Relevant bibliographies by topics / Stream function equations

Contents

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

Academic literature on the topic 'Stream function equations'

Author: Grafiati
Published: 4 June 2021
Last updated: 15 February 2022

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Journal articles on the topic "Stream function equations"

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Reusken, Arnold. "Stream function formulation of surface Stokes equations." IMA Journal of Numerical Analysis 40, no. 1 (2018): 109–39. http://dx.doi.org/10.1093/imanum/dry062.

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AbstractIn this paper we present a derivation of the surface Helmholtz decomposition, discuss its relation to the surface Hodge decomposition and derive a well-posed stream function formulation of a class of surface Stokes problems. We consider a $C^2$ connected (not necessarily simply connected) oriented hypersurface $\varGamma \subset \mathbb{R}^3$ without boundary. The surface gradient, divergence, curl and Laplace operators are defined in terms of the standard differential operators of the ambient Euclidean space $\mathbb{R}^3$. These representations are very convenient for the implementat
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Khan, Waqar, and Faisal Yousafzai. "On the Exact Solutions of Couple Stress Fluids." Advanced Trends in Mathematics 1 (December 2014): 27–32. http://dx.doi.org/10.18052/www.scipress.com/atmath.1.27.

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Exact solutions of the momentum equations of couple stress fluid are investigated. Making use of stream function, the two-dimensional flow equations are transformed into non-linear compatibility equation, and then it is linearized by vorticity function. Stream functions and velocity distributions are discussed for various flow situations.
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Xu, J. Z., W. Y. Ni, and J. Y. Du. "Numerical Solution of Stream Function Equations in Transonic Flows." Journal of Turbomachinery 109, no. 4 (1987): 508–12. http://dx.doi.org/10.1115/1.3262140.

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In order to develop the transonic stream function approach, in this paper one of the momentum equations is employed to form the principal equation of the stream function which does not contain vorticity and entropy terms, and the other one is used to calculate the density directly. Since the density is uniquely determined, the problem that the density is a double-valued function of mass flux in the stream function formulation disappears and the entropy increase across the shock is naturally included. The numerical results for the transonic cascade flow show that the shock obtained from the pre
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Karaa, Samir. "High-order ADI method for stream-function vorticity equations." PAMM 7, no. 1 (2007): 1025601–2. http://dx.doi.org/10.1002/pamm.200700414.

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Atkins, H. L., and H. A. Hassan. "A new stream function formulation for the steady Euler equations." AIAA Journal 23, no. 5 (1985): 701–6. http://dx.doi.org/10.2514/3.8973.

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Auteri, F., and L. Quartapelle. "Galerkin Spectral Method for the Vorticity and Stream Function Equations." Journal of Computational Physics 149, no. 2 (1999): 306–32. http://dx.doi.org/10.1006/jcph.1998.6155.

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Brandner, Philip, and Arnold Reusken. "Finite element error analysis of surface Stokes equations in stream function formulation." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 6 (2020): 2069–97. http://dx.doi.org/10.1051/m2an/2020044.

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We consider a surface Stokes problem in stream function formulation on a simply connected oriented surface Γ ⊂ ℝ3 without boundary. This formulation leads to a coupled system of two second order scalar surface partial differential equations (for the stream function and an auxiliary variable). To this coupled system a trace finite element discretization method is applied. The main topic of the paper is an error analysis of this discretization method, resulting in optimal order discretization error bounds. The analysis applies to the surface finite element method of Dziuk–Elliott, too. We also i
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Spotz, W. F., and G. F. Carey. "High-order compact scheme for the steady stream-function vorticity equations." International Journal for Numerical Methods in Engineering 38, no. 20 (1995): 3497–512. http://dx.doi.org/10.1002/nme.1620382008.

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Ben-Yu, Guo, He Li-Ping, and Mao De-Kang. "On the Two-Dimensional Navier–Stokes Equations in Stream Function Form." Journal of Mathematical Analysis and Applications 205, no. 1 (1997): 1–31. http://dx.doi.org/10.1006/jmaa.1996.5174.

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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.
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Dissertations / Theses on the topic "Stream function equations"

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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 t
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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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Persson, Leif. "Quasi-radial solutions of the p-harmonic equation in the plane and their stream functions." Licentiate thesis, Luleå tekniska universitet, 1988. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-25699.

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Viglioni, Humberto Henrique de Barros. "Dinâmica de vórtices em superfícies com aplicações ao problema de dois vórtices no toro plano." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-03042017-161053/.

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Este trabalho apresenta uma dedução das equações para a dinâmica de vórtices em superfícies utilizando argumentos físicos e balanço de momento, obtendo o resultado já conhecido devido a Boatto/Koiller e Hally. Na primeira parte, elaboramos uma releitura da contribuição de diversos pesquisadores incluindo, além dos já citados, o trabalho de Marchioro e Pulvirenti sobre a propriedade de localização para a equação de Euler e também a importante contribuição de Flucher e Gustafsson no que diz respeito à determinação da função de Green e função de Robin hidrodinâmicas em domínios do plano. Na seg
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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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Chang, Teng-Yuan, and 張騰元. "Numerical study of the two-dimensional Navier-Stokes equations based on the stream function formulation." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/mdxap9.

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碩士<br>國立交通大學<br>應用數學系所<br>106<br>In this paper, the two-dimensional Navier-Stokes equations in streamfunction formulation is considered. We present the theoretical analysis of existence, uniqueness and the long time stability of the numerical solution solved by the first order in time Legendre Galerkin spectral scheme. With this scheme, we proved that the numerical solution is long time stable provided the time step is small enough. Our numerical results are presented in the last chapter to demonstrate the validity of the theoretical results, also included the numerical results of second order
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Chuang, Ching-wei, and 莊敬偉. "Derivation of Higher-Order Mild-Slope Equation Using Stream Function Method." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/17686038429490491297.

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碩士<br>國立成功大學<br>水利及海洋工程學系碩博士班<br>95<br>The mild-slope equation was derived using stream function method. A numerical model was developed by means of finite element method to simulate wave deformation over different types of sea bottom. Computational cases including Booij’s ramp, parabolic mound and sinusoidal bed were used to test the accuracy and valid range of the present model. The model is also applied to a series of submerged breakwaters for describing Bragg resonance of water waves. Comparison of the numerical results with experiments shows that the present model is in a good agreement w
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Leben, Jakob. "A programming language based on recurrence equations and polyhedral compilation for stream processing." Thesis, 2019. http://hdl.handle.net/1828/11008.

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The work presented in this dissertation contributes to the field of programming lan- guage design and implementation for stream processing applications. There is a fast-expanding domain of stream processing applications which demand processing high-volume streams quickly and often in real time. Examples include analysis and synthesis of audio, video and other digital media, sensor array signals, real-time phys- ical simulation etc. High performance is crucial in this domain. When choosing between available programming methods, the programmer often chooses one that maximizes performance
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Beaton, Andrew. "Testing and Refining a Unique Approach for Setting Environmental Flow and Water Level Targets for a Southern Ontario Subwatershed." Thesis, 2012. http://hdl.handle.net/10214/3850.

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In this study Bradford’s (2008) approach for setting ecological flow and water level targets is tested and refined through application within the Lake Simcoe Region Conservation Authority’s (LSRCA) subwatershed of Lover’s Creek. A method for defining subwatershed objectives and identifying habitat specialists through expert input is proposed and tested. The natural regime of each streamflow and wetland site is characterized along with the hydrological alteration at each site. Potential ecological responses to the hydrologic alterations are then hypothesized for the different types of change
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Books on the topic "Stream function equations"

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Greywall, Mahesh S. Computation of three-dimensional flows using two stream functions. Wichita State University, National Institute for Aviation Research, 1991.

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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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Isett, Philip. Constructing the Correction. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0007.

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This chapter explains how the correction is constructed, first by considering the transportation of the phase functions. A solution (v, p, R) to the Euler-Reynolds equations is fixed and a correction v₁ = v + V, p₁ = p + P is presented. Here v is an approximation to the “coarse scale velocity” since the solution ultimately achieved by the process will resemble v at a sufficiently coarse scale. The next step is to eliminate the Transport term. A time cutoff function is also introduced, where the time cutoff itself is differentiated in the Transport term. Finally, the chapter describes the High–
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United States. National Aeronautics and Space Administration., ed. Efficient and accurate explicit integration algorithims with application to viscoplastic models. National Aeronautics and Space Administration, 1994.

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Isett, Philip. Transport Estimates. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0017.

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This chapter derives estimates for quantities which are transported by the coarse scale flow and for their derivatives. It first considers the phase functions which satisfy the Transport equation, with the goal of choosing the lifespan parameter τ‎ sufficiently small so that all the phase functions which appear in the analysis can be guaranteed to remain nonstationary in the time interval, and so that the Stress equation can be solved. In order for these requirements to be met, τ‎ small enough is chosen so that the gradients of the phase functions do not depart significantly from their initial
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Book chapters on the topic "Stream function equations"

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Rieger, E., H. Schütz, D. Wolter, and F. Thiele. "A Comparison of Finite-Difference Approximations for the Stream Function Formulation of the Incompressible Navier-Stokes Equations." In Numerical Treatment of the Navier-Stokes Equations. Vieweg+Teubner Verlag, 1990. http://dx.doi.org/10.1007/978-3-663-14004-7_10.

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Fairag, Faisal. "Two Level Finite Element Technique for Pressure Recovery from Stream Function Formulation of the Navier-Stokes Equations." In Lecture Notes in Computational Science and Engineering. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-56205-1_7.

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Brenn, Günter. "The Equation for the Stokesian Stream Function and Its Solutions." In Mathematical Engineering. Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-51423-8_2.

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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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Steward, David R. "Analytic Elements from Singular Integral Equations." In Analytic Element Method. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198856788.003.0005.

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Solutions to interface problems may be developed using analytic elements with mathematical solutions to the Laplace equation developed by singular integral equations. This formulation leads to solutions with discontinuities occurring across line segments, where the potential or stream function is discontinuous across double layer elements in Section 5.2, and the normal or tangential component of the vector field is discontinuous across single layer elements in Section 5.3. Examples illustrate a broad range of solutions to interface conditions possible with these elements. Series expansions are used to represent the far-field at larger distances from elements in Section 5.4, which leads to higher-order elements with nearly exact solutions and also provides a simpler representation for contiguous strings of adjacent elements. Such strings of elements are used with polygon elements in 5.5 to solve conditions along the interfaces of heterogeneities, and to provide a common series expansion to represent the far-field for a group of neighboring elements. Methods are extended to analytic elements with curvilinear geometry using conformal mappings (Section 5.6) and to three-dimensional fields in Section 5.7.
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Kobayashi, Shiro, Soo-Ik Oh, and Taylan Altan. "Three-Dimensional Problems." In Metal Forming and the Finite-Element Method. Oxford University Press, 1989. http://dx.doi.org/10.1093/oso/9780195044027.003.0017.

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A majority of the finished products made by metal forming are geometrically complex and the metal flow involved is of a three-dimensional nature. Thus, any analysis technique will become more useful in industrial applications if it is capable of solving three-dimensional metal-flow problems. Nagpal and Altan introduced dual-stream functions for describing metal flow in three dimensions. This work showed that the proper selection of a flow function makes the incompressibility requirement automatically satisfied and provides general kinematically admissible velocity fields. Yang and Lee utilized the conformal transformation of a unit circle onto a cross-section in the analysis of curved die extrusion. They derived the stream-line equation from which a kinematically admissible velocity field was determined. The upper-bound method was then applied to determine the extrusion pressure for a rigid-perfectly plastic material. An important aspect of three-dimensional plastic deformation is the analysis of spread in metal-forming operations, such as spread in rolling or in flat tool forging, and spread in compression of noncircular disks. Solutions to such problems have been obtained by the use of Hill’s general method and the upper-bound method. The extension of the finite-element method to solve three-dimensional problems is natural and not new, particularly in the area of elasticity. However, the simulation of three-dimensional forming operations by the finite-element method is relatively recent. Park and Kobayashi described the formulation for the three-dimensional rigid-plastic finite-element method and the implementation of the boundary conditions. They applied this technique to the analysis of block compression between two parallel flat platens. For certain forming problems, such as those involving lateral spread, the use of a simplified three-dimensional element is efficient and some examples can be found for analysis of spread in rolling and flat tool forging. The matrices for evaluation of elemental stiffness equations are defined for a three-dimensional brick element in Chap. 6 and some of them are recapitulated in this section. A three-dimensional brick element used for the analysis is an eight-node hexahedral isoparametric element.
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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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Abdelsabour Fahmy, Mohamed. "A Novel MDD-Based BEM Model for Transient 3T Nonlinear Thermal Stresses in FGA Smart Structures." In Advanced Functional Materials. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.92829.

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The main objective of this chapter is to introduce a novel memory-dependent derivative (MDD) model based on the boundary element method (BEM) for solving transient three-temperature (3T) nonlinear thermal stress problems in functionally graded anisotropic (FGA) smart structures. The governing equations of the considered study are nonlinear and very difficult if not impossible to solve analytically. Therefore, we develop a new boundary element scheme for solving such equations. The numerical results are presented highlighting the effects of the MDD on the temperatures and nonlinear thermal stress distributions and also the effect of anisotropy on the nonlinear thermal stress distributions in FGA smart structures. The numerical results also verify the validity and accuracy of the proposed methodology. The computing performance of the proposed model has been performed using communication-avoiding Arnoldi procedure. We can conclude that the results of this chapter contribute to increase our understanding on the FGA smart structures. Consequently, the results also contribute to the further development of technological and industrial applications of FGA smart structures of various characteristics.
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Alexeyeva, Lyudmila, and Yergali Kurmanov. "Generalized and Fundamental Solutions of Motion Equations of Two-Component Biot’s Medium." In Mathematical Theorems - Boundary Value Problems and Approximations. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.92064.

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Here processes of wave propagation in a two-component Biot’s medium are considered, which are generated by arbitrary forces actions. By using Fourier transformation of generalized functions, a fundamental solution, Green tensor, of motion equations of this medium has been constructed in a non-stationary case and in the case of stationary harmonic oscillation. These tensors describe the processes of wave propagation (in spaces of dimensions 1, 2, 3) under an action of power sources concentrated at coordinates origin, which are described by a singular delta-function. Based on them, generalized solutions of these equations are constructed under the action of various sources of periodic and non-stationary perturbations, which are described by both regular and singular generalized functions. For regular acting forces, integral representations of solutions are given that can be used to calculate the stress-strain state of a porous water-saturated medium.
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Mussardo, Giuseppe. "Form Factors and Correlation Functions." In Statistical Field Theory. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198788102.003.0019.

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At the heart of a quantum field theory are the correlation functions of the various fields. In the case of integrable models, the correlators can be expressed in terms of the spectral series based on the matrix elements on the asymptotic states. These matrix elements, also known as form factors, satisfy a set of functional and recursive equations that can exactly solved in many cases of physical interest. Chapter 19 covers general properties of form factors, Faddeev–Zamolodchikov algebra, symmetric polynomials, kinematical and bound state poles, the operator space and kernel functions, the stress-energy tensor and vacuum expectation values and the Ising model in a magnetic field.
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Conference papers on the topic "Stream function equations"

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Yaonan, Hua, and Wu Wenquan. "Numerical Solution of Transonic Stream Function Equation on S1 Stream Surface in Cascade." In ASME 1986 International Gas Turbine Conference and Exhibit. American Society of Mechanical Engineers, 1986. http://dx.doi.org/10.1115/86-gt-110.

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A method is presented in this paper for calculating transonic flow field in turbomachinery cascades. With respect to non-orthogoanl curvilinear coordinates, the stream function equation governing fluid flow was established. Using the Artificial Compressibility Method, the discretization of the partial differential equation was carried out by use of the standard central difference formula. The set of linear algebraic equations obtained is solved by means of the Direct Matrix Method. In order to overcome the non-uniqueness of density in transonic flow in the stream function method, the velocitie
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HO, P., R. DECHER, and J. HERMANSON. "Grid induced errors in stream function solutions of the Navier-Stokes equations." In 27th Joint Propulsion Conference. American Institute of Aeronautics and Astronautics, 1991. http://dx.doi.org/10.2514/6.1991-2261.

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Zhang, Xing, Shizhao Wang, and Guowei He. "An Immersed Boundary Method Based on Navier-Stokes Equations in Discrete Stream Function Formulation." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-30149.

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A new variant of Immersed Boundary method is proposed in the framework of discrete stream function approach for the Navier-Stokes equations. A parallelized flow solver is developed to simulate two and three-dimensional flow problems involving complex and moving boundaries. The parallel performance of the present flow solver is tested by varying the number of processors used in the simulation. Code validations and applications are also presented, in an order of increasing complexity.
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Marquez, Richard, and Mauricio Gargaglione Prado. "Modelling Downhole Separation Efficiency Using a Stream Function Approach." In ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2009. http://dx.doi.org/10.1115/omae2009-79763.

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A new technique for solving simultaneously the mass and momentum balance equations for a gas-liquid mixture is proposed in this paper. The technique is based on the vorticity-stream function approach, under a cylindrical coordinate system. Important variables such as slip velocity in the radial and vertical direction, characteristic of the bottomhole, gas and liquid flow rates, pressures, flow pattern, among others, are considered simultaneously in the solution of the problem. The two-phase model proposed in this work allows obtaining the liquid and gas velocities fields as well as the two-pha
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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 solve
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Manchu, Ge, Lou Yiping, and Yu Zhengti. "A Method for Transonic Inverse Cascade Design With a Stream Function Equation." In ASME 1986 International Gas Turbine Conference and Exhibit. American Society of Mechanical Engineers, 1986. http://dx.doi.org/10.1115/86-gt-189.

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A new profile design method is developed on the basis of Refs.1–3 for transonic flow. The rotational dynamic stream function equation, which is expressed in functional form of calculated coordinates, is deduced. This method can be used for the calculation of cascade and S1 stream surface of a transonic flow with local shock wave on the blade suction surface. This method consists of two parts. One is a inverse method with a given velocity distribution along the suction surface and a given thickness distribution. Another is a inverse method with given velocity distributions on suction and pressu
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Naixing, Chen, and Zhang Fengxian. "A Comparison Between Full and Simplified Navier-Stokes Equation Solutions for Rotating Blade Cascade Flow on S1 Stream Surface of Revolution." In ASME 1985 International Gas Turbine Conference and Exhibit. American Society of Mechanical Engineers, 1985. http://dx.doi.org/10.1115/85-gt-4.

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A method for solving the Navier-Stokes equations of the rotating blade cascade flow on S1 stream surface of revolution is developed in the present paper. In this paper a complete set of full and simplified Navier-Stokes equations is given which includes stream-function equation, energy equation and entropy equation, equation of state for a perfect gas, formula for estimating density and formulas for calculating viscous forces, work done by viscous force, dissipation function and heat-transfer term. A comparison between the full and the simplified Navier-Stokes equations is made. The viscous te
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8

AbdulNour, Bashar S. "Optimized Accelerating Parameters of Convergence for the Navier-Stokes Equations." In ASME 1992 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/cie1992-0076.

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Abstract An over-relaxation procedure, that includes weighing factors, is applied to the steady, two-dimensional Navier-Stokes equations in order to reduce the computational time. The benefits obtained from this strategy are illustrated by the problem of viscous flow in the entrance region of an unconstricted and a constricted channel. The describing equations are expressed in terms of the stream function and vorticity. The convergence domain for the Successive Over-Relaxation method and the optimum values of the accelerating parameters, which consist of the over-relaxation and weighting facto
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9

Gu, C. W., J. Z. Xu, and J. Y. Du. "A Three-Dimensional Numerical Method for Turbomachinery Blading." In ASME 1992 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/92-gt-291.

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By inversing one of the stream functions and their principal equations in a three–dimensional flow the equations with the second–order partial derivatives of both the coordinate and another stream function are derived. The corresponding boundary conditions are easily specified. Based on these equations and the boundary conditions the convergent solution for turbomachinery blading is obtained. The computational results show that the method is simple and effective.
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10

Haji Mohammadi, Mohammad. "Meshless Local Petrov-Galerkin (MLPG) Method for Incompressible Viscous Fluid Flows." In ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/fedsm2006-98426.

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In this paper, the truly Meshless Local Petrov-Galerkin (MLPG) method is extended for computation of unsteady incompressible flows, governed by the Navier–Stokes equations (NSE), in vorticity-stream function formulation. The present method is a truly meshless method based only on a number of randomly located nodes. The formulation is based on two equations including stream function Poisson equation and vorticity advection-dispersion-reaction eq. (ADRE). The meshless method is based on a local weighted residual method with the Heaviside step function and quartic spline as the test functions res
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