of RANS models depends on many factors, for many practical flows the turbulence models are by far the largest source of uncertainty. As RANS models are used in the design and safety evaluation of many mission-critical systems such as airplanes and nuclear power plants, quantifying their model-form uncertainties has significant implications in enabling risk-informed decision-making. In this work we develop a data-driven, physics-informed Bayesian framework for quantifying model-form uncertainties in RANS simulations. Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., realizability, smoothness, and symmetry). An iterative ensemble Kalman method is used to assimilate the prior knowledge and observation data in a Bayesian framework, and to propagate them to posterior distributions of velocities and other Quantities of Interest (QoIs). We use two representative cases, the flow over periodic hills and the flow in a square duct, to evaluate the performance of the proposed framework. Both cases are challenging for standard RANS turbulence models. Simulation results suggest that, even with very sparse observations, the obtained posterior mean velocities and other QoIs have significantly better agreement with the benchmark data compared to the baseline results. At most locations the posterior distribution adequately captures the true model error within the developed model form uncertainty bounds. The framework is a major improvement over existing black-box, physics-neutral methods for model-form uncertainty quantification, where prior knowledge and details of the models are not exploited. This approach has

Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier–Stokes simulations: A data-driven, physics-informed Bayesian approach

Energy Technology Data Exchange (ETDEWEB)

Xiao, H., E-mail: hengxiao@vt.edu; Wu, J.-L.; Wang, J.-X.; Sun, R.; Roy, C.J.

2016-11-01

Despite their well-known limitations, Reynolds-Averaged Navier–Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering analysis, design and optimization. While the predictive capability of RANS models depends on many factors, for many practical flows the turbulence models are by far the largest source of uncertainty. As RANS models are used in the design and safety evaluation of many mission-critical systems such as airplanes and nuclear power plants, quantifying their model-form uncertainties has significant implications in enabling risk-informed decision-making. In this work we develop a data-driven, physics-informed Bayesian framework for quantifying model-form uncertainties in RANS simulations. Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., realizability, smoothness, and symmetry). An iterative ensemble Kalman method is used to assimilate the prior knowledge and observation data in a Bayesian framework, and to propagate them to posterior distributions of velocities and other Quantities of Interest (QoIs). We use two representative cases, the flow over periodic hills and the flow in a square duct, to evaluate the performance of the proposed framework. Both cases are challenging for standard RANS turbulence models. Simulation results suggest that, even with very sparse observations, the obtained posterior mean velocities and other QoIs have significantly better agreement with the benchmark data compared to the baseline results. At most locations the posterior distribution adequately captures the true model error within the developed model form uncertainty bounds. The framework is a major improvement over existing black-box, physics-neutral methods for model-form uncertainty quantification, where prior knowledge and details of the models are not exploited. This approach

Iterative methods for compressible Navier-Stokes and Euler equations

Energy Technology Data Exchange (ETDEWEB)

Tang, W.P.; Forsyth, P.A.

1996-12-31

This workshop will focus on methods for solution of compressible Navier-Stokes and Euler equations. In particular, attention will be focused on the interaction between the methods used to solve the non-linear algebraic equations (e.g. full Newton or first order Jacobian) and the resulting large sparse systems. Various types of block and incomplete LU factorization will be discussed, as well as stability issues, and the use of Newton-Krylov methods. These techniques will be demonstrated on a variety of model transonic and supersonic airfoil problems. Applications to industrial CFD problems will also be presented. Experience with the use of C++ for solution of large scale problems will also be discussed. The format for this workshop will be four fifteen minute talks, followed by a roundtable discussion.

Onset of chaos in helical vortex breakdown at low Reynolds number

Science.gov (United States)

Pasche, S.; Avellan, F.; Gallaire, F.

2018-06-01

The nonlinear dynamics of a swirling wake flow stemming from a Graboswksi-Berger vortex [Grabowski and Berger, J. Fluid Mech. 75, 525 (1976), 10.1017/S0022112076000360] in a semi-infinite domain is addressed at low Reynolds numbers for a fixed swirl number S =1.095 , defined as the ratio between the characteristic tangential velocity and the centerline axial velocity. In this system, only pure hydrodynamic instabilities develop and interact through the quadratic nonlinearities of the Navier-Stokes equations. Such interactions lead to the onset of chaos at a Reynolds value of Re=220 . This chaotic state is reached by following a Ruelle-Takens-Newhouse scenario, which is initiated by a Hopf bifurcation (the spiral vortex breakdown) as the Reynolds number increases. At larger Reynolds value, a frequency synchronization regime appears followed by a chaotic state again. This scenario is corroborated by nonlinear time series analyses. Stability analysis around the time-average flow and temporal-azimuthal Fourier decomposition of the nonlinear flow distributions both identify successfully the developing vortices and provide deeper insight into the development of the flow patterns leading to this route to chaos. Three single-helical vortices are involved: the primary spiral associated with the spiral vortex breakdown, a downstream spiral, and a near-wake spiral. As the Reynolds number increases, the frequencies of these vortices become closer, increasing their interactions by nonlinearity to eventually generate a strong chaotic axisymmetric oscillation.

Reynolds number dependency in equilibrium two-dimensional turbulence

Science.gov (United States)

Bracco, A.; McWilliams, J.

2009-04-01

We use the Navier-Stokes equations for barotropic turbulence as a zero-order approximation of chaotic space-time patterns and equilibrium distributions that mimic turbulence in geophysical flows. In this overly-simplified set-up for which smooth-solutions exist, we investigate if is possible to bound the uncertainty associated with the numerical domain discretization, i.e. with the limitation imposed by the Reynolds number range we can explore. To do so we analyze a series of stationary barotropic turbulence simulations spanning a large range of Reynolds numbers and run over a three year period for over 300,000 CPU hours. We find a persistent Reynolds number dependency in the energy power spectra and second order vorticity structure function, while distributions of dynamical quantities such as velocity, vorticity, dissipation rates and others are invariant in shape and have variances scaling with the viscosity coefficient according to simple power-laws. The relevance to this work to the possibility of conceptually reducing uncertainties in climate models will be discussed.

Higher-order RANS turbulence models for separated flows

Data.gov (United States)

National Aeronautics and Space Administration — Higher-order Reynolds-averaged Navier-Stokes (RANS) models are developed to overcome the shortcomings of second-moment RANS models in predicting separated flows....

Set of difference spitting schemes for solving the Navier-Stokes incompressible equations in natural variables

International Nuclear Information System (INIS)

Koleshko, S.B.

1989-01-01

A three-parametric set of difference schemes is suggested to solve Navier-Stokes equations with the use of the relaxation form of the continuity equation. The initial equations are stated for time increments. Use is made of splitting the operator into one-dimensional forms that reduce calculations to scalar factorizations. Calculated results for steady- and unsteady-state flows in a cavity are presented

On the spurious pressures generated by certain GFEM solutions of the incompressible Navier-Stokes equations

International Nuclear Information System (INIS)

Sani, R.L.; Gresho, P.M.; Lee, R.L.

1979-01-01

The spurious pressures and acceptable velocities generated when using certain combinations of velocity and pressure approximations in a Galerkin finite element discretization of the primitive variable form of the incompressible Navier-Stokes equations are analyzed both theoretically and numerically for grids composed of quadrilateral finite elements. Schemes for obtaining usable pressure fields from the spurious numerical results are presented for certain cases

Existence of global solutions to free boundary value problems for bipolar Navier-Stokes-Possion systems

Directory of Open Access Journals (Sweden)

Jian Liu

2013-09-01

Full Text Available In this article, we consider the free boundary value problem for one-dimensional compressible bipolar Navier-Stokes-Possion (BNSP equations with density-dependent viscosities. For general initial data with finite energy and the density connecting with vacuum continuously, we prove the global existence of the weak solution. This extends the previous results for compressible NS [27] to NSP.

Upwind algorithm for the parabolized Navier-Stokes equations

Science.gov (United States)

Lawrence, Scott L.; Tannehill, John C.; Chausee, Denny S.

1989-01-01

A new upwind algorithm based on Roe's scheme has been developed to solve the two-dimensional parabolized Navier-Stokes equations. This method does not require the addition of user-specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming (1978) scheme in terms of accuracy, stability, computer time and storage requirements, and programming effort. The new algorithm has been validated by applying it to three laminar test cases, including flat-plate boundary-layer flow, hypersonic flow past a 15-deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with results obtained using the conventional Beam-Warming algorithm.

Effects of thermal fluctuations and fluid compressibility on hydrodynamic synchronization of microrotors at finite oscillatory Reynolds number: a multiparticle collision dynamics simulation study.

Science.gov (United States)

Theers, Mario; Winkler, Roland G

2014-08-28

We investigate the emergent dynamical behavior of hydrodynamically coupled microrotors by means of multiparticle collision dynamics (MPC) simulations. The two rotors are confined in a plane and move along circles driven by active forces. Comparing simulations to theoretical results based on linearized hydrodynamics, we demonstrate that time-dependent hydrodynamic interactions lead to synchronization of the rotational motion. Thermal noise implies large fluctuations of the phase-angle difference between the rotors, but synchronization prevails and the ensemble-averaged time dependence of the phase-angle difference agrees well with analytical predictions. Moreover, we demonstrate that compressibility effects lead to longer synchronization times. In addition, the relevance of the inertia terms of the Navier-Stokes equation are discussed, specifically the linear unsteady acceleration term characterized by the oscillatory Reynolds number ReT. We illustrate the continuous breakdown of synchronization with the Reynolds number ReT, in analogy to the continuous breakdown of the scallop theorem with decreasing Reynolds number.

Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations

International Nuclear Information System (INIS)

Fouxon, Itzhak; Oz, Yaron

2008-01-01

We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them

Conformal field theory as microscopic dynamics of incompressible Euler and Navier-Stokes equations.

Science.gov (United States)

Fouxon, Itzhak; Oz, Yaron

2008-12-31

We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.

Computation of high Reynolds number internal/external flows

International Nuclear Information System (INIS)

Cline, M.C.; Wilmoth, R.G.

1981-01-01

A general, user oriented computer program, called VNAP2, has been developed to calculate high Reynolds number, internal/external flows. VNAP2 solves the two-dimensional, time-dependent Navier-Stokes equations. The turbulence is modeled with either a mixing-length, a one transport equation, or a two transport equation model. Interior grid points are computed using the explicit MacCormack scheme with special procedures to speed up the calculation in the fine grid. All boundary conditions are calculated using a reference plane characteristic scheme with the viscous terms treated as source terms. Several internal, external, and internal/external flow calculations are presented

Computation of high Reynolds number internal/external flows

Science.gov (United States)

Cline, M. C.; Wilmoth, R. G.

1981-01-01

A general, user oriented computer program, called VNAP2, was developed to calculate high Reynolds number, internal/ external flows. The VNAP2 program solves the two dimensional, time dependent Navier-Stokes equations. The turbulence is modeled with either a mixing-length, a one transport equation, or a two transport equation model. Interior grid points are computed using the explicit MacCormack Scheme with special procedures to speed up the calculation in the fine grid. All boundary conditions are calculated using a reference plane characteristic scheme with the viscous terms treated as source terms. Several internal, external, and internal/external flow calculations are presented.

Solving the incompressible surface Navier-Stokes equation by surface finite elements

Science.gov (United States)

Reuther, Sebastian; Voigt, Axel

2018-01-01

We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus g (S ) . The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding R3, penalization of the normal component, a Chorin projection method, and discretization in space by surface finite elements for each component. The approach thus requires only standard ingredients which most finite element implementations can offer. We compare computational results with discrete exterior calculus simulations on a torus and demonstrate the interplay of the flow field with the topology by showing realizations of the Poincaré-Hopf theorem on n-tori.

An Equal-Order DG Method for the Incompressible Navier-Stokes Equations

KAUST Repository

Cockburn, Bernardo

2008-12-20

We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability of this equal-order approach is ensured by a pressure stabilization term. A simple element-by-element post-processing procedure is used to provide globally divergence-free velocity approximations. For small data, we prove the existence and uniqueness of discrete solutions and carry out an error analysis of the method. A series of numerical results are presented that validate our theoretical findings. © 2008 Springer Science+Business Media, LLC.

Scaling properties of the two-dimensional randomly stirred Navier-Stokes equation.

Science.gov (United States)

Mazzino, Andrea; Muratore-Ginanneschi, Paolo; Musacchio, Stefano

2007-10-05

We inquire into the scaling properties of the 2D Navier-Stokes equation sustained by a force field with Gaussian statistics, white noise in time, and with a power-law correlation in momentum space of degree 2 - 2 epsilon. This is at variance with the setting usually assumed to derive Kraichnan's classical theory. We contrast accurate numerical experiments with the different predictions provided for the small epsilon regime by Kraichnan's double cascade theory and by renormalization group analysis. We give clear evidence that for all epsilon, Kraichnan's theory is consistent with the observed phenomenology. Our results call for a revision in the renormalization group analysis of (2D) fully developed turbulence.

Parallelization of Unsteady Adaptive Mesh Refinement for Unstructured Navier-Stokes Solvers

Science.gov (United States)

Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.

2014-01-01

This paper explores the implementation of the MPI parallelization in a Navier-Stokes solver using adaptive mesh re nement. Viscous and inviscid test problems are considered for the purpose of benchmarking, as are implicit and explicit time advancement methods. The main test problem for comparison includes e ects from boundary layers and other viscous features and requires a large number of grid points for accurate computation. Ex- perimental validation against double cone experiments in hypersonic ow are shown. The adaptive mesh re nement shows promise for a staple test problem in the hypersonic com- munity. Extension to more advanced techniques for more complicated ows is described.

Towards a Navier Stokes-Darcy Upscaling Based on Permeability Tensor Computation

KAUST Repository

Lieb, M.

2012-06-02

The micro scale simulation of CO2 sequestration involves complex, porous-like geometries. For the generation of such geometries, we present two approaches: In 2D, we construct a fractured domain by channel networks. In 3D, we approximate sand grain-like scenarios by dense sphere packings. The flow through these structures is simulated with the incompressible Navier-Stokes solver of the PDE framework Peano. Using an upscaling scheme, the results of the micro scale are used as input data for a Darcy solver on the coarse scales. The coupling concept and the scenario generators are presented together with first simulation results showing the validity of the approach.

Towards a Navier Stokes-Darcy Upscaling Based on Permeability Tensor Computation

KAUST Repository

Lieb, M.; Neckel, T.; Bungartz, H.-J.; Sun, Shuyu

2012-01-01

The micro scale simulation of CO2 sequestration involves complex, porous-like geometries. For the generation of such geometries, we present two approaches: In 2D, we construct a fractured domain by channel networks. In 3D, we approximate sand grain-like scenarios by dense sphere packings. The flow through these structures is simulated with the incompressible Navier-Stokes solver of the PDE framework Peano. Using an upscaling scheme, the results of the micro scale are used as input data for a Darcy solver on the coarse scales. The coupling concept and the scenario generators are presented together with first simulation results showing the validity of the approach.

Implementation of compact finite-difference method to parabolized Navier-Stokes equations

International Nuclear Information System (INIS)

Esfahanian, V.; Hejranfar, K.; Darian, H.M.

2005-01-01

The numerical simulation of the Parabolized Navier-Stokes (PNS) equations for supersonic/hypersonic flow field is obtained by using the fourth-order compact finite-difference method. The PNS equations in the general curvilinear coordinates are solved by using the implicit finite-difference algorithm of Beam and Warming. A shock fitting procedure is utilized to obtain the accurate solution in the vicinity of the shock. The computations are performed for hypersonic axisymmetric flow over a blunt cone. The present results for the flow field along with those of the second-order method are presented and accuracy analysis is performed to insure the fourth-order accuracy of the method. (author)

On lower bounds for possible blow-up solutions to the periodic Navier-Stokes equation

International Nuclear Information System (INIS)

Cortissoz, Jean C.; Montero, Julio A.; Pinilla, Carlos E.

2014-01-01

We show a new lower bound on the H .3/2 (T 3 ) norm of a possible blow-up solution to the Navier-Stokes equation, and also comment on the extension of this result to the whole space. This estimate can be seen as a natural limiting result for Leray's blow-up estimates in L p (R 3 ), 3 .5/2 (T 3 ), and give the corresponding extension to the case of the whole space

Euler and Navier endash Stokes limits of the Uehling endash Uhlenbeck quantum kinetic equations

International Nuclear Information System (INIS)

Arlotti, L.; Lachowicz, M.

1997-01-01

The Uehling endash Uhlenbeck evolution equations for gases of identical quantum particles either fermions or bosons, in the case in which the collision kernel does not depend on the distribution function, are considered. The existence of solutions and their asymptotic relations with solutions of the hydrodynamic equations both at the level of the Euler system and at the level of the Navier endash Stokes system are proved. copyright 1997 American Institute of Physics

2D study of wind forces around multiple cooling towers using ...

African Journals Online (AJOL)

A comprehensive numerical study for the determination of wind pressure coefficients on multiple cooling towers by simulating turbulence using Reynolds Averaged Navier-Stokes Equations (RANS) models of Computational Fluid Dynamics techniques (CFD) such as, Standard k −ε , RNG k −ε , Realizable k −ε and Reynolds ...

ARC2D - EFFICIENT SOLUTION METHODS FOR THE NAVIER-STOKES EQUATIONS (DEC RISC ULTRIX VERSION)

Science.gov (United States)

Biyabani, S. R.

1994-01-01

ARC2D is a computational fluid dynamics program developed at the NASA Ames Research Center specifically for airfoil computations. The program uses implicit finite-difference techniques to solve two-dimensional Euler equations and thin layer Navier-Stokes equations. It is based on the Beam and Warming implicit approximate factorization algorithm in generalized coordinates. The methods are either time accurate or accelerated non-time accurate steady state schemes. The evolution of the solution through time is physically realistic; good solution accuracy is dependent on mesh spacing and boundary conditions. The mathematical development of ARC2D begins with the strong conservation law form of the two-dimensional Navier-Stokes equations in Cartesian coordinates, which admits shock capturing. The Navier-Stokes equations can be transformed from Cartesian coordinates to generalized curvilinear coordinates in a manner that permits one computational code to serve a wide variety of physical geometries and grid systems. ARC2D includes an algebraic mixing length model to approximate the effect of turbulence. In cases of high Reynolds number viscous flows, thin layer approximation can be applied. ARC2D allows for a variety of solutions to stability boundaries, such as those encountered in flows with shocks. The user has considerable flexibility in assigning geometry and developing grid patterns, as well as in assigning boundary conditions. However, the ARC2D model is most appropriate for attached and mildly separated boundary layers; no attempt is made to model wake regions and widely separated flows. The techniques have been successfully used for a variety of inviscid and viscous flowfield calculations. The Cray version of ARC2D is written in FORTRAN 77 for use on Cray series computers and requires approximately 5Mb memory. The program is fully vectorized. The tape includes variations for the COS and UNICOS operating systems. Also included is a sample routine for CONVEX

Effects of droplet interactions on droplet transport at intermediate Reynolds numbers

Science.gov (United States)

Shuen, Jian-Shun

1987-01-01

Effects of droplet interactions on drag, evaporation, and combustion of a planar droplet array, oriented perpendicular to the approaching flow, are studied numerically. The three-dimensional Navier-Stokes equations, with variable thermophysical properties, are solved using finite-difference techniques. Parameters investigated include the droplet spacing, droplet Reynolds number, approaching stream oxygen concentration, and fuel type. Results are obtained for the Reynolds number range of 5 to 100, droplet spacings from 2 to 24 diameters, oxygen concentrations of 0.1 and 0.2, and methanol and n-butanol fuels. The calculations show that the gasification rates of interacting droplets decrease as the droplet spacings decrease. The reduction in gasification rates is significant only at small spacings and low Reynolds numbers. For the present array orientation, the effects of interactions on the gasification rates diminish rapidly for Reynolds numbers greater than 10 and spacings greater than 6 droplet diameters. The effects of adjacent droplets on drag are shown to be small.

Strong solutions for the Navier-Stokes equations on bounded and unbounded domains with a moving boundary

Directory of Open Access Journals (Sweden)

Juergen Saal

2007-02-01

Full Text Available It is proved under mild regularity assumptions on the data that the Navier-Stokes equations in bounded and unbounded noncylindrical regions admit a unique local-in-time strong solution. The result is based on maximal regularity estimates for the in spatial regions with a moving boundary obtained in [16] and the contraction mapping principle.

A superlinearly convergent finite volume method for the incompressible Navier-Stokes equations on staggered unstructured grids

International Nuclear Information System (INIS)

Vidovic, D.; Segal, A.; Wesseling, P.

2004-01-01

A method for linear reconstruction of staggered vector fields with special treatment of the divergence is presented. An upwind-biased finite volume scheme for solving the unsteady incompressible Navier-Stokes equations on staggered unstructured triangular grids that uses this reconstruction is described. The scheme is applied to three benchmark problems and is found to be superlinearly convergent in space

An adaptive Petrov-Galerkin formulation for solving the compressible Euler and Navier-Stokes

International Nuclear Information System (INIS)

Almeida, Regina Celia Cerqueira de

1993-01-01

A space-time finite element finite element formulation for the compressible Euler and Navier-Stokes equations is proposed. The present work develops a stable generalized CAU method which represents shocks and boundary-layers accurately. An h-adaptive remeshing refinement, which takes into account directional stretching and stretching ratio, is used leading to a very good way to indicate and refine the flow regions with singularities. Numerical experiment were conducted for some steady and unsteady problems and the performance of the proposed methods is discussed. (author)

Stream function-vorticity finite elements and the resolution of the Navier-Stokes equations

International Nuclear Information System (INIS)

Almeida, R.C.C. de.

1987-07-01

A stream function-vorticity finite element formulation for the solution of the Navier-Stokes equations is proposed. The present work shows a procedure to solve the problem posed by the no-slip conditions on solid frontiers which can also be applied to flow problems in a multi-connected domain. Moreover, a methodology to solve the pressure is developed using the stream function-vorticity approximate solution. Numerical experiments were conducted for some steady and unsteady problems and the performance of the proposed methods is discussed. (author) [pt

Finite volume methods for the incompressible Navier-Stokes equations on unstructured grids

Energy Technology Data Exchange (ETDEWEB)

Meese, Ernst Arne

1998-07-01

Most solution methods of computational fluid dynamics (CFD) use structured grids based on curvilinear coordinates for compliance with complex geometries. In a typical industry application, about 80% of the time used to produce the results is spent constructing computational grids. Recently the use of unstructured grids has been strongly advocated. For unstructured grids there are methods for generating them automatically on quite complex domains. This thesis focuses on the design of Navier-Stokes solvers that can cope with unstructured grids and ''low quality grids'', thus reducing the need for human intervention in the grid generation.

Study of blade-tower interaction using a 2D Navier-Stokes solver

Energy Technology Data Exchange (ETDEWEB)

Bertagnolio, F [Risoe National Lab., Wind Energy and Atmospheric Physics Dept., Roskilde (Denmark)

1999-03-01

The aim of this work is to model and study the dynamic interaction of the fluid flow with the structure which occurs when the blades of a wind turbine are passing in front of (or possibly behind) the tower. In order to capture the whole complexity of this phenomenon, the full unsteady Navier-Stokes equations for an incompressible fluid are used as a model. A new computational technique is described. For the sake of simplicity, we restrict ourselves to two-dimensional cases. The present methodology is illustrated by the computation of a wind turbine-like configuration in a periodic domain. (au)

On a modified form of navier-stokes equations for three-dimensional flows.

Science.gov (United States)

Venetis, J

2015-01-01

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces.

Coupling Navier-stokes and Cahn-hilliard Equations in a Two-dimensional Annular flow Configuration

KAUST Repository

Vignal, Philippe

2015-06-01

In this work, we present a novel isogeometric analysis discretization for the Navier-Stokes- Cahn-Hilliard equation, which uses divergence-conforming spaces. Basis functions generated with this method can have higher-order continuity, and allow to directly discretize the higher- order operators present in the equation. The discretization is implemented in PetIGA-MF, a high-performance framework for discrete differential forms. We present solutions in a two- dimensional annulus, and model spinodal decomposition under shear flow.

On incompressible limits for the Navier-Stokes system on unbounded domains under slip boundary conditions

Czech Academy of Sciences Publication Activity Database

Donatelli, D.; Feireisl, Eduard; Novotný, A.

2010-01-01

Roč. 13, č. 4 (2010), s. 783-798 ISSN 1531-3492 R&D Projects: GA MŠk LC06052; GA ČR GA201/08/0315 Institutional research plan: CEZ:AV0Z10190503 Keywords : Navier-Stokes equations * singular limits * low Mach number * compressible fluids * unbounded domains Subject RIV: BA - General Mathematics Impact factor: 0.874, year: 2010 http://www.aimsciences.org/journals/displayArticles.jsp?paperID=4976

Nearly Interactive Parabolized Navier-Stokes Solver for High Speed Forebody and Inlet Flows

Science.gov (United States)

Benson, Thomas J.; Liou, May-Fun; Jones, William H.; Trefny, Charles J.

2009-01-01

A system of computer programs is being developed for the preliminary design of high speed inlets and forebodies. The system comprises four functions: geometry definition, flow grid generation, flow solver, and graphics post-processor. The system runs on a dedicated personal computer using the Windows operating system and is controlled by graphical user interfaces written in MATLAB (The Mathworks, Inc.). The flow solver uses the Parabolized Navier-Stokes equations to compute millions of mesh points in several minutes. Sample two-dimensional and three-dimensional calculations are demonstrated in the paper.

Computational Fluid Dynamics (CFD) Computations With Zonal Navier-Stokes Flow Solver (ZNSFLOW) Common High Performance Computing Scalable Software Initiative (CHSSI) Software

National Research Council Canada - National Science Library

Edge, Harris

1999-01-01

...), computational fluid dynamics (CFD) 6 project. Under the project, a proven zonal Navier-Stokes solver was rewritten for scalable parallel performance on both shared memory and distributed memory high performance computers...

Convergence analysis of a class of massively parallel direction splitting algorithms for the Navier-Stokes equations in simple domains

KAUST Repository

Guermond, Jean-Luc; Minev, Peter D.; Salgado, Abner J.

2012-01-01

We provide a convergence analysis for a new fractional timestepping technique for the incompressible Navier-Stokes equations based on direction splitting. This new technique is of linear complexity, unconditionally stable and convergent, and suitable for massive parallelization. © 2012 American Mathematical Society.

Hydrodynamics beyond Navier-Stokes: the slip flow model.

Science.gov (United States)

Yudistiawan, Wahyu P; Ansumali, Santosh; Karlin, Iliya V

2008-07-01

Recently, analytical solutions for the nonlinear Couette flow demonstrated the relevance of the lattice Boltzmann (LB) models to hydrodynamics beyond the continuum limit [S. Ansumali, Phys. Rev. Lett. 98, 124502 (2007)]. In this paper, we present a systematic study of the simplest LB kinetic equation-the nine-bit model in two dimensions--in order to quantify it as a slip flow approximation. Details of the aforementioned analytical solution are presented, and results are extended to include a general shear- and force-driven unidirectional flow in confined geometry. Exact solutions for the velocity, as well as for pertinent higher-order moments of the distribution functions, are obtained in both Couette and Poiseuille steady-state flows for all values of rarefaction parameter (Knudsen number). Results are compared with the slip flow solution by Cercignani, and a good quantitative agreement is found for both flow situations. Thus, the standard nine-bit LB model is characterized as a valid and self-consistent slip flow model for simulations beyond the Navier-Stokes approximation.

Disentangling the triadic interactions in Navier-Stokes equations.

Science.gov (United States)

Sahoo, Ganapati; Biferale, Luca

2015-10-01

We study the role of helicity in the dynamics of energy transfer in a modified version of the Navier-Stokes equations with explicit breaking of the mirror symmetry. We select different set of triads participating in the dynamics on the basis of their helicity content. In particular, we remove the negative helically polarized Fourier modes at all wave numbers except for those falling on a localized shell of wave number, |k| ~ k(m). Changing k(m) to be above or below the forcing scale, k(f), we are able to assess the energy transfer of triads belonging to different interaction classes. We observe that when the negative helical modes are present only at a wave number smaller than the forced wave numbers, an inverse energy cascade develops with an accumulation of energy on a stationary helical condensate. Vice versa, when negative helical modes are present only at a wave number larger than the forced wave numbers, a transition from backward to forward energy transfer is observed in the regime when the minority modes become energetic enough.

The hybridized Discontinuous Galerkin method for Implicit Large-Eddy Simulation of transitional turbulent flows

Science.gov (United States)

Fernandez, P.; Nguyen, N. C.; Peraire, J.

2017-05-01

We present a high-order Implicit Large-Eddy Simulation (ILES) approach for transitional aerodynamic flows. The approach encompasses a hybridized Discontinuous Galerkin (DG) method for the discretization of the Navier-Stokes (NS) equations, and a parallel preconditioned Newton-GMRES solver for the resulting nonlinear system of equations. The combination of hybridized DG methods with an efficient solution procedure leads to a high-order accurate NS solver that is competitive to alternative approaches, such as finite volume and finite difference codes, in terms of computational cost. The proposed approach is applied to transitional flows over the NACA 65-(18)10 compressor cascade and the Eppler 387 wing at Reynolds numbers up to 460,000. Grid convergence studies are presented and the required resolution to capture transition at different Reynolds numbers is investigated. Numerical results show rapid convergence and excellent agreement with experimental data. In short, this work aims to demonstrate the potential of high-order ILES for simulating transitional aerodynamic flows. This is illustrated through numerical results and supported by theoretical considerations.

Existence and Stability of Spatial Plane Waves for the Incompressible Navier-Stokes in R^3

Science.gov (United States)

Correia, Simão; Figueira, Mário

2018-03-01

We consider the three-dimensional incompressible Navier-Stokes equation on the whole space. We observe that this system admits a L^∞ family of global spatial plane wave solutions, which are connected with the two-dimensional equation. We then proceed to prove local well-posedness over a space which includes L^3(R^3) and these solutions. Finally, we prove L^3-stability of spatial plane waves, with no condition on their size.

Status for the two-dimensional Navier-Stokes solver EllipSys2D

Energy Technology Data Exchange (ETDEWEB)

Bertagnolio, F.; Soerensen, N.; Johansen, J.

2001-08-01

This report sets up an evaluation of two-dimensional Navier-Stokes solver EllipSys2D in its present state. This code is used for blade aerodynamics simulations in the Aeroelastic Design group at Risoe. Two airfoils are investigated by computing the flow at several angles of attack ranging from the linear to the stalled region. The computational data are compared to experimental data and numerical results from other computational codes. Several numerical aspects are studied, as mesh dependency, convective scheme, steady state versus unsteady computations, transition modelling. Some general conclusions intended to help in using this code for numerical simulations are given. (au)

An upwind algorithm for the parabolized Navier-Stokes equations

Science.gov (United States)

Lawrence, S. L.; Tannehill, J. C.; Chaussee, D. S.

1986-01-01

A new upwind algorithm based on Roe's scheme has been developed to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method does not require the addition of user specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming scheme in terms of accuracy, stability, computer time and storage, and programming effort. The new algorithm has been validated by applying it to three laminar test cases including flat plate boundary-layer flow, hypersonic flow past a 15 deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with the results obtained using the conventional Beam-Warming algorithm.

The Navier-Stokes equations an elementary functional analytic approach

CERN Document Server

Sohr, Hermann

2001-01-01

The primary objective of this monograph is to develop an elementary and self­ contained approach to the mathematical theory of a viscous incompressible fluid in a domain 0 of the Euclidean space ]Rn, described by the equations of Navier­ Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers' convenience, in the first two chapters we collect without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain O. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n = 2,3 that are also most significant from the physical point of view. For mathematical generality, we will develop the lin­ earized theory for all n 2 2. Although the functional-analytic approach developed here is, in principle, known ...

The Navier-Stokes equations an elementary functional analytic approach

CERN Document Server

Sohr, Hermann

2001-01-01

The primary objective of this monograph is to develop an elementary and self-contained approach to the mathematical theory of a viscous, incompressible fluid in a domain of the Euclidean space, described by the equations of Navier-Stokes. Moreover, the theory is presented for completely general domains, in particular, for arbitrary unbounded, nonsmooth domains. Therefore, restriction was necessary to space dimensions two and three, which are also the most significant from a physical point of view. For mathematical generality, however, the linearized theory is expounded for general dimensions higher than one. Although the functional analytic approach developed here is, in principle, known to specialists, the present book fills a gap in the literature providing a systematic treatment of a subject that has been documented until now only in fragments. The book is mainly directed to students familiar with basic tools in Hilbert and Banach spaces. However, for the readers’ convenience, some fundamental properties...

Generalized conjugate-gradient methods for the Navier-Stokes equations

Science.gov (United States)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1991-01-01

A generalized conjugate-gradient method is used to solve the two-dimensional, compressible Navier-Stokes equations of fluid flow. The equations are discretized with an implicit, upwind finite-volume formulation. Preconditioning techniques are incorporated into the new solver to accelerate convergence of the overall iterative method. The superiority of the new solver is demonstrated by comparisons with a conventional line Gauss-Siedel Relaxation solver. Computational test results for transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (M = 6.0 shock-on-shock phenoena on a cylindrical leading edge) are presented. When applied to the transonic cascade case, the new solver is 4.4 times faster in terms of number of iterations and 3.1 times faster in terms of CPU time than the Relaxation solver. For the hypersonic shock case, the new solver is 3.0 times faster in terms of number of iterations and 2.2 times faster in terms of CPU time than the Relaxation solver.

On the Critical One Component Regularity for 3-D Navier-Stokes System: General Case

Science.gov (United States)

Chemin, Jean-Yves; Zhang, Ping; Zhang, Zhifei

2017-06-01

Let us consider initial data {v_0} for the homogeneous incompressible 3D Navier-Stokes equation with vorticity belonging to {L^{3/2}\\cap L^2}. We prove that if the solution associated with {v_0} blows up at a finite time {T^\\star}, then for any p in {]4,∞[}, and any unit vector e of {R^3}, the L p norm in time with value in \\dot{H}^{1/2 + 2/p } of {(v|e)_{R^3}} blows up at {T^\\star}.

An adaptive Petrov-Galerkin formulation for solving the compressible Euler and Navier-Stokes; Uma formulacao de Petrov-Galerkin para a resolucao das equacoes de Euler e Navier-Stokes compressivel usando tecnicas adaptativas

Energy Technology Data Exchange (ETDEWEB)

Almeida, Regina Celia Cerqueira de

1993-12-31

A space-time finite element finite element formulation for the compressible Euler and Navier-Stokes equations is proposed. The present work develops a stable generalized CAU method which represents shocks and boundary-layers accurately. An h-adaptive remeshing refinement, which takes into account directional stretching and stretching ratio, is used leading to a very good way to indicate and refine the flow regions with singularities. Numerical experiment were conducted for some steady and unsteady problems and the performance of the proposed methods is discussed. (author) 63 refs., 40 figs.

An adaptive Petrov-Galerkin formulation for solving the compressible Euler and Navier-Stokes; Uma formulacao de Petrov-Galerkin para a resolucao das equacoes de Euler e Navier-Stokes compressivel usando tecnicas adaptativas

Energy Technology Data Exchange (ETDEWEB)

Almeida, Regina Celia Cerqueira de

1994-12-31

A space-time finite element finite element formulation for the compressible Euler and Navier-Stokes equations is proposed. The present work develops a stable generalized CAU method which represents shocks and boundary-layers accurately. An h-adaptive remeshing refinement, which takes into account directional stretching and stretching ratio, is used leading to a very good way to indicate and refine the flow regions with singularities. Numerical experiment were conducted for some steady and unsteady problems and the performance of the proposed methods is discussed. (author) 63 refs., 40 figs.

A frequency domain linearized Navier-Stokes method including acoustic damping by eddy viscosity using RANS

Science.gov (United States)

Holmberg, Andreas; Kierkegaard, Axel; Weng, Chenyang

2015-06-01

In this paper, a method for including damping of acoustic energy in regions of strong turbulence is derived for a linearized Navier-Stokes method in the frequency domain. The proposed method is validated and analyzed in 2D only, although the formulation is fully presented in 3D. The result is applied in a study of the linear interaction between the acoustic and the hydrodynamic field in a 2D T-junction, subject to grazing flow at Mach 0.1. Part of the acoustic energy at the upstream edge of the junction is shed as harmonically oscillating disturbances, which are conveyed across the shear layer over the junction, where they interact with the acoustic field. As the acoustic waves travel in regions of strong shear, there is a need to include the interaction between the background turbulence and the acoustic field. For this purpose, the oscillation of the background turbulence Reynold's stress, due to the acoustic field, is modeled using an eddy Newtonian model assumption. The time averaged flow is first solved for using RANS along with a k-ε turbulence model. The spatially varying turbulent eddy viscosity is then added to the spatially invariant kinematic viscosity in the acoustic set of equations. The response of the 2D T-junction to an incident acoustic field is analyzed via a plane wave scattering matrix model, and the result is compared to experimental data for a T-junction of rectangular ducts. A strong improvement in the agreement between calculation and experimental data is found when the modification proposed in this paper is implemented. Discrepancies remaining are likely due to inaccuracies in the selected turbulence model, which is known to produce large errors e.g. for flows with significant rotation, which the grazing flow across the T-junction certainly is. A natural next step is therefore to test the proposed methodology together with more sophisticated turbulence models.

Y spaces and global smooth solution of fractional Navier-Stokes equations with initial value in the critical oscillation spaces

Science.gov (United States)

Yang, Qixiang; Yang, Haibo

2018-04-01

For fractional Navier-Stokes equations and critical initial spaces X, one used to establish the well-posedness in the solution space which is contained in C (R+ , X). In this paper, for heat flow, we apply parameter Meyer wavelets to introduce Y spaces Y m , β where Y m , β is not contained in C (R+, B˙∞ 1 - 2 β , ∞). Consequently, for 1/2 global well-posedness of fractional Navier-Stokes equations with small initial data in all the critical oscillation spaces. The critical oscillation spaces may be any Besov-Morrey spaces (B˙p,q γ1 ,γ2 (Rn)) n or any Triebel-Lizorkin-Morrey spaces (F˙p,q γ1 ,γ2 (Rn)) n where 1 ≤ p , q ≤ ∞ , 0 ≤γ2 ≤ n/p, γ1 -γ2 = 1 - 2 β. These critical spaces include many known spaces. For example, Besov spaces, Sobolev spaces, Bloch spaces, Q-spaces, Morrey spaces and Triebel-Lizorkin spaces etc.

Reynolds Number Effect on Spatial Development of Viscous Flow Induced by Wave Propagation Over Bed Ripples

Science.gov (United States)

Dimas, Athanassios A.; Kolokythas, Gerasimos A.

Numerical simulations of the free-surface flow, developing by the propagation of nonlinear water waves over a rippled bottom, are performed assuming that the corresponding flow is two-dimensional, incompressible and viscous. The simulations are based on the numerical solution of the Navier-Stokes equations subject to the fully-nonlinear free-surface boundary conditions and appropriate bottom, inflow and outflow boundary conditions. The equations are properly transformed so that the computational domain becomes time-independent. For the spatial discretization, a hybrid scheme is used where central finite-differences, in the horizontal direction, and a pseudo-spectral approximation method with Chebyshev polynomials, in the vertical direction, are applied. A fractional time-step scheme is used for the temporal discretization. Over the rippled bed, the wave boundary layer thickness increases significantly, in comparison to the one over flat bed, due to flow separation at the ripple crests, which generates alternating circulation regions. The amplitude of the wall shear stress over the ripples increases with increasing ripple height or decreasing Reynolds number, while the corresponding friction force is insensitive to the ripple height change. The amplitude of the form drag forces due to dynamic and hydrostatic pressures increase with increasing ripple height but is insensitive to the Reynolds number change, therefore, the percentage of friction in the total drag force decreases with increasing ripple height or increasing Reynolds number.

Entropic lattice Boltzmann representations required to recover Navier-Stokes flows.

Science.gov (United States)

Keating, Brian; Vahala, George; Yepez, Jeffrey; Soe, Min; Vahala, Linda

2007-03-01

There are two disparate formulations of the entropic lattice Boltzmann scheme: one of these theories revolves around the analog of the discrete Boltzmann H function of standard extensive statistical mechanics, while the other revolves around the nonextensive Tsallis entropy. It is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of entropy resulting in Tsallis-like forms. However, with the imposition of the pressure tensor moment constraint, as is fundamentally necessary for the recovery of the Navier-Stokes equations, it is proved that the entropy function must be of the discrete Boltzmann form. Three-dimensional simulations are performed which illustrate some of the differences between standard lattice Boltzmann and entropic lattice Boltzmann schemes, as well as the role played by the number of phase-space velocities used in the discretization.

The fundamental solution of linearized nonstationary Navier-Stokes equations of motion around a rotating and translating body

Czech Academy of Sciences Publication Activity Database

Farwig, R.; Guenther, R.; Thomann, E.; Nečasová, Šárka

2014-01-01

Roč. 34, č. 2 (2014), s. 511-529 ISSN 1078-0947 R&D Projects: GA ČR(CZ) GAP201/11/1304; GA MŠk LC06052 Institutional support: RVO:67985840 Keywords : fundamental solution * linearized problem * Navier-Stokes problem Subject RIV: BA - General Mathematics Impact factor: 0.826, year: 2014 http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=8831

A fast Poisson solver for unsteady incompressible Navier-Stokes equations on the half-staggered grid

Science.gov (United States)

Golub, G. H.; Huang, L. C.; Simon, H.; Tang, W. -P.

1995-01-01

In this paper, a fast Poisson solver for unsteady, incompressible Navier-Stokes equations with finite difference methods on the non-uniform, half-staggered grid is presented. To achieve this, new algorithms for diagonalizing a semi-definite pair are developed. Our fast solver can also be extended to the three dimensional case. The motivation and related issues in using this second kind of staggered grid are also discussed. Numerical testing has indicated the effectiveness of this algorithm.

Discretely Self-Similar Solutions to the Navier-Stokes Equations with Besov Space Data

Science.gov (United States)

Bradshaw, Zachary; Tsai, Tai-Peng

2017-12-01

We construct self-similar solutions to the three dimensional Navier-Stokes equations for divergence free, self-similar initial data that can be large in the critical Besov space {\\dot{B}_{p,∞}^{3/p-1}} where 3 1. These results extend those of uc(Bradshaw) and uc(Tsai) (Ann Henri Poincaré 2016. https://doi.org/10.1007/s00023-016-0519-0) which dealt with initial data in L 3 w since {L^3_w\\subsetneq \\dot{B}_{p,∞}^{3/p-1}} for p > 3. We also provide several concrete examples of vector fields in the relevant function spaces.

Stability of Planar Rarefaction Wave to 3D Full Compressible Navier-Stokes Equations

Science.gov (United States)

Li, Lin-an; Wang, Teng; Wang, Yi

2018-05-01

We prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, compressible Navier-Stokes equations with the heat-conductivities in an infinite long flat nozzle domain {R × T^2} . Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying wave structures, which are crucial for overcoming the difficulties due to the wave propagation in the transverse directions x 2 and x 3 and its interactions with the planar rarefaction wave in x 1 direction.

Large Scale Flutter Data for Design of Rotating Blades Using Navier-Stokes Equations

Science.gov (United States)

Guruswamy, Guru P.

2012-01-01

A procedure to compute flutter boundaries of rotating blades is presented; a) Navier-Stokes equations. b) Frequency domain method compatible with industry practice. Procedure is initially validated: a) Unsteady loads with flapping wing experiment. b) Flutter boundary with fixed wing experiment. Large scale flutter computation is demonstrated for rotating blade: a) Single job submission script. b) Flutter boundary in 24 hour wall clock time with 100 cores. c) Linearly scalable with number of cores. Tested with 1000 cores that produced data in 25 hrs for 10 flutter boundaries. Further wall-clock speed-up is possible by performing parallel computations within each case.

Consistency, Verification, and Validation of Turbulence Models for Reynolds-Averaged Navier-Stokes Applications

Science.gov (United States)

Rumsey, Christopher L.

2009-01-01

In current practice, it is often difficult to draw firm conclusions about turbulence model accuracy when performing multi-code CFD studies ostensibly using the same model because of inconsistencies in model formulation or implementation in different codes. This paper describes an effort to improve the consistency, verification, and validation of turbulence models within the aerospace community through a website database of verification and validation cases. Some of the variants of two widely-used turbulence models are described, and two independent computer codes (one structured and one unstructured) are used in conjunction with two specific versions of these models to demonstrate consistency with grid refinement for several representative problems. Naming conventions, implementation consistency, and thorough grid resolution studies are key factors necessary for success.

Regularity criterion for solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations and associated computations.

Science.gov (United States)

Gibbon, John D; Pal, Nairita; Gupta, Anupam; Pandit, Rahul

2016-12-01

We consider the three-dimensional (3D) Cahn-Hilliard equations coupled to, and driven by, the forced, incompressible 3D Navier-Stokes equations. The combination, known as the Cahn-Hilliard-Navier-Stokes (CHNS) equations, is used in statistical mechanics to model the motion of a binary fluid. The potential development of singularities (blow-up) in the contours of the order parameter ϕ is an open problem. To address this we have proved a theorem that closely mimics the Beale-Kato-Majda theorem for the 3D incompressible Euler equations [J. T. Beale, T. Kato, and A. J. Majda, Commun. Math. Phys. 94, 61 (1984)CMPHAY0010-361610.1007/BF01212349]. By taking an L^{∞} norm of the energy of the full binary system, designated as E_{∞}, we have shown that ∫_{0}^{t}E_{∞}(τ)dτ governs the regularity of solutions of the full 3D system. Our direct numerical simulations (DNSs) of the 3D CHNS equations for (a) a gravity-driven Rayleigh Taylor instability and (b) a constant-energy-injection forcing, with 128^{3} to 512^{3} collocation points and over the duration of our DNSs confirm that E_{∞} remains bounded as far as our computations allow.

Particles at fluid-fluid interfaces: A new Navier-Stokes-Cahn-Hilliard surface- phase-field-crystal model.

Science.gov (United States)

Aland, Sebastian; Lowengrub, John; Voigt, Axel

2012-10-01

Colloid particles that are partially wetted by two immiscible fluids can become confined to fluid-fluid interfaces. At sufficiently high volume fractions, the colloids may jam and the interface may crystallize. The fluids together with the interfacial colloids form an emulsion with interesting material properties and offer an important route to new soft materials. A promising approach to simulate these emulsions was presented in Aland et al. [Phys. Fluids 23, 062103 (2011)], where a Navier-Stokes-Cahn-Hilliard model for the macroscopic two-phase fluid system was combined with a surface phase-field-crystal model for the microscopic colloidal particles along the interface. Unfortunately this model leads to spurious velocities which require very fine spatial and temporal resolutions to accurately and stably simulate. In this paper we develop an improved Navier-Stokes-Cahn-Hilliard-surface phase-field-crystal model based on the principles of mass conservation and thermodynamic consistency. To validate our approach, we derive a sharp interface model and show agreement with the improved diffuse interface model. Using simple flow configurations, we show that the new model has much better properties and does not lead to spurious velocities. Finally, we demonstrate the solid-like behavior of the crystallized interface by simulating the fall of a solid ball through a colloid-laden multiphase fluid.

On regularity of a weak solution to the Navier–Stokes equations with the generalized Navier slip boundary conditions

Czech Academy of Sciences Publication Activity Database

Neustupa, Jiří; Penel, P.

2018-01-01

Roč. 2018, March (2018), č. článku 4617020. ISSN 1687-9120 R&D Projects: GA ČR(CZ) GA17-01747S Institutional support: RVO:67985840 Keywords : Navier-Stokes equations Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.643, year: 2016 https://www.hindawi.com/journals/amp/2018/4617020/

On the energy inequality for weak solutions to the Navier-Stokes equations of compressible fluids on unbounded domains

Czech Academy of Sciences Publication Activity Database

Dell'Oro, Filippo; Feireisl, Eduard

2015-01-01

Roč. 128, November (2015), s. 136-148 ISSN 0362-546X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : compressible Navier-Stokes equations * unbounded domain * weak solutions * energy inequality Subject RIV: BA - General Mathematics Impact factor: 1.125, year: 2015 http://www.sciencedirect.com/science/article/pii/S0362546X15002692

Simulating variable-density flows with time-consistent integration of Navier-Stokes equations

Science.gov (United States)

Lu, Xiaoyi; Pantano, Carlos

2017-11-01

In this talk, we present several features of a high-order semi-implicit variable-density low-Mach Navier-Stokes solver. A new formulation to solve pressure Poisson-like equation of variable-density flows is highlighted. With this formulation of the numerical method, we are able to solve all variables with a uniform order of accuracy in time (consistent with the time integrator being used). The solver is primarily designed to perform direct numerical simulations for turbulent premixed flames. Therefore, we also address other important elements, such as energy-stable boundary conditions, synthetic turbulence generation, and flame anchoring method. Numerical examples include classical non-reacting constant/variable-density flows, as well as turbulent premixed flames.

Involving the Navier-Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method.

Science.gov (United States)

Verschaeve, Joris C G

2011-06-13

By means of the continuity equation of the incompressible Navier-Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

Error estimates for a numerical method for the compressible Navier-Stokes system on sufficiently smooth domains

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Hošek, Radim; Maltese, D.; Novotný, A.

2017-01-01

Roč. 51, č. 1 (2017), s. 279-319 ISSN 0764-583X EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes system * finite element numerical method * finite volume numerical method Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.727, year: 2016 http://www.esaim-m2an.org/ articles /m2an/abs/2017/01/m2an150157/m2an150157.html

A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations

Czech Academy of Sciences Publication Activity Database

Neustupa, Jiří

2014-01-01

Roč. 139, č. 4 (2014), s. 685-698 ISSN 0862-7959 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * suitable weak solution * regularity Subject RIV: BA - General Mathematics http://hdl.handle.net/10338.dmlcz/144145

The application of Flamelet Generated Manifolds in partailly-premixed flames

NARCIS (Netherlands)

Ramaekers, W.J.S.; Albrecht, B.A.; Oijen, van J.A.; Goey, de L.P.H.; Eggels, R.L.G.M.

2005-01-01

To reduce harmful emissions numerical models are developed to simulate combustion processes in engineering applications. In this paper a model for partially-premixed combustion used in Reynolds Averaged Navier-Stokes Simulations (RANS) is presented. A flamelet approach combined with a Probability

3D Navier-Stokes simulations of a rotor designed for maximum aerodynamic efficiency

DEFF Research Database (Denmark)

Johansen, Jeppe; Madsen Aagaard, Helge; Gaunaa, Mac

2007-01-01

a constant load was assumed. The rotor design was obtained using an Actuator Disc model and was subsequently verified using both a free wake Lifting Line method and a full 3D Navier-Stokes solver. Excellent agreement was obtained using the three models. Global mechanical power coefficient, CP, reached...... a value of slightly above 0.51, while global thrust coefficient, CT, was 0.87. The local power coefficient, Cp, increased to slightly above the Betz limit on the inner part of the rotor as well as the local thrust coefficient, Ct, increased to a value above 1.1. This agrees well with the theory of de...

Regularity of a weak solution to the Navier--Stokes equations via one component of a spectral projection of vorticity

Czech Academy of Sciences Publication Activity Database

Neustupa, Jiří; Penel, P.

2014-01-01

Roč. 46, č. 2 (2014), s. 1681-1700 ISSN 0036-1410 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equations * weak solution * regularity criteria Subject RIV: BA - General Mathematics Impact factor: 1.265, year: 2014 http://epubs.siam.org/doi/abs/10.1137/120874874

Stochastic solutions of Navier-Stokes equations: an experimental evidence.

Science.gov (United States)

Djurek, Ivan; Djurek, Danijel; Petosić, Antonio

2010-12-01

An electrodynamic loudspeaker has been operated in anharmonic regime indicated by the nonlinear ordinary differential equation when spring constant γ in restoring term, as well as, viscoelasticity of the membrane material, increases with displacement. For driving currents in the range of 2.8-3.3 A, doubling of the vibration period appears, while for currents in the range of 3.3-3.6 A, multiple sequences of subharmonic vibrations begin with f/4 and 3f/4. An application of currents higher than 3.6 A results in a spectrum, characteristic for the chaotic state. The loudspeaker was then operated in a closed chamber, and subharmonic vibrations disappeared by an evacuation. Subsequent injection of air revoked them again at ∼ 120 mbar (Re(')=476) when air viscous forces dominate the Morse convection. At 430 mbar (Re=538) single vibration state was restored, and the phenomenon is in an agreement with prediction of the five mode truncation procedure applied to the Navier-Stokes equations describing a two-dimensional incompressible fluid. © 2010 American Institute of Physics.

The Vlasov-Navier-Stokes System in a 2D Pipe: Existence and Stability of Regular Equilibria

Science.gov (United States)

Glass, Olivier; Han-Kwan, Daniel; Moussa, Ayman

2018-05-01

In this paper, we study the Vlasov-Navier-Stokes system in a 2D pipe with partially absorbing boundary conditions. We show the existence of stationary states for this system near small Poiseuille flows for the fluid phase, for which the kinetic phase is not trivial. We prove the asymptotic stability of these states with respect to appropriately compactly supported perturbations. The analysis relies on geometric control conditions which help to avoid any concentration phenomenon for the kinetic phase.

Validation of the actuator line/Navier Stokes technique using mexico measurements

DEFF Research Database (Denmark)

Shen, Wen Zhong; Zhu, Wei Jun; Sørensen, Jens Nørkær

2010-01-01

This paper concerns the contribution of DTU MEK in the international research collaboration project (MexNext) within the framework of IEA Annex 29 to validate aerodynamic models or CFD codes using the existing measurements made in the previous EU funded projectMEXICO (Model Experiments in Control......This paper concerns the contribution of DTU MEK in the international research collaboration project (MexNext) within the framework of IEA Annex 29 to validate aerodynamic models or CFD codes using the existing measurements made in the previous EU funded projectMEXICO (Model Experiments...... in Controlled Conditions). The Actuator Line/Navier Stokes (AL/NS) technique developed at DTU is validated against the detailed MEXICO measurements. The AL/NS computations without the DNW wind tunnel with speeds of 10m/s, 15m/s and 24m/s. Comparisons of blade loading between computations and measurements show...

Airborne spread of expiratory droplet nuclei between the occupants of indoor environments: a review

DEFF Research Database (Denmark)

Ai, Z.T.; Melikov, Arsen Krikor

2018-01-01

Reynolds-averaged Navier-Stokes modelling. Future research needs in three areas are identified: the importance of the direction of indoor airflow patterns, the dynamics of airborne transmission, and the application of CFD simulations. This article is protected by copyright. All rights reserved....

Computing the flow past Vortex Generators : Comparison between RANS Simulations and Experiments

NARCIS (Netherlands)

Manolesos, M.; Sorensen, NN; Troldborg, N.; Florentie, L.; Papadakis, G; Voutsinas, S.

2016-01-01

The flow around a wind turbine airfoil equipped with Vortex Generators (VGs) is examined. Predictions from three different Reynolds Averaged Navier Stokes (RANS) solvers with two different turbulence models and two different VG modelling approaches are compared between them and with experimental

Investigation of the use of Prandtl/Navier--Stokes equation procedures for two-dimensional incompressible flows

International Nuclear Information System (INIS)

Anderson, C.R.; Reider, M.B.

1994-01-01

The technique of combining solutions of the Prandtl equations with solutions of the Navier--Stokes equations to compute incompressible flow around two-dimensional bodies is investigated herein. Computational evidence is presented which shows that if the ''obvious'' coupling is used to combine the solutions, then the resulting solution is not accurate. An alternate coupling procedure is described which greatly improves the accuracy of the solutions obtained with the combined equation approach. An alternate coupling that can be used to create a more accurate vortex sheet/vortex blob method is then shown

Hybrid RANS/LES method for high Reynolds numbers, applied to atmospheric flow over complex terrain

DEFF Research Database (Denmark)

Bechmann, Andreas; Sørensen, Niels N.; Johansen, Jeppe

2007-01-01

  The use of Large-Eddy Simulation (LES) to predict wall-bounded flows has presently been limited to low Reynolds number flows. Since the number of computational grid points required to resolve the near-wall turbulent structures increase rapidly with Reynolds number, LES has been unattainable...... for flows at high Reynolds numbers. To reduce the computational cost of traditional LES a hybrid method is proposed in which the near-wall eddies are modelled in a Reynolds-averaged sense. Close to walls the flow is treated with the RANS-equations and this layer act as wall model for the outer flow handled...... by LES. The wellknown high Reynolds number two-equation k - ǫ turbulence model is used in the RANS layer and the model automatically switches to a two-equation k - ǫ subgrid-scale stress model in the LES region. The approach can be used for flow over rough walls. To demonstrate the ability...

Simulation of an ITER-like dissipative divertor plasma with a combined edge plasma Navier-Stokes neutral model

International Nuclear Information System (INIS)

Knoll, D.A.; McHugh, P.R.; Krasheninnikov, S.I.; Sigmar, D.J.

1996-01-01

A combined edge plasma/Navier-Stokes neutral transport model is used to simulate dissipative divertor plasmas in the collisional limit for neutrals on a simplified two-dimensional slab geometry with ITER-like plasma conditions and scale lengths. The neutral model contains three momentum equations which are coupled to the plasma through ionization, recombination, and ion-neutral elastic collisions. The neutral transport coefficients are evaluated including both ion-neutral and neutral-neutral collisions. (orig.)

Application of the FUN3D Unstructured-Grid Navier-Stokes Solver to the 4th AIAA Drag Prediction Workshop Cases

Science.gov (United States)

Lee-Rausch, Elizabeth M.; Hammond, Dana P.; Nielsen, Eric J.; Pirzadeh, S. Z.; Rumsey, Christopher L.

2010-01-01

FUN3D Navier-Stokes solutions were computed for the 4th AIAA Drag Prediction Workshop grid convergence study, downwash study, and Reynolds number study on a set of node-based mixed-element grids. All of the baseline tetrahedral grids were generated with the VGRID (developmental) advancing-layer and advancing-front grid generation software package following the gridding guidelines developed for the workshop. With maximum grid sizes exceeding 100 million nodes, the grid convergence study was particularly challenging for the node-based unstructured grid generators and flow solvers. At the time of the workshop, the super-fine grid with 105 million nodes and 600 million elements was the largest grid known to have been generated using VGRID. FUN3D Version 11.0 has a completely new pre- and post-processing paradigm that has been incorporated directly into the solver and functions entirely in a parallel, distributed memory environment. This feature allowed for practical pre-processing and solution times on the largest unstructured-grid size requested for the workshop. For the constant-lift grid convergence case, the convergence of total drag is approximately second-order on the finest three grids. The variation in total drag between the finest two grids is only 2 counts. At the finest grid levels, only small variations in wing and tail pressure distributions are seen with grid refinement. Similarly, a small wing side-of-body separation also shows little variation at the finest grid levels. Overall, the FUN3D results compare well with the structured-grid code CFL3D. The FUN3D downwash study and Reynolds number study results compare well with the range of results shown in the workshop presentations.

Boundary Layers for the Navier-Stokes Equations Linearized Around a Stationary Euler Flow

Science.gov (United States)

Gie, Gung-Min; Kelliher, James P.; Mazzucato, Anna L.

2018-03-01

We study the viscous boundary layer that forms at small viscosity near a rigid wall for the solution to the Navier-Stokes equations linearized around a smooth and stationary Euler flow (LNSE for short) in a smooth bounded domain Ω \\subset R^3 under no-slip boundary conditions. LNSE is supplemented with smooth initial data and smooth external forcing, assumed ill-prepared, that is, not compatible with the no-slip boundary condition. We construct an approximate solution to LNSE on the time interval [0, T], 0Math J 45(3):863-916, 1996), Xin and Yanagisawa (Commun Pure Appl Math 52(4):479-541, 1999), and Gie (Commun Math Sci 12(2):383-400, 2014).

Optimization of air-curtain sealing efficiency with respect to heat transfer in naturally ventilated buildings

NARCIS (Netherlands)

Khayrullina, A.; Hooff, van T.A.J.; Blocken, B.J.E.; van Heijst, G.J.F.; Sun, Y.; Pei, J.; Zhao, X

This study presents results of coupled 3D steady Reynolds-averaged Navier-Stokes (RANS) Computational Fluid Dynamics (CFD) simulations of an isolated naturally-ventilated building with the application of an air curtain to prevent heat transfer across a doorway. The considered parameters include air

Nonlinear Eddy Viscosity Models applied to Wind Turbine Wakes

DEFF Research Database (Denmark)

Laan, van der, Paul Maarten; Sørensen, Niels N.; Réthoré, Pierre-Elouan

2013-01-01

The linear k−ε eddy viscosity model and modified versions of two existing nonlinear eddy viscosity models are applied to single wind turbine wake simulations using a Reynolds Averaged Navier-Stokes code. Results are compared with field wake measurements. The nonlinear models give better results...

Predicting wind farm wake interaction with RANS: an investigation of the Coriolis force

DEFF Research Database (Denmark)

van der Laan, Paul; Hansen, Kurt Schaldemose; Sørensen, Niels N.

2015-01-01

A Reynolds-averaged Navier-Stokes code is used to simulate the interaction of two neighboring wind farms. The influence of the Coriolis force is investigated by modeling the atmospheric surface/boundary layer with three different methodologies. The results show that the Coriolis force is negligible...

Large Eddy Simulations using oodlesDST

Science.gov (United States)

2016-01-01

Research Agency DST-Group-TR-3205 ABSTRACT The oodlesDST code is based on OpenFOAM software and performs Large Eddy Simulations of......maritime platforms using a variety of simulation techniques. He is currently using OpenFOAM software to perform both Reynolds Averaged Navier-Stokes

Unsteady Navier-Stokes computations over airfoils using both fixed and dynamic meshes

Science.gov (United States)

Rumsey, Christopher L.; Anderson, W. Kyle

1989-01-01

A finite volume implicit approximate factorization method which solves the thin layer Navier-Stokes equations was used to predict unsteady turbulent flow airfoil behavior. At a constant angle of attack of 16 deg, the NACA 0012 airfoil exhibits an unsteady periodic flow field with the lift coefficient oscillating between 0.89 and 1.60. The Strouhal number is 0.028. Results are similar at 18 deg, with a Strouhal number of 0.033. A leading edge vortex is shed periodically near maximum lift. Dynamic mesh solutions for unstalled airfoil flows show general agreement with experimental pressure coefficients. However, moment coefficients and the maximum lift value are underpredicted. The deep stall case shows some agreement with experiment for increasing angle of attack, but is only qualitatively comparable past stall and for decreasing angle of attack.

Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations

Science.gov (United States)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2014-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

Investigation of Velocity Distribution in Open Channel Flows Based on Conditional Average of Turbulent Structures

Directory of Open Access Journals (Sweden)

Yu Han

2017-01-01

Full Text Available We report the development of a new analytical model similar to the Reynolds-averaged Navier-Stokes equations to determine the distribution of streamwise velocity by considering the bursting phenomenon. It is found that, in two-dimensional (2D flows, the underlying mechanism of the wake law in 2D uniform flow is actually a result of up/down events. A special experiment was conducted to examine the newly derived analytical model, and good agreement is achieved between the experimental data in the inner region and the model’s prediction. The obtained experimental data were also used to examine the DML-Law (dip-modified-log-law, MLW-Law (modified-log-wake law, and CML-Law (Cole’s wake law, and the agreement is not very satisfactory in the outer region.

The steady Navier–Stokes problem with the inhomogeneous Navier-type boundary conditions in a 2D multiply-connected bounded domain

Czech Academy of Sciences Publication Activity Database

Neustupa, Jiří

2015-01-01

Roč. 35, č. 3 (2015), s. 201-212 ISSN 0174-4747 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : steady Navier-Stokes problem * slip boundary conditions Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/anly.2015.35.issue-3/anly-2014-1304/anly-2014-1304. xml

Numerical investigation of the vortex-induced vibration of an elastically mounted circular cylinder at high Reynolds number (Re = 104 and low mass ratio using the RANS code.

Directory of Open Access Journals (Sweden)

Niaz Bahadur Khan

Full Text Available This study numerically investigates the vortex-induced vibration (VIV of an elastically mounted rigid cylinder by using Reynolds-averaged Navier-Stokes (RANS equations with computational fluid dynamic (CFD tools. CFD analysis is performed for a fixed-cylinder case with Reynolds number (Re = 104 and for a cylinder that is free to oscillate in the transverse direction and possesses a low mass-damping ratio and Re = 104. Previously, similar studies have been performed with 3-dimensional and comparatively expensive turbulent models. In the current study, the capability and accuracy of the RANS model are validated, and the results of this model are compared with those of detached eddy simulation, direct numerical simulation, and large eddy simulation models. All three response branches and the maximum amplitude are well captured. The 2-dimensional case with the RANS shear-stress transport k-w model, which involves minimal computational cost, is reliable and appropriate for analyzing the characteristics of VIV.

A deflation based parallel algorithm for spectral element solution of the incompressible Navier-Stokes equations

Energy Technology Data Exchange (ETDEWEB)

Fischer, P.F. [Brown Univ., Providence, RI (United States)

1996-12-31

Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In the context of operator splitting formulations, it is the pressure solve which is the most computationally challenging, despite its elliptic origins. We seek to improve existing spectral element iterative methods for the pressure solve in order to overcome the slow convergence frequently observed in the presence of highly refined grids or high-aspect ratio elements.

Three-dimensional poor man's Navier-Stokes equation: a discrete dynamical system exhibiting k(-5/3) inertial subrange energy scaling.

Science.gov (United States)

McDonough, J M

2009-06-01

Outline of the derivation and mathematical and physical interpretations are presented for a discrete dynamical system known as the "poor man's Navier-Stokes equation." Numerical studies demonstrate that velocity fields produced by this dynamical system are similar to those seen in laboratory experiments and in detailed simulations, and they lead to scaling for the turbulence kinetic energy spectrum in accord with Kolmogorov K41 theory.

Machine Learning Algorithms for prediction of regions of high Reynolds Averaged Navier Stokes Uncertainty

Science.gov (United States)

Mishra, Aashwin; Iaccarino, Gianluca

2017-11-01

In spite of their deficiencies, RANS models represent the workhorse for industrial investigations into turbulent flows. In this context, it is essential to provide diagnostic measures to assess the quality of RANS predictions. To this end, the primary step is to identify feature importances amongst massive sets of potentially descriptive and discriminative flow features. This aids the physical interpretability of the resultant discrepancy model and its extensibility to similar problems. Recent investigations have utilized approaches such as Random Forests, Support Vector Machines and the Least Absolute Shrinkage and Selection Operator for feature selection. With examples, we exhibit how such methods may not be suitable for turbulent flow datasets. The underlying rationale, such as the correlation bias and the required conditions for the success of penalized algorithms, are discussed with illustrative examples. Finally, we provide alternate approaches using convex combinations of regularized regression approaches and randomized sub-sampling in combination with feature selection algorithms, to infer model structure from data. This research was supported by the Defense Advanced Research Projects Agency under the Enabling Quantification of Uncertainty in Physical Systems (EQUiPS) project (technical monitor: Dr Fariba Fahroo).

An efficient iterative method for the generalized Stokes problem

Energy Technology Data Exchange (ETDEWEB)

Sameh, A. [Univ. of Minnesota, Twin Cities, MN (United States); Sarin, V. [Univ. of Illinois, Urbana, IL (United States)

1996-12-31

This paper presents an efficient iterative scheme for the generalized Stokes problem, which arises frequently in the simulation of time-dependent Navier-Stokes equations for incompressible fluid flow. The general form of the linear system is where A = {alpha}M + vT is an n x n symmetric positive definite matrix, in which M is the mass matrix, T is the discrete Laplace operator, {alpha} and {nu} are positive constants proportional to the inverses of the time-step {Delta}t and the Reynolds number Re respectively, and B is the discrete gradient operator of size n x k (k < n). Even though the matrix A is symmetric and positive definite, the system is indefinite due to the incompressibility constraint (B{sup T}u = 0). This causes difficulties both for iterative methods and commonly used preconditioners. Moreover, depending on the ratio {alpha}/{nu}, A behaves like the mass matrix M at one extreme and the Laplace operator T at the other, thus complicating the issue of preconditioning.

Energy exchange analysis in droplet dynamics via the Navier-Stokes-Cahn-Hilliard model

Science.gov (United States)

Espath, L. F. R.; Sarmiento, A. F.; Vignal, P.; Varga, B. O. N.; Cortes, A. M. A.; Dalcin, L.; Calo, V. M.

2016-06-01

We develop the energy budget equation of the coupled Navier-Stokes-Cahn-Hilliard (NSCH) system. We use the NSCH equations to model the dynamics of liquid droplets in a liquid continuum. Buoyancy effects are accounted for through the Boussinesq assumption. We physically interpret each quantity involved in the energy exchange to further insight into the model. Highly resolved simulations involving density-driven flows and merging of droplets allow us to analyze these energy budgets. In particular, we focus on the energy exchanges when droplets merge, and describe flow features relevant to this phenomenon. By comparing our numerical simulations to analytical predictions and experimental results available in the literature, we conclude that modeling droplet dynamics within the framework of NSCH equations is a sensible approach worth further research.

Projection of the rotation form Navier-Stokes equation onto the half-staggered grid

Energy Technology Data Exchange (ETDEWEB)

Cho, Ji Ryong [Inje University, Kimhae (Korea, Republic of)

2016-07-15

A projection method for computing incompressible fluid flow is proposed. For the method, the rotation form Navier-Stokes equation (NSE), for which the velocity and the total pressure are employed, is discretized on the half-staggered, finite difference spatial grid. The total pressure couples the static pressure gradient and the convection of momentum in the continuous NSE while the half-staggered grid provides weak pressure-velocity coupling in discrete space. These two features interact synergistically for the discretized NSE to produce smooth pressure fields without additional numerical artifacts such as the momentum interpolation. The method preserves the kinetic energy at the inviscid limit condition. Numerical solutions of the decaying Taylor vortex, the inviscid Taylor vortex, the sudden expansion channel and the square-prism wake are presented.

Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier-Stokes system modeling coral fertilization

Science.gov (United States)

Espejo, Elio; Winkler, Michael

2018-04-01

The interplay of chemotaxis, convection and reaction terms is studied in the particular framework of a refined model for coral broadcast spawning, consisting of three equations describing the population densities of unfertilized sperms and eggs and the concentration of a chemical released by the latter, coupled to the incompressible Navier-Stokes equations. Under mild assumptions on the initial data, global existence of classical solutions to an associated initial-boundary value problem in bounded planar domains is established. Moreover, all these solutions are shown to approach a spatially homogeneous equilibrium in the large time limit.

An iteration for indefinite and non-symmetric systems and its application to the Navier-Stokes equations

Energy Technology Data Exchange (ETDEWEB)

Wathen, A. [Oxford Univ. (United Kingdom); Golub, G. [Stanford Univ., CA (United States)

1996-12-31

A simple fixed point linearisation of the Navier-Stokes equations leads to the Oseen problem which after appropriate discretisation yields large sparse linear systems with coefficient matrices of the form (A B{sup T} B -C). Here A is non-symmetric but its symmetric part is positive definite, and C is symmetric and positive semi-definite. Such systems arise in other situations. In this talk we will describe and present some analysis for an iteration based on an indefinite and symmetric preconditioner of the form (D B{sup T} B -C).

Asymptotic preserving error estimates for numerical solutions of compressible Navier-Stokes equations in the low Mach number regime

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Medviďová-Lukáčová, M.; Nečasová, Šárka; Novotný, A.; She, Bangwei

2018-01-01

Roč. 16, č. 1 (2018), s. 150-183 ISSN 1540-3459 R&D Projects: GA ČR GA16-03230S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes system * finite element numerical method * finite volume numerical method * asymptotic preserving schemes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.865, year: 2016 http://epubs.siam.org/doi/10.1137/16M1094233

The Role of the Pressure in the Partial Regularity Theory for Weak Solutions of the Navier-Stokes Equations

Science.gov (United States)

Chamorro, Diego; Lemarié-Rieusset, Pierre-Gilles; Mayoufi, Kawther

2018-04-01

We study the role of the pressure in the partial regularity theory for weak solutions of the Navier-Stokes equations. By introducing the notion of dissipative solutions, due to D uchon and R obert (Nonlinearity 13:249-255, 2000), we will provide a generalization of the Caffarelli, Kohn and Nirenberg theory. Our approach sheels new light on the role of the pressure in this theory in connection to Serrin's local regularity criterion.

Divergent expansion, Borel summability and three-dimensional Navier-Stokes equation.

Science.gov (United States)

Costin, Ovidiu; Luo, Guo; Tanveer, Saleh

2008-08-13

We describe how the Borel summability of a divergent asymptotic expansion can be expanded and applied to nonlinear partial differential equations (PDEs). While Borel summation does not apply for non-analytic initial data, the present approach generates an integral equation (IE) applicable to much more general data. We apply these concepts to the three-dimensional Navier-Stokes (NS) system and show how the IE approach can give rise to local existence proofs. In this approach, the global existence problem in three-dimensional NS systems, for specific initial condition and viscosity, becomes a problem of asymptotics in the variable p (dual to 1/t or some positive power of 1/t). Furthermore, the errors in numerical computations in the associated IE can be controlled rigorously, which is very important for nonlinear PDEs such as NS when solutions are not known to exist globally.Moreover, computation of the solution of the IE over an interval [0,p0] provides sharper control of its p-->infinity behaviour. Preliminary numerical computations give encouraging results.

Fast chemical reaction in two-dimensional Navier-Stokes flow: initial regime.

Science.gov (United States)

Ait-Chaalal, Farid; Bourqui, Michel S; Bartello, Peter

2012-04-01

This paper studies an infinitely fast bimolecular chemical reaction in a two-dimensional biperiodic Navier-Stokes flow. The reactants in stoichiometric quantities are initially segregated by infinite gradients. The focus is placed on the initial stage of the reaction characterized by a well-defined one-dimensional material contact line between the reactants. Particular attention is given to the effect of the diffusion κ of the reactants. This study is an idealized framework for isentropic mixing in the lower stratosphere and is motivated by the need to better understand the effect of resolution on stratospheric chemistry in climate-chemistry models. Adopting a Lagrangian straining theory approach, we relate theoretically the ensemble mean of the length of the contact line, of the gradients along it, and of the modulus of the time derivative of the space-average reactant concentrations (here called the chemical speed) to the joint probability density function of the finite-time Lyapunov exponent λ with two times τ and τ[over ̃]. The time 1/λ measures the stretching time scale of a Lagrangian parcel on a chaotic orbit up to a finite time t, while τ measures it in the recent past before t, and τ[over ̃] in the early part of the trajectory. We show that the chemical speed scales like κ(1/2) and that its time evolution is determined by rare large events in the finite-time Lyapunov exponent distribution. The case of smooth initial gradients is also discussed. The theoretical results are tested with an ensemble of direct numerical simulations (DNSs) using a pseudospectral model.

Cpu/gpu Computing for AN Implicit Multi-Block Compressible Navier-Stokes Solver on Heterogeneous Platform

Science.gov (United States)

Deng, Liang; Bai, Hanli; Wang, Fang; Xu, Qingxin

2016-06-01

CPU/GPU computing allows scientists to tremendously accelerate their numerical codes. In this paper, we port and optimize a double precision alternating direction implicit (ADI) solver for three-dimensional compressible Navier-Stokes equations from our in-house Computational Fluid Dynamics (CFD) software on heterogeneous platform. First, we implement a full GPU version of the ADI solver to remove a lot of redundant data transfers between CPU and GPU, and then design two fine-grain schemes, namely “one-thread-one-point” and “one-thread-one-line”, to maximize the performance. Second, we present a dual-level parallelization scheme using the CPU/GPU collaborative model to exploit the computational resources of both multi-core CPUs and many-core GPUs within the heterogeneous platform. Finally, considering the fact that memory on a single node becomes inadequate when the simulation size grows, we present a tri-level hybrid programming pattern MPI-OpenMP-CUDA that merges fine-grain parallelism using OpenMP and CUDA threads with coarse-grain parallelism using MPI for inter-node communication. We also propose a strategy to overlap the computation with communication using the advanced features of CUDA and MPI programming. We obtain speedups of 6.0 for the ADI solver on one Tesla M2050 GPU in contrast to two Xeon X5670 CPUs. Scalability tests show that our implementation can offer significant performance improvement on heterogeneous platform.

Renormalization group in the theory of fully developed turbulence. Problem of the infrared relevant corrections to the Navier-Stokes equation

International Nuclear Information System (INIS)

Antonov, N.V.; Borisenok, S.V.; Girina, V.I.

1996-01-01

Within the framework of the renormalization group approach to the theory of fully developed turbulence we consider the problem of possible IR relevant corrections to the Navier-Stokes equation. We formulate an exact criterion of the actual IR relevance of the corrections. In accordance with this criterion we verify the IR relevance for certain classes of composite operators. 17 refs., 2 tabs

Regularity criterion for solutions to the Navier Stokes equations in the whole 3D space based on two vorticity components

Czech Academy of Sciences Publication Activity Database

Guo, Z.; Kučera, P.; Skalák, Zdeněk

2018-01-01

Roč. 458, č. 1 (2018), s. 755-766 ISSN 0022-247X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985874 Keywords : Navier Stokes equations * conditional regularity * regularity criteria * vorticity * Besov spaces * bony decomposition Subject RIV: BA - General Mathematics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 1.064, year: 2016

On robustness of a strong solution to the Navier–Stokes equations with Navier's boundary conditions in the L3-norm

Czech Academy of Sciences Publication Activity Database

Kučera, P.; Neustupa, Jiří

2017-01-01

Roč. 30, č. 4 (2017), s. 1564-1583 ISSN 0951-7715 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equations * slip boundary conditions * regularity Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.767, year: 2016 http://iopscience.iop.org/article/10.1088/1361-6544/aa6166/meta

Level Set Projection Method for Incompressible Navier-Stokes on Arbitrary Boundaries

KAUST Repository

Williams-Rioux, Bertrand

2012-01-12

Second order level set projection method for incompressible Navier-Stokes equations is proposed to solve flow around arbitrary geometries. We used rectilinear grid with collocated cell centered velocity and pressure. An explicit Godunov procedure is used to address the nonlinear advection terms, and an implicit Crank-Nicholson method to update viscous effects. An approximate pressure projection is implemented at the end of the time stepping using multigrid as a conventional fast iterative method. The level set method developed by Osher and Sethian [17] is implemented to address real momentum and pressure boundary conditions by the advection of a distance function, as proposed by Aslam [3]. Numerical results for the Strouhal number and drag coefficients validated the model with good accuracy for flow over a cylinder in the parallel shedding regime (47 < Re < 180). Simulations for an array of cylinders and an oscillating cylinder were performed, with the latter demonstrating our methods ability to handle dynamic boundary conditions.

Navier-Stokes Aerodynamic Simulation of the V-22 Osprey on the Intel Paragon MPP

Science.gov (United States)

Vadyak, Joseph; Shrewsbury, George E.; Narramore, Jim C.; Montry, Gary; Holst, Terry; Kwak, Dochan (Technical Monitor)

1995-01-01

The paper will describe the Development of a general three-dimensional multiple grid zone Navier-Stokes flowfield simulation program (ENS3D-MPP) designed for efficient execution on the Intel Paragon Massively Parallel Processor (MPP) supercomputer, and the subsequent application of this method to the prediction of the viscous flowfield about the V-22 Osprey tiltrotor vehicle. The flowfield simulation code solves the thin Layer or full Navier-Stoke's equation - for viscous flow modeling, or the Euler equations for inviscid flow modeling on a structured multi-zone mesh. In the present paper only viscous simulations will be shown. The governing difference equations are solved using a time marching implicit approximate factorization method with either TVD upwind or central differencing used for the convective terms and central differencing used for the viscous diffusion terms. Steady state or Lime accurate solutions can be calculated. The present paper will focus on steady state applications, although time accurate solution analysis is the ultimate goal of this effort. Laminar viscosity is calculated using Sutherland's law and the Baldwin-Lomax two layer algebraic turbulence model is used to compute the eddy viscosity. The Simulation method uses an arbitrary block, curvilinear grid topology. An automatic grid adaption scheme is incorporated which concentrates grid points in high density gradient regions. A variety of user-specified boundary conditions are available. This paper will present the application of the scalable and superscalable versions to the steady state viscous flow analysis of the V-22 Osprey using a multiple zone global mesh. The mesh consists of a series of sheared cartesian grid blocks with polar grids embedded within to better simulate the wing tip mounted nacelle. MPP solutions will be shown in comparison to equivalent Cray C-90 results and also in comparison to experimental data. Discussions on meshing considerations, wall clock execution time

Oscillatory Stokes Flow Past a Slip Cylinder

Science.gov (United States)

Palaniappan, D.

2013-11-01

Two-dimensional transient slow viscous flow past a circular cylinder with Navier slip boundary conditions is considered in the limit of low-Reynolds number. The oscillatory Stokes flow problem around a cylinder is solved using the stream function method leading to an analytic solution in terms of modified Bessel functions of the second kind. The corresponding steady-state behavior yields the familiar paradoxical result first detected by Stokes. It is noted that the two key parameters, viz., the frequency λ, and the slip coefficient ξ have a significant impact on the flow field in the vicinity of the cylinder contour. In the limit of very low frequency, the flow is dominated by a term containing a well-known biharmonic function found by Stokes that has a singular behavior at infinity. Local streamlines for small times show interesting flow patterns. Attached eddies due to flow separation - observed in the no-slip case - either get detached or pushed away from the cylinder surface as ξ is varied. Computed asymptotic results predict that the flow exhibits inviscid behavior far away from the cylinder in the frequency range 0 < λ << 1 . Although the frequency of oscillations is finite, our exact solutions reveal fairly rapid transitions in the flow domain. Research Enhancement grant, TAMUCC.

On the Coupling of Incompressible Stokes or Navier–Stokes and Darcy Flows Through Porous Media

KAUST Repository

Girault, V.; Kanschat, G.; Riviè re, B.

2012-01-01

In this chapter, we present the theoretical analysis of coupled incompressible Navier-Stokes (or Stokes) flows and Darcy flows with the Beavers-Joseph-Saffman interface condition. We discuss alternative interface and porous media models. We review

Challenges in simulating coastal effects on an offshore wind farm

DEFF Research Database (Denmark)

van der Laan, Paul; Peña, Alfredo; Volker, Patrick

2017-01-01

The effect of a coastline on an offshore wind farm is investigated with a Reynolds-averaged Navier-Stokes (RANS) model. The trends of the RANS model compare relatively well with results from a mesoscale model and measurements of wind turbine power. In addition, challenges of modeling a large domain...

Implementation of an Euler/Navier-Stokes finite element algorithm on the Connection Machine

International Nuclear Information System (INIS)

Shapiro, R.A.

1991-01-01

Massively parallel computers such as the Connection Machine (CM-2) have the potential to reduce significantly the computational cost for large problems of interest to the aerospace community. This paper examines the applicability of the CM-2 to an explicit, time-marching finite element solution method for the Euler and Navier-Stokes equations. The CM-2 architecture and the CM FORTRAN language are introduced. The paper points out some of the pitfalls involved in putting this code on the CM-2, with emphasis on interprocessor communications issues. The use of the FastGraph communication compiler and grid renumbering to reduce communication costs is discussed. Performance comparisons which indicate the approximate equivalence of a uniprocessor Cray and 1/8 of a CM-2 (8192 processors) for some typical problems are presented. 8 refs

A representation of curved boundaries for the solution of the Navier-Stokes equations on a staggered three-dimensional Cartesian grid

International Nuclear Information System (INIS)

Kirkpatrick, M.P.; Armfield, S.W.; Kent, J.H.

2003-01-01

A method is presented for representing curved boundaries for the solution of the Navier-Stokes equations on a non-uniform, staggered, three-dimensional Cartesian grid. The approach involves truncating the Cartesian cells at the boundary surface to create new cells which conform to the shape of the surface. We discuss in some detail the problems unique to the development of a cut cell method on a staggered grid. Methods for calculating the fluxes through the boundary cell faces, for representing pressure forces and for calculating the wall shear stress are derived and it is verified that the new scheme retains second-order accuracy in space. In addition, a novel 'cell-linking' method is developed which overcomes problems associated with the creation of small cells while avoiding the complexities involved with other cell-merging approaches. Techniques are presented for generating the geometric information required for the scheme based on the representation of the boundaries as quadric surfaces. The new method is tested for flow through a channel placed oblique to the grid and flow past a cylinder at Re=40 and is shown to give significant improvement over a staircase boundary formulation. Finally, it is used to calculate unsteady flow past a hemispheric protuberance on a plate at a Reynolds number of 800. Good agreement is obtained with experimental results for this flow

Solution of the Euler and Navier-Stokes equations on MIMD distributed memory multiprocessors using cyclic reduction

International Nuclear Information System (INIS)

Curchitser, E.N.; Pelz, R.B.; Marconi, F.

1992-01-01

The Euler and Navier-Stokes equations are solved for the steady, two-dimensional flow over a NACA 0012 airfoil using a 1024 node nCUBE/2 multiprocessor. Second-order, upwind-discretized difference equations are solved implicitly using ADI factorization. Parallel cyclic reduction is employed to solve the block tridiagonal systems. For realistic problems, communication times are negligible compared to calculation times. The processors are tightly synchronized, and their loads are well balanced. When the flux Jacobians flux are frozen, the wall-clock time for one implicit timestep is about equal to that of a multistage explicit scheme. 10 refs

Turbine Internal and Film Cooling Modeling For 3D Navier-Stokes Codes

Science.gov (United States)

DeWitt, Kenneth; Garg Vijay; Ameri, Ali

2005-01-01

The aim of this research project is to make use of NASA Glenn on-site computational facilities in order to develop, validate and apply aerodynamic, heat transfer, and turbine cooling models for use in advanced 3D Navier-Stokes Computational Fluid Dynamics (CFD) codes such as the Glenn-" code. Specific areas of effort include: Application of the Glenn-HT code to specific configurations made available under Turbine Based Combined Cycle (TBCC), and Ultra Efficient Engine Technology (UEET) projects. Validating the use of a multi-block code for the time accurate computation of the detailed flow and heat transfer of cooled turbine airfoils. The goal of the current research is to improve the predictive ability of the Glenn-HT code. This will enable one to design more efficient turbine components for both aviation and power generation. The models will be tested against specific configurations provided by NASA Glenn.

Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas.

Science.gov (United States)

Kolvin, Itamar; Livne, Eli; Meerson, Baruch

2010-08-01

We show that, in dimension higher than one, heat diffusion and viscosity cannot arrest thermal collapse in a freely evolving dilute granular gas, even in the absence of gravity. Thermal collapse involves a finite-time blowup of the gas density. It was predicted earlier in ideal, Euler hydrodynamics of dilute granular gases in the absence of gravity, and in nonideal, Navier-Stokes granular hydrodynamics in the presence of gravity. We determine, analytically and numerically, the dynamic scaling laws that characterize the gas flow close to collapse. We also investigate bifurcations of a freely evolving dilute granular gas in circular and wedge-shaped containers. Our results imply that, in general, thermal collapse can only be arrested when the gas density becomes comparable with the close-packing density of grains. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.

Natural upward cross-ventilation potential of a leeward sawtooth roof for a single zone building model

NARCIS (Netherlands)

Peren Montero, J.I.; Ramponi, R.; van Hooff, T.A.J.; Blocken, B.J.E.; Leite, B.C.C.; Schlünzen, H.

2014-01-01

The ventilation potential of four leeward sawtooth roof shapes (B1, C1, D1 and E1) is evaluated under normal wind incidence angle (θ = 0°). 3D Reynolds-Averaged Navier-Stokes (RANS) Computational Fluid Dynamics (CFD) simulations are performed in combination with five turbulence models and the

Design of a centrifugal compressor impeller using multi-objective optimization algorithm

International Nuclear Information System (INIS)

Kim, Jin Hyuk; Husain, Afzal; Kim, Kwang Yong; Choi, Jae Ho

2009-01-01

This paper presents a design optimization of a centrifugal compressor impeller with hybrid multi-objective evolutionary algorithm (hybrid MOEA). Reynolds-averaged Navier-Stokes equations with shear stress transport turbulence model are discretized by finite volume approximations and solved on hexahedral grids for flow analyses. Two objectives, i.e., isentropic efficiency and total pressure ratio are selected with four design variables defining impeller hub and shroud contours in meridional contours to optimize the system. Non-dominated Sorting of Genetic Algorithm (NSGA-II) with ε-constraint strategy for local search coupled with Radial Basis Neural Network model is used for multi-objective optimization. The optimization results show that isentropic efficiencies and total pressure ratios of the five cluster points at the Pareto-optimal solutions are enhanced by multi-objective optimization.

Design of a centrifugal compressor impeller using multi-objective optimization algorithm

Energy Technology Data Exchange (ETDEWEB)

Kim, Jin Hyuk; Husain, Afzal; Kim, Kwang Yong [Inha University, Incheon (Korea, Republic of); Choi, Jae Ho [Samsung Techwin Co., Ltd., Changwon (Korea, Republic of)

2009-07-01

This paper presents a design optimization of a centrifugal compressor impeller with hybrid multi-objective evolutionary algorithm (hybrid MOEA). Reynolds-averaged Navier-Stokes equations with shear stress transport turbulence model are discretized by finite volume approximations and solved on hexahedral grids for flow analyses. Two objectives, i.e., isentropic efficiency and total pressure ratio are selected with four design variables defining impeller hub and shroud contours in meridional contours to optimize the system. Non-dominated Sorting of Genetic Algorithm (NSGA-II) with {epsilon}-constraint strategy for local search coupled with Radial Basis Neural Network model is used for multi-objective optimization. The optimization results show that isentropic efficiencies and total pressure ratios of the five cluster points at the Pareto-optimal solutions are enhanced by multi-objective optimization.

Navier-Stokes equations an introduction with applications

CERN Document Server

Łukaszewicz, Grzegorz

2016-01-01

This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from students to engineers and mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations. Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior o...

Heat transfer in an axisymmetric stagnation flow at high Reynolds numbers on a cylinder using perturbation techniques

International Nuclear Information System (INIS)

Rahimi, A. B.

2003-01-01

Although there are many papers on the subject of heat transfer in an axisymmetric stagnation flow on a cylinder, the available knowledge is mainly for low Reynolds numbers and not much information exists for the same problem at large Reynolds numbers. In this work, the problem of heat transfer in an axisymmetric stagnation flow on a cylinder is solved at large Reynolds numbers using perturbation techniques. Starting from Navier-Stokes equations within a boundary layer approximation and using similarity transformations, the governing equations are obtained in the form of differential equations. The inverse of the Reynolds number is introduced as the perturbation parameter. This parameter appears in front of the highest-order terms and, as it tends to zero, reduces the order of the governing equations and produces singularities. In this paper, the flow field is divided into two regions; rapid changes in the region near wall and slow changes away from the wall. Thus, the flow is found to have dual-layer characteristics. Using inner and outer expansion produces uniform values of the relevant quantities

Hypersonic Navier Stokes Comparisons to Orbiter Flight Data

Science.gov (United States)

Campbell, Charles H.; Nompelis, Ioannis; Candler, Graham; Barnhart, Michael; Yoon, Seokkwan

2009-01-01

Hypersonic chemical nonequilibrium simulations of low earth orbit entry flow fields are becoming increasingly commonplace as software and computational capabilities become more capable. However, development of robust and accurate software to model these environments will always encounter a significant barrier in developing a suite of high quality calibration cases. The US3D hypersonic nonequilibrium Navier Stokes analysis capability has been favorably compared to a number of wind tunnel test cases. Extension of the calibration basis for this software to Orbiter flight conditions will provide an incremental increase in confidence. As part of the Orbiter Boundary Layer Transition Flight Experiment and the Hypersonic Thermodynamic Infrared Measurements project, NASA is performing entry flight testing on the Orbiter to provide valuable aerothermodynamic heating data. An increase in interest related to orbiter entry environments is resulting from this activity. With the advent of this new data, comparisons of the US3D software to the new flight testing data is warranted. This paper will provide information regarding the framework of analyses that will be applied with the US3D analysis tool. In addition, comparisons will be made to entry flight testing data provided by the Orbiter BLT Flight Experiment and HYTHIRM projects. If data from digital scans of the Orbiter windward surface become available, simulations will also be performed to characterize the difference in surface heating between the CAD reference OML and the digitized surface provided by the surface scans.

EFFECT OF GEOMETRIC CONFIGURATIONS ON HYDRODYNAMIC PERFORMANCE ASSESSMENT OF A MARINE PROPELLER

Directory of Open Access Journals (Sweden)

Samir. E. Belhenniche

2016-12-01

Full Text Available The present paper deals with the effect of the geometric characteristics on the propeller hydrodynamic performances. Several propeller configurations are created by changing number of blades, expanded area and pitch ratios. The Reynolds-Averaged Navier-Stokes (RANS equations are solved using the commercial code FLUENT 6.3.26. The standard

Fluid Simulation in the Movies: Navier and Stokes Must Be Circulating in Their Graves

Science.gov (United States)

Tessendorf, Jerry

2010-11-01

Fluid simulations based on the Incompressible Navier-Stokes equations are commonplace computer graphics tools in the visual effects industry. These simulations mostly come from custom C++ code written by the visual effects companies. Their significant impact in films was recognized in 2008 with Academy Awards to four visual effects companies for their technical achievement. However artists are not fluid dynamicists, and fluid dynamics simulations are expensive to use in a deadline-driven production environment. As a result, the simulation algorithms are modified to limit the computational resources, adapt them to production workflow, and to respect the client's vision of the film plot. Eulerian solvers on fixed rectangular grids use a mix of momentum solvers, including Semi-Lagrangian, FLIP, and QUICK. Incompressibility is enforced with FFT, Conjugate Gradient, and Multigrid methods. For liquids, a levelset field tracks the free surface. Smooth Particle Hydrodynamics is also used, and is part of a hybrid Eulerian-SPH liquid simulator. Artists use all of them in a mix and match fashion to control the appearance of the simulation. Specially designed forces and boundary conditions control the flow. The simulation can be an input to artistically driven procedural particle simulations that enhance the flow with more detail and drama. Post-simulation processing increases the visual detail beyond the grid resolution. Ultimately, iterative simulation methods that fit naturally in the production workflow are extremely desirable but not yet successful. Results from some efforts for iterative methods are shown, and other approaches motivated by the history of production are proposed.

An Empirical Model for Vane-Type Vortex Generators in a Navier-Stokes Code

Science.gov (United States)

Dudek, Julianne C.

2005-01-01

An empirical model which simulates the effects of vane-type vortex generators in ducts was incorporated into the Wind-US Navier-Stokes computational fluid dynamics code. The model enables the effects of the vortex generators to be simulated without defining the details of the geometry within the grid, and makes it practical for researchers to evaluate multiple combinations of vortex generator arrangements. The model determines the strength of each vortex based on the generator geometry and the local flow conditions. Validation results are presented for flow in a straight pipe with a counter-rotating vortex generator arrangement, and the results are compared with experimental data and computational simulations using a gridded vane generator. Results are also presented for vortex generator arrays in two S-duct diffusers, along with accompanying experimental data. The effects of grid resolution and turbulence model are also examined.

Toward a CFD nose-to-tail capability - Hypersonic unsteady Navier-Stokes code validation

Science.gov (United States)

Edwards, Thomas A.; Flores, Jolen

1989-01-01

Computational fluid dynamics (CFD) research for hypersonic flows presents new problems in code validation because of the added complexity of the physical models. This paper surveys code validation procedures applicable to hypersonic flow models that include real gas effects. The current status of hypersonic CFD flow analysis is assessed with the Compressible Navier-Stokes (CNS) code as a case study. The methods of code validation discussed to beyond comparison with experimental data to include comparisons with other codes and formulations, component analyses, and estimation of numerical errors. Current results indicate that predicting hypersonic flows of perfect gases and equilibrium air are well in hand. Pressure, shock location, and integrated quantities are relatively easy to predict accurately, while surface quantities such as heat transfer are more sensitive to the solution procedure. Modeling transition to turbulence needs refinement, though preliminary results are promising.

Cellular neural networks, the Navier-Stokes equation, and microarray image reconstruction.

Science.gov (United States)

Zineddin, Bachar; Wang, Zidong; Liu, Xiaohui

2011-11-01

Although the last decade has witnessed a great deal of improvements achieved for the microarray technology, many major developments in all the main stages of this technology, including image processing, are still needed. Some hardware implementations of microarray image processing have been proposed in the literature and proved to be promising alternatives to the currently available software systems. However, the main drawback of those proposed approaches is the unsuitable addressing of the quantification of the gene spot in a realistic way without any assumption about the image surface. Our aim in this paper is to present a new image-reconstruction algorithm using the cellular neural network that solves the Navier-Stokes equation. This algorithm offers a robust method for estimating the background signal within the gene-spot region. The MATCNN toolbox for Matlab is used to test the proposed method. Quantitative comparisons are carried out, i.e., in terms of objective criteria, between our approach and some other available methods. It is shown that the proposed algorithm gives highly accurate and realistic measurements in a fully automated manner within a remarkably efficient time.

3-D Navier-Stokes Analysis of Blade Root Aerodynamics for a Tiltrotor Aircraft In Cruise

Science.gov (United States)

Romander, Ethan

2006-01-01

The blade root area of a tiltrotor aircraft's rotor is constrained by a great many factors, not the least of which is aerodynamic performance in cruise. For this study, Navier-Stokes CFD techniques are used to study the aerodynamic performance in cruise of a rotor design as a function of airfoil thickness along the blade and spinner shape. Reducing airfoil thickness along the entire blade will be shown to have the greatest effect followed by smaller but still significant improvements achieved by reducing the thickness of root airfoils only. Furthermore, altering the shape of the spinner will be illustrated as a tool to tune the aerodynamic performance very near the blade root.

Numerical investigation of the high Reynolds number 3D flow field generated by a self-propelling manta ray

Science.gov (United States)

Pederzani, Jean-Noel; Haj-Hariri, Hossein

2012-11-01

An embedded-boundary (or cut-cell) method for complex geometry with moving boundaries is used to solve the three dimensional Navier-Stokes equation around a self-propelling manta swimming at moderately high Reynolds numbers. The motion of the ray is prescribed using a kinematic model fitted to actual biological data. The dependence of thrust production mechanism on Strouhal and Reynolds numbers is investigated. The vortex core structures are accurately plotted and a correlation between wake structures and propulsive performance is established. This insight is critical in understanding the key flow features that a bio-inspired autonomous vehicle should reproduce in order to swim efficiently. The solution method is implemented, on a block-structured Cartesian grid using a cut-cell approach enabling the code to correctly evaluate the wall shear-stress, a key feature necessary at higher Reynolds. To enhance computational efficiency, a parallel adaptive mesh refinement technique is used. The present method is validated against published experimental results. Supported by ONR MURI.

On a theorem of Cattabriga related to Stokes equations

International Nuclear Information System (INIS)

Georgescu, V.

1978-01-01

We study the ''generalized Stokes boundary value problem'', which is a (generalization of a) linearized version of Navier-Stokes equations and we show the existence and unicity of the weak solution. It is known that these results can be used to prove the existence of weak (local) solutions to the Navier-Stokes equations. However, we are mainly interested in the method of proving it will be seen how easy the result follows from some general theorems about differential forms on a Riemannian manifold. (author)

Comment on "Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua".

Science.gov (United States)

Felderhof, B U

2013-08-01

Recently, a critical test of the Navier-Stokes-Fourier equations for compressible fluid continua was proposed [H. Brenner, Phys. Rev. E 87, 013014 (2013)]. It was shown that the equations of bivelocity hydrodynamics imply that a compressible fluid in an isolated rotating circular cylinder attains a nonequilibrium steady state with a nonuniform temperature increasing radially with distance from the axis. We demonstrate that statistical mechanical arguments, involving Hamiltonian dynamics and ergodicity due to irregularity of the wall, lead instead to a thermal equilibrium state with uniform temperature. This is the situation to be expected in experiment.

Synthesis of the scientific activity. Resolution of compressible Navier-Stokes equations for steady supersonic and transonic regimes

International Nuclear Information System (INIS)

Angrand, F.

1990-10-01

In this HDR (Accreditation to Supervise Researches) report, the author gives an overview of his activities in the field of numerical methods, notably in the field of fluid mechanics and aeronautics. He more particularly addresses the resolution of Euler equations of gas dynamics in transonic and supersonic regimes (equations, centered and off-centered flow calculation, case of one-dimensional and non linear systems), the extension of this work to Navier-Stokes equations (equations, grid adaptation), the study of resolution methods and cost optimisation (Runge-Kutta method, implicit schemes, multi-grid approach). He also addresses the case of hypersonic flows behind a base

Numerical prediction of a bulb turbine performance hill chart through RANS simulations

International Nuclear Information System (INIS)

Guénette, V; Houde, S; Ciocan, G D; Deschênes, C; Dumas, G; Huang, J

2012-01-01

Within the framework of an international research consortium on low-head hydraulic turbine flow dynamics, the predictive behavior of Reynolds Averaged Navier-Stokes (RANS) simulations of the efficiency (η) hill chart of a bulb turbine is investigated. The paper presents the impacts of the blade tip gap and the hub gaps on performance predictions.

Finite Volume Methods for Incompressible Navier-Stokes Equations on Collocated Grids with Nonconformal Interfaces

DEFF Research Database (Denmark)

Kolmogorov, Dmitry

turbine computations, collocated grid-based SIMPLE-like algorithms are developed for computations on block-structured grids with nonconformal interfaces. A technique to enhance both the convergence speed and the solution accuracy of the SIMPLE-like algorithms is presented. The erroneous behavior, which...... versions of the SIMPLE algorithm. The new technique is implemented in an existing conservative 2nd order finite-volume scheme flow solver (EllipSys), which is extended to cope with grids with nonconformal interfaces. The behavior of the discrete Navier-Stokes equations is discussed in detail...... Block LU relaxation scheme is shown to possess several optimal conditions, which enables to preserve high efficiency of the multigrid solver on both conformal and nonconformal grids. The developments are done using a parallel MPI algorithm, which can handle multiple numbers of interfaces with multiple...

Simulation of dense recombining divertor plasmas with a Navier endash Stokes neutral transport model

International Nuclear Information System (INIS)

Knoll, D.A.; McHugh, P.R.; Krasheninnikov, S.I.; Sigmar, D.J.

1996-01-01

A two-dimensional combined edge plasma Navier endash Stokes neutral transport model is presented for the simulation of dense recombining divertor plasmas. This model includes ions, electrons, and neutral atoms which undergo Coulomb collisions, electron impact ionization, ion endash neutral elastic collisions, three-body and radiative recombination, and neutral endash neutral collisions. The advanced fully implicit solution algorithm is briefly described and a variety of results on a model geometry are presented. It is shown that interesting neutral flow patterns can exist and that these flows can convect significant energy. A solution that ignores neutral endash neutral collisions is shown to be quantitatively different from one that includes neutral endash neutral collisions. Solutions are also shown to be sensitive to the plasma opacity for Lyman α radiation. copyright 1996 American Institute of Physics

The deposition of aerosols on cylinders in crossflow: a time dependent study

International Nuclear Information System (INIS)

Ilias, S.; Douglas, P.L.

1985-01-01

This paper discusses the study of the deposition of aerosols on cylinders due to inertial impaction based on the solution of Navier-Stokes equation. The solution of the velocity-stream function formulation of Navier-Stokes equation can simulate a realistic flow field for virtually an unlimited range of Reynolds number

Examination of wall functions for a Parabolized Navier-Stokes code for supersonic flow

Energy Technology Data Exchange (ETDEWEB)

Alsbrooks, T.H. [New Mexico Univ., Albuquerque, NM (United States). Dept. of Mechanical Engineering

1993-04-01

Solutions from a Parabolized Navier-Stokes (PNS) code with an algebraic turbulence model are compared with wall functions. The wall functions represent the turbulent flow profiles in the viscous sublayer, thus removing many grid points from the solution procedure. The wall functions are intended to replace the computed profiles between the body surface and a match point in the logarithmic region. A supersonic adiabatic flow case was examined first. This adiabatic case indicates close agreement between computed velocity profiles near the wall and the wall function for a limited range of suitable match points in the logarithmic region. In an attempt to improve marching stability, a laminar to turbulent transition routine was implemented at the start of the PNS code. Implementing the wall function with the transitional routine in the PNS code is expected to reduce computational time while maintaining good accuracy in computed skin friction.

Examination of wall functions for a Parabolized Navier-Stokes code for supersonic flow

Energy Technology Data Exchange (ETDEWEB)

Alsbrooks, T.H. (New Mexico Univ., Albuquerque, NM (United States). Dept. of Mechanical Engineering)

1993-01-01

Solutions from a Parabolized Navier-Stokes (PNS) code with an algebraic turbulence model are compared with wall functions. The wall functions represent the turbulent flow profiles in the viscous sublayer, thus removing many grid points from the solution procedure. The wall functions are intended to replace the computed profiles between the body surface and a match point in the logarithmic region. A supersonic adiabatic flow case was examined first. This adiabatic case indicates close agreement between computed velocity profiles near the wall and the wall function for a limited range of suitable match points in the logarithmic region. In an attempt to improve marching stability, a laminar to turbulent transition routine was implemented at the start of the PNS code. Implementing the wall function with the transitional routine in the PNS code is expected to reduce computational time while maintaining good accuracy in computed skin friction.

Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number.

Science.gov (United States)

Klewicki, J C; Chini, G P; Gibson, J F

2017-03-13

Recent and on-going advances in mathematical methods and analysis techniques, coupled with the experimental and computational capacity to capture detailed flow structure at increasingly large Reynolds numbers, afford an unprecedented opportunity to develop realistic models of high Reynolds number turbulent wall-flow dynamics. A distinctive attribute of this new generation of models is their grounding in the Navier-Stokes equations. By adhering to this challenging constraint, high-fidelity models ultimately can be developed that not only predict flow properties at high Reynolds numbers, but that possess a mathematical structure that faithfully captures the underlying flow physics. These first-principles models are needed, for example, to reliably manipulate flow behaviours at extreme Reynolds numbers. This theme issue of Philosophical Transactions of the Royal Society A provides a selection of contributions from the community of researchers who are working towards the development of such models. Broadly speaking, the research topics represented herein report on dynamical structure, mechanisms and transport; scale interactions and self-similarity; model reductions that restrict nonlinear interactions; and modern asymptotic theories. In this prospectus, the challenges associated with modelling turbulent wall-flows at large Reynolds numbers are briefly outlined, and the connections between the contributing papers are highlighted.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'. © 2017 The Author(s).

On the Coupling of Incompressible Stokes or Navier–Stokes and Darcy Flows Through Porous Media

KAUST Repository

Girault, V.

2012-11-03

In this chapter, we present the theoretical analysis of coupled incompressible Navier-Stokes (or Stokes) flows and Darcy flows with the Beavers-Joseph-Saffman interface condition. We discuss alternative interface and porous media models. We review some finite element methods used by several authors in this coupling and present numerical experiments.

Computational simulations of vocal fold vibration: Bernoulli versus Navier-Stokes.

Science.gov (United States)

Decker, Gifford Z; Thomson, Scott L

2007-05-01

The use of the mechanical energy (ME) equation for fluid flow, an extension of the Bernoulli equation, to predict the aerodynamic loading on a two-dimensional finite element vocal fold model is examined. Three steady, one-dimensional ME flow models, incorporating different methods of flow separation point prediction, were compared. For two models, determination of the flow separation point was based on fixed ratios of the glottal area at separation to the minimum glottal area; for the third model, the separation point determination was based on fluid mechanics boundary layer theory. Results of flow rate, separation point, and intraglottal pressure distribution were compared with those of an unsteady, two-dimensional, finite element Navier-Stokes model. Cases were considered with a rigid glottal profile as well as with a vibrating vocal fold. For small glottal widths, the three ME flow models yielded good predictions of flow rate and intraglottal pressure distribution, but poor predictions of separation location. For larger orifice widths, the ME models were poor predictors of flow rate and intraglottal pressure, but they satisfactorily predicted separation location. For the vibrating vocal fold case, all models resulted in similar predictions of mean intraglottal pressure, maximum orifice area, and vibration frequency, but vastly different predictions of separation location and maximum flow rate.

Local vibrations and lift performance of low Reynolds number airfoil

Directory of Open Access Journals (Sweden)

TariqAmin Khan

2017-06-01

Full Text Available The 2D incompressible Navier-Stokes equations are solved based on the finite volume method and dynamic mesh technique is used to carry out partial fluid structure interaction. The local flexible structure (hereinafter termed as flexible structure vibrates in a single mode located on the upper surface of the airfoil. The Influence of vibration frequency and amplitude are examined and the corresponding fluid flow characteristics are investigated which add complexity to the inherent problem in unsteady flow. The study is conducted for flow over NACA0012 airfoil at 600≤Re≤3000 at a low angle of attack. Vibration of flexible structure induces a secondary vortex which modifies the pressure distribution and lift performance of the airfoil. At some moderate vibration amplitude, frequency synchronization or lock-in phenomenon occurs when the vibration frequency is close to the characteristic frequency of rigid airfoil. Evolution and shedding of vortices corresponding to the deformation of flexible structure depends on the Reynolds number. In the case of Re≤1000, the deformation of flexible structure is considered in-phase with the vortex shedding i.e., increasing maximum lift is linked with the positive deformation of flexible structure. At Re=1500 a phase shift of about 1/π exists while they are out-of-phase at Re>1500. Moreover, the oscillation amplitude of lift coefficient increases with increasing vibration amplitude for Re≤1500 while it decreases with increasing vibration amplitude for Re>1500. As a result of frequency lock-in, the average lift coefficient is increased with increasing vibration amplitude for all investigated Reynolds numbers (Re. The maximum increase in the average lift coefficient is 19.72% within the range of investigated parameters.

Introduction to COFFE: The Next-Generation HPCMP CREATE-AV CFD Solver

Science.gov (United States)

Glasby, Ryan S.; Erwin, J. Taylor; Stefanski, Douglas L.; Allmaras, Steven R.; Galbraith, Marshall C.; Anderson, W. Kyle; Nichols, Robert H.

2016-01-01

HPCMP CREATE-AV Conservative Field Finite Element (COFFE) is a modular, extensible, robust numerical solver for the Navier-Stokes equations that invokes modularity and extensibility from its first principles. COFFE implores a flexible, class-based hierarchy that provides a modular approach consisting of discretization, physics, parallelization, and linear algebra components. These components are developed with modern software engineering principles to ensure ease of uptake from a user's or developer's perspective. The Streamwise Upwind/Petrov-Galerkin (SU/PG) method is utilized to discretize the compressible Reynolds-Averaged Navier-Stokes (RANS) equations tightly coupled with a variety of turbulence models. The mathematics and the philosophy of the methodology that makes up COFFE are presented.

Influence of anisotropy on anomalous scaling of a passive scalar advected by the Navier-Stokes velocity field.

Science.gov (United States)

Jurcisinová, E; Jurcisin, M; Remecký, R

2009-10-01

The influence of weak uniaxial small-scale anisotropy on the stability of the scaling regime and on the anomalous scaling of the single-time structure functions of a passive scalar advected by the velocity field governed by the stochastic Navier-Stokes equation is investigated by the field theoretic renormalization group and operator-product expansion within one-loop approximation of a perturbation theory. The explicit analytical expressions for coordinates of the corresponding fixed point of the renormalization-group equations as functions of anisotropy parameters are found, the stability of the three-dimensional Kolmogorov-like scaling regime is demonstrated, and the dependence of the borderline dimension d(c) is an element of (2,3] between stable and unstable scaling regimes is found as a function of the anisotropy parameters. The dependence of the turbulent Prandtl number on the anisotropy parameters is also briefly discussed. The influence of weak small-scale anisotropy on the anomalous scaling of the structure functions of a passive scalar field is studied by the operator-product expansion and their explicit dependence on the anisotropy parameters is present. It is shown that the anomalous dimensions of the structure functions, which are the same (universal) for the Kraichnan model, for the model with finite time correlations of the velocity field, and for the model with the advection by the velocity field driven by the stochastic Navier-Stokes equation in the isotropic case, can be distinguished by the assumption of the presence of the small-scale anisotropy in the systems even within one-loop approximation. The corresponding comparison of the anisotropic anomalous dimensions for the present model with that obtained within the Kraichnan rapid-change model is done.

Generalized extended Navier-Stokes theory: multiscale spin relaxation in molecular fluids.

Science.gov (United States)

Hansen, J S

2013-09-01

This paper studies the relaxation of the molecular spin angular velocity in the framework of generalized extended Navier-Stokes theory. Using molecular dynamics simulations, it is shown that for uncharged diatomic molecules the relaxation time decreases with increasing molecular moment of inertia per unit mass. In the regime of large moment of inertia the fast relaxation is wave-vector independent and dominated by the coupling between spin and the fluid streaming velocity, whereas for small inertia the relaxation is slow and spin diffusion plays a significant role. The fast wave-vector-independent relaxation is also observed for highly packed systems. The transverse and longitudinal spin modes have, to a good approximation, identical relaxation, indicating that the longitudinal and transverse spin viscosities have same value. The relaxation is also shown to be isomorphic invariant. Finally, the effect of the coupling in the zero frequency and wave-vector limit is quantified by a characteristic length scale; if the system dimension is comparable to this length the coupling must be included into the fluid dynamical description. It is found that the length scale is independent of moment of inertia but dependent on the state point.

On the stability of projection methods for the incompressible Navier-Stokes equations based on high-order discontinuous Galerkin discretizations

Science.gov (United States)

Fehn, Niklas; Wall, Wolfgang A.; Kronbichler, Martin

2017-12-01

The present paper deals with the numerical solution of the incompressible Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space. For DG methods applied to the dual splitting projection method, instabilities have recently been reported that occur for small time step sizes. Since the critical time step size depends on the viscosity and the spatial resolution, these instabilities limit the robustness of the Navier-Stokes solver in case of complex engineering applications characterized by coarse spatial resolutions and small viscosities. By means of numerical investigation we give evidence that these instabilities are related to the discontinuous Galerkin formulation of the velocity divergence term and the pressure gradient term that couple velocity and pressure. Integration by parts of these terms with a suitable definition of boundary conditions is required in order to obtain a stable and robust method. Since the intermediate velocity field does not fulfill the boundary conditions prescribed for the velocity, a consistent boundary condition is derived from the convective step of the dual splitting scheme to ensure high-order accuracy with respect to the temporal discretization. This new formulation is stable in the limit of small time steps for both equal-order and mixed-order polynomial approximations. Although the dual splitting scheme itself includes inf-sup stabilizing contributions, we demonstrate that spurious pressure oscillations appear for equal-order polynomials and small time steps highlighting the necessity to consider inf-sup stability explicitly.

Workshop report - A validation study of Navier-Stokes codes for transverse injection into a Mach 2 flow

Science.gov (United States)

Eklund, Dean R.; Northam, G. B.; Mcdaniel, J. C.; Smith, Cliff

1992-01-01

A CFD (Computational Fluid Dynamics) competition was held at the Third Scramjet Combustor Modeling Workshop to assess the current state-of-the-art in CFD codes for the analysis of scramjet combustors. Solutions from six three-dimensional Navier-Stokes codes were compared for the case of staged injection of air behind a step into a Mach 2 flow. This case was investigated experimentally at the University of Virginia and extensive in-stream data was obtained. Code-to-code comparisons have been made with regard to both accuracy and efficiency. The turbulence models employed in the solutions are believed to be a major source of discrepancy between the six solutions.

A diffusion tensor imaging tractography algorithm based on Navier-Stokes fluid mechanics.

Science.gov (United States)

Hageman, Nathan S; Toga, Arthur W; Narr, Katherine L; Shattuck, David W

2009-03-01

We introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging (DTI) volumes. We customize the Navier-Stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the DTI image volume. We then estimate the most likely connection paths between points in the DTI volume using a metric derived from the fluid velocity vector field. We validate our algorithm using digital DTI phantoms based on a helical shape. Our method segmented the structure of the phantom with less distortion than was produced using implementations of heat-based partial differential equation (PDE) and streamline based methods. In addition, our method was able to successfully segment divergent and crossing fiber geometries, closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts. To assess the performance of our algorithm on anatomical data, we applied our method to DTI volumes from normal human subjects. Our method produced paths that were consistent with both known anatomy and directionally encoded color images of the DTI dataset.

Fast pressure-correction method for incompressible Navier-Stokes equations in curvilinear coordinates

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Aithal, Abhiram; Ferrante, Antonino

2017-11-01

In order to perform direct numerical simulations (DNS) of turbulent flows over curved surfaces and axisymmetric bodies, we have developed the numerical methodology to solve the incompressible Navier-Stokes (NS) equations in curvilinear coordinates for orthogonal meshes. The orthogonal meshes are generated by solving a coupled system of non-linear Poisson equations. The NS equations in orthogonal curvilinear coordinates are discretized in space on a staggered mesh using second-order central-difference scheme and are solved with an FFT-based pressure-correction method. The momentum equation is integrated in time using the second-order Adams-Bashforth scheme. The velocity field is advanced in time by applying the pressure correction to the approximate velocity such that it satisfies the divergence free condition. The novelty of the method stands in solving the variable coefficient Poisson equation for pressure using an FFT-based Poisson solver rather than the slower multigrid methods. We present the verification and validation results of the new numerical method and the DNS results of transitional flow over a curved axisymmetric body.

Unstructed Navier-Stokes Analysis of Wind-Tunnel Aeroelastic Effects on TCA Model 2

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Frink, Neal T.; Allison, Dennis O.; Parikh, Paresh C.

1999-01-01

The aim of this work is to demonstrate a simple technique which accounts for aeroelastic deformations experienced by HSR wind-tunnel models within CFD computations. With improved correlations, CFD can become a more effective tool for augmenting the post-test understanding of experimental data. The present technique involves the loose coupling of a low-level structural representation within the ELAPS code, to an unstructured Navier-Stokes flow solver, USM3Dns. The ELAPS model is initially calibrated against bending characteristics of the wind-tunnel model. The strength of this method is that, with a single point calibration of a simple structural representation, the static aeroelastic effects can be accounted for in CFD calculations across a range of test conditions. No prior knowledge of the model deformation during the wind-on test is required. This approach has been successfully applied to the high aspect-ratio planforms of subsonic transports. The current challenge is to adapt the procedure to low aspect-ratio planforms typical of HSR configurations.

Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code

Science.gov (United States)

Bartels, Robert E.

2005-01-01

A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a finite element solution of either user defined or automatically generated macro-elements. Macro-elements are hexagonal finite elements created from a subset of points from the full mesh. When assembled, the finite element system spans the complete flow domain. Macro-element moduli vary according to the distance to the nearest surface, resulting in extremely stiff elements near a moving surface and very pliable elements away from boundaries. Solution of the finite element system for the imposed boundary deflections generally produces smoothly varying nodal deflections. The manner in which distance to the nearest surface has been found to critically influence the quality of the element deformation. The second step is a transfinite interpolation which distributes the macro-element nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.

Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

Science.gov (United States)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2015-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

Solution method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

International Nuclear Information System (INIS)

Rosenfeld, M.; Kwak, D.; Vinokur, M.

1988-01-01

A solution method based on a fractional step approach is developed for obtaining time-dependent solutions of the three-dimensional, incompressible Navier-Stokes equations in generalized coordinate systems. The governing equations are discretized conservatively by finite volumes using a staggered mesh system. The primitive variable formulation uses the volume fluxes across the faces of each computational cell as dependent variables. This procedure, combined with accurate and consistent approximations of geometric parameters, is done to satisfy the discretized mass conservation equation to machine accuracy as well as to gain favorable convergence properties of the Poisson solver. The discretized equations are second-order-accurate in time and space and no smoothing terms are added. An approximate-factorization scheme is implemented in solving the momentum equations. A novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two and three-dimensional solutions are compared with other numerical and experimental results to validate the present method. 23 references

Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

Science.gov (United States)

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-05-01

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.