Relevant bibliographies by topics / Stream function-vorticity

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Stream function-vorticity'

Author: Grafiati
Published: 4 June 2025
Last updated: 6 July 2025

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Journal articles on the topic "Stream function-vorticity"

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Sousa, E., and I. J. Sobey. "Effect of boundary vorticity discretization on explicit stream-function vorticity calculations." International Journal for Numerical Methods in Fluids 49, no. 4 (2005): 371–93. http://dx.doi.org/10.1002/fld.1001.

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Papa, Touty Traore, Dieng Moussa, Faye Seydou, Ndiaye Mor, and Diagne Issa. "Numerical Study of Navier-Stokes Equations in Vorticity/Stream Function Formulation on the Torus in Two-Dimensional Flow under MATLAB." Journal of Scientific and Engineering Research 10, no. 5 (2023): 236–42. https://doi.org/10.5281/zenodo.10458711.

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<strong>Abstract </strong>The Navier-Stokes equations can be rearranged in 2D incompressible flows in terms of stream function and vorticity. In many areas of applications, the stream function and vorticity form of the Navier Stokes equations shows important effect into the mechanisms leading the flow than the first variables formulation. It&rsquo;s also useful for numerical study it avoids some problems resulting from the discretization. In this work a numerical approach with the stream function and vorticity is used with a discretization of the governing equations and the boundary conditions in the domain included in a square of unit length where the upper boundary (the lid) at y = 1, moves with a constant velocity U = 1. The Reynolds number based on the size of the domain, the velocity of the moving wall, density &rho; = 1 and viscosity &micro; = 0.001 is Re = 500. A code is developed under MATLAB software. The evolution of the vorticity field is determined in term of time. To do this, a differential finite method is used.
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Sommeria, J., C. Staquet, and R. Robert. "Final equilibrium state of a two-dimensional shear layer." Journal of Fluid Mechanics 233 (December 1991): 661–89. http://dx.doi.org/10.1017/s0022112091000642.

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We test a new statistical theory of organized structures in two-dimensional turbulence by direct numerical stimulations of the Navier–Stokes equations, using a pseudo-spectral method. We apply the theory to the final equilibrium state of a shear layer evolving from a band of uniform vorticity: a relationship between vorticity and stream function is predicted by maximizing an entropy with the constraints due the constants of the motion. A partial differential equation for the stream function is then obtained. In the particular case of a very thin initial vorticity band, the Stuart's vortices appear to be a family of solutions for this equation. In more general cases we do not solve the equation, but we test the theory by inspecting the relationship between stream function and vorticity in the final equilibrium state of the numerical computation. An excellent agreement is obtained in regions with strong vorticity mixing. However, local equilibrium is obtained before a complete mixing can occur in the whole fluid domain.
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Waugh, D. W., and D. G. Dritschel. "The stability of filamentary vorticity in two-dimensional geophysical vortex-dynamics models." Journal of Fluid Mechanics 231 (October 1991): 575–98. http://dx.doi.org/10.1017/s002211209100352x.

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The linear stability of filaments or strips of ‘potential’ vorticity in a background shear flow is investigated for a class of two-dimensional, inviscid, non-divergent models having a linear inversion relation between stream function and potential vorticity. In general, the potential vorticity is not simply the Laplacian of the stream function – the case which has received the greatest attention historically. More general inversion relationships between stream function and potential vorticity are geophysically motivated and give an impression of how certain classic results, such as the stability of strips of vorticity, hold under more general circumstances.In all models, a strip of potential vorticity is unstable in the absence of a background shear flow. Imposing a shear flow that reverses the total shear across the strip, however, brings about stability, independent of the Green-function inversion operator that links the stream function to the potential vorticity. But, if the Green-function inversion operator has a sufficiently short interaction range, the strip can also be stabilized by shear having the same sense as the shear of the strip. Such stabilization by ‘co-operative’ shear does not occur when the inversion operator is the inverse Laplacian. Nonlinear calculations presented show that there is only slight disruption to the strip for substantially less adverse shear than necessary for linear stability, while for co-operative shear, there is major disruption to the strip. It is significant that the potential vorticity of the imposed flow necessary to create shear of a given value increases dramatically as the interaction range of the inversion operator decreases, making shear stabilization increasingly less likely. This implies an increased propensity for filaments to ‘roll-up’ into small vortices as the interaction range decreases, a finding consistent with many numerical calculations performed using the quasi-geostrophic model.
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Dubois, François, Michel Salaün, and Stéphanie Salmon. "Vorticity–velocity-pressure and stream function-vorticity formulations for the Stokes problem." Journal de Mathématiques Pures et Appliquées 82, no. 11 (2003): 1395–451. http://dx.doi.org/10.1016/j.matpur.2003.09.002.

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Dubois, François, Michel Salaün, and Stéphanie Salmon. "Discrete harmonics for stream function-vorticity Stokes problem." Numerische Mathematik 92, no. 4 (2002): 711–42. http://dx.doi.org/10.1007/s002110100369.

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Sousa, E., and I. J. Sobey. "Numerical stability of unsteady stream-function vorticity calculations." Communications in Numerical Methods in Engineering 19, no. 6 (2003): 407–19. http://dx.doi.org/10.1002/cnm.600.

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Pokhrel, Puskar R., and Shiva P. Pudasaini. "Stream function - vorticity formulation of mixture mass flow." International Journal of Non-Linear Mechanics 121 (May 2020): 103317. http://dx.doi.org/10.1016/j.ijnonlinmec.2019.103317.

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GUERMOND, J. L., та L. QUARTAPELLE. "WEAK APPROXIMATION OF THE ψ–ω EQUATIONS WITH EXPLICIT VISCOUS DIFFUSION". Mathematical Models and Methods in Applied Sciences 10, № 01 (2000): 85–98. http://dx.doi.org/10.1142/s0218202500000070.

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This paper describes a variational formulation for solving the 2-D time-dependent incompressible Navier–Stokes equations expressed in the stream function and vorticity. The difference between the proposed approach and the standard one is that the vorticity equation is interpreted as an evolution equation for the stream function while the Poisson equation is used as an expression for evaluating the distribution of vorticity in the domain and on the boundary. A time discretization is adopted with the viscous diffusion made explicit, which leads to split the incompressibility from the viscosity. In some sense, the present method generalizes to the variational framework a well-known idea which is used in finite differences approximations and that is based on a Taylor series expansion of the stream function near the boundary. Some conditional stability results and error estimates are given.
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Mackinnon, R. J., G. F. Carey, and P. Murray. "A procedure for calcualting vorticity boundary conditions in the stream-function-vorticity method." Communications in Applied Numerical Methods 6, no. 1 (1990): 47–48. http://dx.doi.org/10.1002/cnm.1630060107.

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Dissertations / Theses on the topic "Stream function-vorticity"

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Bermejo, Rodolfo. "Analysis of a Galerkin-Characteristic algorithm for the potential vorticity-stream function equations." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/30561.

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In this thesis we develop and analyze a Galerkin-Characteristic method to integrate the potential vorticity equations of a baroclinic ocean. The method proposed is a two stage inductive algorithm. In the first stage the material derivative of the potential vorticity is approximated by combining Galerkin-Characteristic and Particle methods. This yield a computationally efficient algorithm for this stage. Such an algorithm consists of updating the dependent variable at the grid points by cubic spline interpolation at the foot of the characteristic curves of the advective component of the equations. The algorithm is unconditionally stable and conservative for Δt = O(h). The error analysis with respect to L² -norm shows that the algorithm converges with order O(h); however, in the maximum norm it is proved that for sufficiently smooth functions the foot of the characteristic curves are superconvergent points of order O(h⁴ /Δt). The second stage of the algorithm is a projection of the Lagrangian representation of the flow onto the Cartesian space-time Eularian representation coordinated with Crank-Nicholson Finite Elements. The error analysis for this stage with respect to L²-norm shows that the approximation component of the global error is O(h²) for the free-slip boundary condition, and O(h) for the no-slip boundary condition. These estimates represent an improvement with respect to other estimates for the vorticity previously reported in the literature. The evolutionary component of the global error is equal to K(Δt² + h), where K is a constant that depends on the derivatives of the advective quantity along the Characteristic. Since the potential vorticity is a quasi-conservative quantitiy, one can conclude that K is in general small. Numerical experiments illustrate our theoretical results for both stages of the method.<br>Science, Faculty of<br>Mathematics, Department of<br>Graduate
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Ghadi, Fatth-Allah. "Résolution par la méthode des éléments finis des équations de Navier-Stokes en formulation (v-w)." Saint-Etienne, 1994. http://www.theses.fr/1994STET4010.

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Dans ce travail, nous proposons une méthode mixte en fonction de courant-tourbillon pour résoudre le problème de Stokes dans des domaines bornes réguliers de r. Nous établissons par la suite des estimations d'erreur dans le cadre des formulations mixtes classiques. Du point de vue numérique, nous mettons en oeuvre une méthode basée sur l'approximation d'une base harmonique pour résoudre le problème de Stokes. Par ailleurs nous étendons cette méthode au cas du problème de Navier-Stokes et afin de combattre la convection dominante nous faisons appel à la technique de Petrov-Galerkin
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Fang, Zhigang. "Stream function-vorticity-pressure functional solution of the steady Euler equations." Thesis, 1988. http://spectrum.library.concordia.ca/5820/1/NL44887.pdf.

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Ho, Ping-Huan, and 何秉寰. "Using the Moving Particle Method With Eularian Mesh toSolve Lid-Driven Cavity Flow Problem in Stream Function-vorticity Formulation." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/55603312173627893916.

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碩士<br>國立高雄海洋科技大學<br>輪機工程研究所<br>101<br>This study focused on applying the method of dual particles to solve the lid-driven cavity flow problem in stream function–vorticity formulation. The method of dual particles includes the Lagrangian particle which possesses the convection behavior, while another Eulerian particle does not have such flowing characteristic effect. Using the property of the Eulerian particle, a fixed grid framework can be constructed. This paper considered three different schemes to evaluate the diffusion effect occurring in Lagrangian particle. They are particle smoothing (PS), smoothing difference (SD) and local mesh (LM). The PS scheme is formulated by superimposing contribution from distributed particles; SD scheme by combining the PS and Taylor series analysis and LM is derived based on a referenced mesh. The numerical results obtained by using the dual particle method proposed in the present study of the lid-driven cavity flow problem for various Reynolds numbers indicated that the more accurate solutions are attained in the formulation of stream function-vorticity rather than the formulation in primitive variables, especially under very high Reynolds numbers. The resultant simulations are observed deviated from the reference data for coarse meshes, however, when fine meshes are adopted, the simulation results obtained are in good agreement with the literatures.
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Books on the topic "Stream function-vorticity"

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E, Tezduyar T., and Lyndon B. Johnson Space Center, eds. Finite element techniques for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation: Interim report for the work performed under NASA-Johnson Space Center. Dept. of Mechanical Engineering, University of Houston, 1987.

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Book chapters on the topic "Stream function-vorticity"

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Behnia, M., and G. Vahl Davis. "Fine Mesh Solutions Using Stream Function-Vorticity Formulation." In Numerical Simulation of Oscillatory Convection on Low-Pr Fluids. Vieweg+Teubner Verlag, 1990. http://dx.doi.org/10.1007/978-3-322-87877-9_3.

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Behnia, M., G. Vahl Davis, F. Stella, and G. Guj. "A Comparison of Velocity-Vorticity and Stream Function-Vorticity Formulations for Pr=0." In Numerical Simulation of Oscillatory Convection on Low-Pr Fluids. Vieweg+Teubner Verlag, 1990. http://dx.doi.org/10.1007/978-3-322-87877-9_4.

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Kandelousi, Mohsen Sheikholeslami, and Davood Domairry Ganji. "CVFEM stream function-vorticity solution." In Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method. Elsevier, 2015. http://dx.doi.org/10.1016/b978-0-12-802950-3.00002-3.

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Sheikholeslami, Mohsen. "Simulation of Vorticity Stream Function Formulation by Means of CVFEM." In Application of Control Volume Based Finite Element Method (CVFEM) for Nanofluid Flow and Heat Transfer. Elsevier, 2019. http://dx.doi.org/10.1016/b978-0-12-814152-6.00002-3.

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"CVFEM Stream Function-Vorticity Solution for a Lid Driven Cavity Flow." In Basic Control Volume Finite Element Methods for Fluids and Solids. Co-Published with Indian Institute of Science (IISc), Bangalore, India, 2009. http://dx.doi.org/10.1142/9789812834997_0009.

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Lopez, Omar D., Sergio Pedraza, and Jose R. Toro. "Simulation of Axisymmetric Flows with Swirl in Vorticity- Stream Function Variables Using the Lattice Boltzmann Method." In Vortex Structures in Fluid Dynamic Problems. InTech, 2017. http://dx.doi.org/10.5772/65650.

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Furbish, David Jon. "Turbulent Boundary-Layer Shear Flows." In Fluid Physics in Geology. Oxford University Press, 1997. http://dx.doi.org/10.1093/oso/9780195077018.003.0019.

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Turbulent shear flows next to solid boundaries are one of the most important types of flow in geology. In such flows, turbulence is generated primarily by boundary effects; vorticity originates near a boundary in association with the velocity gradients that arise from the no-slip condition at the boundary. Such gradients provide a ready source of vorticity for eddies and eddy-like structures to develop in response to the destabilizing effects of inertial forces, and then move outward into the adjacent flow. Eddies are also generated within the wakes of bumps that comprise boundary roughness, for example, sediment particles on the bed of a stream channel (Example Problem 11.4.2). As we have seen in Chapter 14, the fluctuating motions of turbulence involve, over any elementary area, fluxes of fluid momentum that are manifest as apparent (Reynolds) stresses. In addition, the complex motions of eddies and eddy-like structures efficiently advect heat and solutes from one place to another within a turbulent flow, and thereby facilitate mixing of heat and solutes throughout the fluid. For similar reasons, turbulent motions are responsible for lofting fine sediment into the fluid column of a stream channel and in the atmosphere. We will concentrate in this chapter on steady unidirectional flows where the mean streamwise velocity varies only in the coordinate direction normal to a boundary and the mean velocity normal to the boundary is zero. We also will adopt a classic treatment of turbulent boundary flow in developing the idea of L. Prandtl’s mixing-length hypothesis, from which we will obtain the logarithmic velocity law, a function that describes how the mean streamwise velocity varies in the coordinate direction normal to a boundary. In developing Prandtl’s hypothesis, we will see that the presence of apparent stresses associated with fluctuating motions leads to the idea of an eddy viscosity or apparent viscosity. Unlike the Newtonian viscosity, the eddy viscosity is a function of the mean velocity, and therefore coordinate position. This means that the eddy viscosity cannot, in general, be removed from stress terms involving spatial derivatives, as we previously did with the Newtonian viscosity in simplifying the Navier–Stokes equations.
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Alemseged Worku, Nahom. "Basics of Fluid Dynamics." In Computational Overview of Fluid Structure Interaction. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.96312.

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In this chapter, studies on basic properties of fluids are conducted. Mathematical and scientific backgrounds that helps sprint well into studies on fluid mechanics is provided. The Reynolds Transport theorem and its derivation is presented. The well-known Conservation laws, Conservation of Mass, Conservation of Momentum and Conservation of Energy, which are the foundation of almost all Engineering mechanics simulation are derived from Reynolds transport theorem and through intuition. The Navier–Stokes equation for incompressible flows are fully derived consequently. To help with the solution of the Navier–Stokes equation, the velocity and pressure terms Navier–Stokes equation are reduced into a vorticity stream function. Classification of basic types of Partial differential equations and their corresponding properties is discussed. Finally, classification of different types of flows and their corresponding characteristics in relation to their corresponding type of PDEs are discussed.
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Feistauer, M., J. Felcman, and I. Straskraba. "Finite Difference and Finite Volume Methods for Nonlinear Hyperbolic Systems and the Euler Equations." In Mathematical and Computational Methods for Compressible Flow. Oxford University PressOxford, 2003. http://dx.doi.org/10.1093/oso/9780198505884.003.0004.

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Abstract In modern technologies one often encounters the necessity to solve compressible flow with a complicated structure. There are several conceivable models of compressible flow. Let us mention, for example, the model of inviscid, stationary, irrotational or rotational subsonic flow using the stream function formulation, and the models of transonic flow based on the small perturbation equation or full potential equation. There exists an extensive literature about the finite difference or finite element methods for the numerical solution of these models. (For a survey of mathematical and numerical methods for these models, see (Feistauer, 1998).) In a number of problems, the potential models are not sufficiently accurate, particularly in high speed (transonic or hypersonic) flow, because of the appearance of the so-called strong shocks with large entropy and vorticity production. This leads to the necessity of using the complete system of conservation laws consisting of the continuity equation, the Euler equations of motion and the energy equation (called the Euler equations in brief), which has been widely used during the last few decades for the modelling of flows in aeronautics, the aviation industry and steam or gas turbine design. Successively, the Euler equations have begun to be applied also to low Mach number problems on the one hand and to problems with chemical reactions on the other. These models neglect, of course, viscosity, but in many situations they give good results, reliable from the point of view of comparisons with experiments.
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Conference papers on the topic "Stream function-vorticity"

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MARQUES, LEANDRO, Gustavo Anjos, and JOSE PONTES. "BLOOD FLOW SIMULATION USING STREAM FUNCTION-VORTICITY FEM FORMULATION." In II Congresso Brasileiro de Fluidodinâmica Computacional. Galoa, 2018. http://dx.doi.org/10.17648/cbcfd-83749.

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Xie, X. L., and W. W. Mar. "2D vorticity and stream function solutions based on curvilinear coordinates." In Third International Conference on Experimental Mechanics, edited by Xiaoping Wu, Yuwen Qin, Jing Fang, and Jingtang Ke. SPIE, 2002. http://dx.doi.org/10.1117/12.468772.

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DAVIS, R., J. CARTER, and M. HAFEZ. "Three-dimensional viscous flow solutions with a vorticity-stream function formulation." In 25th AIAA Aerospace Sciences Meeting. American Institute of Aeronautics and Astronautics, 1987. http://dx.doi.org/10.2514/6.1987-601.

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Wei, Xueyong, Mike C. L. Ward, Dejiang Lu, and Zhuangde Jiang. "Simulation of Rarefied Gas Flow in Microchannel Based on Vorticity-Stream Function Method." In 2007 First International Conference on Integration and Commercialization of Micro and Nanosystems. ASMEDC, 2007. http://dx.doi.org/10.1115/mnc2007-21120.

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Vorticity-stream function method is successfully used to solve an incompressible gas flow in the parallel-plates micro-channel. A new formula in finite difference scheme is developed to describe the boundary vorticity based on the slip boundary theory and Taylor series expansion. Results show that the boundary vorticity are not only influenced by the Knudsen number (Kn) but also influenced by the tangential momentum accommodation coefficient (TMAC).
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Rakshit, Sukanta, and Harsha Bojja. "Analysis of Flow in a Concentric Cylindrical Vessel Using Stream and Vorticity Function." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-13020.

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This paper reports the numerical results of flow in a concentric cylindrical vessel. Velocity plots are shown to illustrate the swirling cylinder flow inside the cylinder having free surface on top and constant rotating bottom wall. The analysis is carried out axisymmetric using Stream function and Vorticity method by writing Navier-Stokes equation and continuity equation in cylindrical coordinates in form of stream functions and azimuthal vorticity components eliminating the pressure component. Using Finite Difference Schemes, modified Navier-Stokes equation and continuity equations are solved by explicit methods. No-slip boundary condition is assumed at wall to minimize the discontinuity. Vortex formation is shown using contour plots and variation in Reynolds number and dimensions are considered as variable for the system. As the Reynolds number is increased the system undergoes vortex breakdown. Result clearly indicates the formation of another vortex near the free surface illustrating the phenomena of vortex breakdown. Effect of aspect ratio in the nature flow is also shown in the paper. Comparison of numerically achieved results and experimental results are done for validation.
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Arthur Campos, Rafael Gabler Gontijo, and Francisco Ricardo Cunha. "Numerical study of a Magnetic Fluid Boundary Layer using the Vorticity-Stream function Formulation." In 23rd ABCM International Congress of Mechanical Engineering. ABCM Brazilian Society of Mechanical Sciences and Engineering, 2015. http://dx.doi.org/10.20906/cps/cob-2015-1578.

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Carnevale, Luis, Gustavo Anjos, and Norberto Mangiavacchi. "Stream Function-Vorticity Formulation And Heat Transport using FEM For Unstructured Meshes and Complex Domains." In II Congresso Brasileiro de Fluidodinâmica Computacional. Galoa, 2018. http://dx.doi.org/10.17648/cbcfd-83701.

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Carnevale, Luís Henrique, Gustavo Rabello dos Anjos, and Norberto Mangiavacchi. "STREAM FUNCTION-VORTICITY FORMULATION APPLIED IN THE CONJUGATED HEAT PROBLEM USING THE FEM WITH UNSTRUCTURED MESH." In Brazilian Congress of Thermal Sciences and Engineering. ABCM, 2018. http://dx.doi.org/10.26678/abcm.encit2018.cit18-0173.

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Mayeli, Peyman, Tzekih Tsai, and Gregory Sheard. "Studying the natural convection problem in a square cavity by a new vorticity-stream-function approach." In 22nd Australasian Fluid Mechanics Conference AFMC2020. The University of Queensland, 2020. http://dx.doi.org/10.14264/b2c1622.

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Carnevale, Luís Henrique, Norberto Mangiavacchi, and Gustavo Rabello dos Anjos. "SEMI-LAGRANGEAN METHOD APPLIED IN THE CONJUGATED HEAT PROBLEM USING AN AXISYMMETRICAL STREAM FUNCTION-VORTICITY FORMULATION." In 25th International Congress of Mechanical Engineering. ABCM, 2019. http://dx.doi.org/10.26678/abcm.cobem2019.cob2019-1152.

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