Journal articles: 'Stokes expansion'

1

Chang, Hsien-Kuo, and Jin-Cheng Liou. "Fixed-frequency Stokes wave expansion." Ocean Engineering 33, no. 3-4 (March 2006): 417–24. http://dx.doi.org/10.1016/j.oceaneng.2005.04.020.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Consiglieri, Luisa. "Thermal Expansion on Stokes–Fourier Systems." SIAM Journal on Mathematical Analysis 44, no. 3 (January 2012): 1831–60. http://dx.doi.org/10.1137/110832665.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Sadiq, Muhammad Adil. "Boundary Layer Flow due to the Vibration of a Sphere." Journal of Applied Mathematics 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/191606.

Full text

Abstract:

Boundary layer flow of the Newtonian fluid that is caused by the vibration of inner sphere while the outer sphere is at rest is calculated. Vishik-Lyusternik (Nayfeh refers to this method as the method of composite expansions) method is employed to construct an asymptotic expansion of the solution of the Navier-Stokes equations in the limit of high-frequency vibrations for Reynolds number ofO(1). The effect of the Stokes drift of fluid particles is also considered.

APA, Harvard, Vancouver, ISO, and other styles

4

Wang, Jin. "An asymptotic expansion for Stokes waves with viscosity." Fluid Dynamics Research 40, no. 2 (February 2008): 155–61. http://dx.doi.org/10.1016/j.fluiddyn.2007.08.001.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Lisboa, Kleber Marques, Jian Su, and Renato M. Cotta. "Vector eigenfunction expansion in the integral transform solution of transient natural convection." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 8 (August 5, 2019): 2684–708. http://dx.doi.org/10.1108/hff-10-2018-0543.

Full text

Abstract:

Purpose The purpose of this work is to revisit the integral transform solution of transient natural convection in differentially heated cavities considering a novel vector eigenfunction expansion for handling the Navier-Stokes equations on the primitive variables formulation. Design/methodology/approach The proposed expansion base automatically satisfies the continuity equation and, upon integral transformation, eliminates the pressure field and reduces the momentum conservation equations to a single set of ordinary differential equations for the transformed time-variable potentials. The resulting eigenvalue problem for the velocity field expansion is readily solved by the integral transform method itself, while a traditional Sturm–Liouville base is chosen for expanding the temperature field. The coupled transformed initial value problem is numerically solved with a well-established solver based on a backward differentiation scheme. Findings A thorough convergence analysis is undertaken, in terms of truncation orders of the expansions for the vector eigenfunction and for the velocity and temperature fields. Finally, numerical results for selected quantities are critically compared to available benchmarks in both steady and transient states, and the overall physical behavior of the transient solution is examined for further verification. Originality/value A novel vector eigenfunction expansion is proposed for the integral transform solution of the Navier–Stokes equations in transient regime. The new physically inspired eigenvalue problem with the associated integmaral transformation fully shares the advantages of the previously obtained integral transform solutions based on the streamfunction-only formulation of the Navier–Stokes equations, while offering a direct and formal extension to three-dimensional flows.

APA, Harvard, Vancouver, ISO, and other styles

6

POZRIKIDIS, C. "Expansion of a compressible gas bubble in Stokes flow." Journal of Fluid Mechanics 442 (August 24, 2001): 171–89. http://dx.doi.org/10.1017/s0022112001004992.

Full text

Abstract:

The flow-induced deformation of an inviscid bubble occupied by a compressible gas and suspended in an ambient viscous liquid is considered at low Reynolds numbers with particular reference to the pressure developing inside the bubble. Ambient fluid motion alters the bubble pressure with respect to that established in the quiescent state, and requires the bubble to expand or contract according to an assumed equation of state. When changes in the bubble volume are prohibited by a global constraint on the total volume of the flow, the ambient pressure is modified while the bubble pressure remains constant during the deformation. A numerical method is developed for evaluating the pressure inside a two-dimensional bubble in an ambient Stokes flow on the basis of the normal component of the interfacial force balance involving the capillary pressure, the normal viscous stress, and the pressure at the free surface on the side of the liquid; the last is computed by evaluating a strongly singular integral. Dynamical simulations of bubble deformation are performed using the boundary integral method properly implemented to remove the multiplicity of solutions due to the a priori unknown rate of expansion, and three particular problems are discussed in detail: the shrinkage of a bubble at a specified rate, the deformation of a bubble subject to simple shear flow, and the deformation of a bubble subject to a purely elongational flow. In the case of shrinkage, it is found that the surface tension plays a critical role in determining the behaviour of the bubble pressure near the critical time when the bubble disappears. In the case of shear or elongational flow, it is found that the bubble contracts during an initial period of deformation from the circular shape, and then it expands to obtain a stationary shape whose area is higher than that assumed in the quiescent state. Expansion may destabilize the bubble by raising the capillary number above the critical threshold under which stationary shapes can be found.

APA, Harvard, Vancouver, ISO, and other styles

7

Hassine, Maatoug, and Mohamed Masmoudi. "The topological asymptotic expansion for the Quasi-Stokes problem." ESAIM: Control, Optimisation and Calculus of Variations 10, no. 4 (October 2004): 478–504. http://dx.doi.org/10.1051/cocv:2004016.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Ólafsdóttir, E. I., A. B. Olde Daalhuis, and J. Vanneste. "Stokes-multiplier expansion in an inhomogeneous differential equation with a small parameter." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2059 (June 15, 2005): 2243–56. http://dx.doi.org/10.1098/rspa.2005.1479.

Full text

Abstract:

Accurate approximations to the solutions of a second-order inhomogeneous equation with a small parameter ϵ are derived using exponential asymptotics. The subdominant homogeneous solutions that are switched on by an inhomogeneous solution through a Stokes phenomenon are computed. The computation relies on a resurgence relation, and it provides the ϵ -dependent Stokes multiplier in the form of a power series. The ϵ -dependence of the Stokes multiplier is related to constants of integration that can be chosen arbitrarily in the WKB-type construction of the homogeneous solution. The equation under study governs the evolution of special solutions of the Boussinesq equations for rapidly rotating, strongly stratified fluids. In this context, the switching on of subdominant homogeneous solutions is interpreted as the generation of exponentially small inertia–gravity waves.

APA, Harvard, Vancouver, ISO, and other styles

9

Khuri, Suheil A. "Biorthogonality condition for creeping motion in annular trenches." International Journal of Mathematics and Mathematical Sciences 24, no. 9 (2000): 613–16. http://dx.doi.org/10.1155/s0161171200004002.

Full text

Abstract:

The biorthogonality condition for Stokes flow in annular trenches bounded by horizontal parallel planes and concentric vertical cylinders is derived. This condition, is needed to compute the coefficients of the eigenfunction expansion solution of the corresponding Stokes flow problem.

APA, Harvard, Vancouver, ISO, and other styles

10

Antonov, Nikolay, Nikolay Gulitskiy, Maria Kostenko, and Tomáš Lučivjanský. "Passive Advection of a Vector Field by Compressible Turbulent Flow: Renormalizations Group Analysis near d = 4." Universe 5, no. 1 (January 18, 2019): 37. http://dx.doi.org/10.3390/universe5010037.

Full text

Abstract:

The renormalization group approach and the operator product expansion technique are applied to the model of a passively advected vector field by a turbulent velocity field. The latter is governed by the stochastic Navier-Stokes equation for a compressible fluid. The model is considered in the vicinity of space dimension d = 4 and the perturbation theory is constructed within a double expansion scheme in y and ε = 4 − d , where y describes scaling behaviour of the random force that enters the Navier-Stokes equation. The properties of the correlation functions are investigated, and anomalous scaling and multifractal behaviour are established. All calculations are performed in the leading order of y, ε expansion (one-loop approximation).

APA, Harvard, Vancouver, ISO, and other styles

11

Costin, Ovidiu, Guo Luo, and Saleh Tanveer. "Divergent expansion, Borel summability and three-dimensional Navier–Stokes equation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1876 (May 16, 2008): 2775–88. http://dx.doi.org/10.1098/rsta.2008.0052.

Full text

Abstract:

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, p 0 ] provides sharper control of its p →∞ behaviour. Preliminary numerical computations give encouraging results.

APA, Harvard, Vancouver, ISO, and other styles

12

Morosi, Carlo, and Livio Pizzocchero. "On the Reynolds number expansion for the Navier–Stokes equations." Nonlinear Analysis: Theory, Methods & Applications 95 (January 2014): 156–74. http://dx.doi.org/10.1016/j.na.2013.08.029.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Haupt, Sue Ellen, and John P. Boyd. "Modeling nonlinear resonance: A modification to the stokes' perturbation expansion." Wave Motion 10, no. 1 (January 1988): 83–98. http://dx.doi.org/10.1016/0165-2125(88)90008-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Choi, J. E., M. K. Sreedhar, and F. Stern. "Stokes Layers in Horizontal-Wave Outer Flows." Journal of Fluids Engineering 118, no. 3 (September 1, 1996): 537–45. http://dx.doi.org/10.1115/1.2817792.

Full text

Abstract:

Results are reported of a computational study investigating the responses of flat plate boundary layers and wakes to horizontal wave outer flows. Solutions are obtained for temporal, spatial, and traveling waves using Navier Stokes, boundary layer, and perturbation expansion equations. A wide range of parameters are considered for all the three waves. The results are presented in terms of Stokes-layer overshoots, phase leads (lags), and streaming. The response to the temporal wave showed all the previously reported features. The magnitude and nature of the response are small and simple such that it is essentially a small disturbance on the steady solution. Results are explainable in terms of one parameter ξ (the frequency of oscillation). For the spatial wave, the magnitude and the nature of the response are significantly increased and complex such that it cannot be considered simply a small disturbance on the without-wave solution. The results are explainable in terms of the two parameters λ−1 and x/λ (where λ is the wavelength). A clear asymmetry is observed in the wake response for the spatial wave. An examination of components of the perturbation expansion equations indicates that the asymmetry is a first-order effect due to nonlinear interaction between the steady and first-harmonic velocity components. For the traveling wave, the responses are more complex and an additional parameter, c (the wave speed), is required to explain the results. In general, for small wave speeds the results are similar to a spatial wave, whereas for higher wave speeds the response approaches the temporal wave response. The boundary layer and perturbation expansion solutions compares well with the Navier Stokes solution in their range of validity.

APA, Harvard, Vancouver, ISO, and other styles

15

BLANC, F., O. GIPOULOUX, G. PANASENKO, and A. M. ZINE. "ASYMPTOTIC ANALYSIS AND PARTIAL ASYMPTOTIC DECOMPOSITION OF DOMAIN FOR STOKES EQUATION IN TUBE STRUCTURE." Mathematical Models and Methods in Applied Sciences 09, no. 09 (December 1999): 1351–78. http://dx.doi.org/10.1142/s0218202599000609.

Full text

Abstract:

The Stokes problem posed in tube structures (or finite rod structures (see Panasenko10)), i.e. in connected finite unions of the thin cylinders with the ratio of the diameter to the height of the order [Formula: see text], is considered. The asymptotic expansion of the solution is built and justified. Boundary layers are studied. Earlier the Navier–Stokes problem in one thin domain was considered by Nazarov.8 The method of asymptotic partial decomposition of the domain (MAPDD) (see Panasenko11) is applied and justified for the Stokes problem posed in a tube structures. This method reduces the initial Stokes problem to the Stokes problem in some small parts of the domain (where the boundary layers are "concentrated".)

APA, Harvard, Vancouver, ISO, and other styles

16

Balajewicz, Maciej J., Earl H. Dowell, and Bernd R. Noack. "Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier–Stokes equation." Journal of Fluid Mechanics 729 (July 18, 2013): 285–308. http://dx.doi.org/10.1017/jfm.2013.278.

Full text

Abstract:

AbstractWe generalize the POD-based Galerkin method for post-transient flow data by incorporating Navier–Stokes equation constraints. In this method, the derived Galerkin expansion minimizes the residual like POD, but with the power balance equation for the resolved turbulent kinetic energy as an additional optimization constraint. Thus, the projection of the Navier–Stokes equation on to the expansion modes yields a Galerkin system that respects the power balance on the attractor. The resulting dynamical system requires no stabilizing eddy-viscosity term – contrary to other POD models of high-Reynolds-number flows. The proposed Galerkin method is illustrated with two test cases: two-dimensional flow inside a square lid-driven cavity and a two-dimensional mixing layer. Generalizations for more Navier–Stokes constraints, e.g. Reynolds equations, can be achieved in straightforward variation of the presented results.

APA, Harvard, Vancouver, ISO, and other styles

17

Cao, Dat, and Luan Hoang. "Long-time asymptotic expansions for Navier-Stokes equations with power-decaying forces." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 2 (January 22, 2019): 569–606. http://dx.doi.org/10.1017/prm.2018.154.

Full text

Abstract:

AbstractThe Navier-Stokes equations for viscous, incompressible fluids are studied in the three-dimensional periodic domains, with the body force having an asymptotic expansion, when time goes to infinity, in terms of power-decaying functions in a Sobolev-Gevrey space. Any Leray-Hopf weak solution is proved to have an asymptotic expansion of the same type in the same space, which is uniquely determined by the force, and independent of the individual solutions. In case the expansion is convergent, we show that the next asymptotic approximation for the solution must be an exponential decay. Furthermore, the convergence of the expansion and the range of its coefficients, as the force varies are investigated.

APA, Harvard, Vancouver, ISO, and other styles

18

Chapman, S. Jonathan, and David B. Mortimer. "Exponential asymptotics and Stokes lines in a partial differential equation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2060 (June 22, 2005): 2385–421. http://dx.doi.org/10.1098/rspa.2005.1475.

Full text

Abstract:

A singularly perturbed linear partial differential equation motivated by the geometrical model for crystal growth is considered. A steepest descent analysis of the Fourier transform solution identifies asymptotic contributions from saddle points, end points and poles, and the Stokes lines across which these may be switched on and off. These results are then derived directly from the equation by optimally truncating the naïve perturbation expansion and smoothing the Stokes discontinuities. The analysis reveals two new types of Stokes switching: a higher-order Stokes line which is a Stokes line in the approximation of the late terms of the asymptotic series, and which switches on or off Stokes lines themselves; and a second-generation Stokes line, in which a subdominant exponential switched on at a primary Stokes line is itself responsible for switching on another smaller exponential. The ‘new’ Stokes lines discussed by Berk et al . (Berk et al . 1982 J. Math. Phys. 23 , 988–1002) are second-generation Stokes lines, while the ‘vanishing’ Stokes lines discussed by Aoki et al . (Aoki et al . 1998 In Microlocal analysis and complex Fourier analysis (ed. K. F. T. Kawai), pp. 165–176) are switched off by a higher-order Stokes line.

APA, Harvard, Vancouver, ISO, and other styles

19

XU, KUN, and ZHAOLI GUO. "GENERALIZED GAS DYNAMIC EQUATIONS WITH MULTIPLE TRANSLATIONAL TEMPERATURES." Modern Physics Letters B 23, no. 03 (January 30, 2009): 237–40. http://dx.doi.org/10.1142/s0217984909018096.

Full text

Abstract:

Based on a multiple stage BGK-type collision model and the Chapman–Enskog expansion, the corresponding macroscopic gas dynamics equations in three-dimensional space will be derived. The new gas dynamic equations have the same structure as the Navier–Stokes equations, but the stress strain relationship in the Navier–Stokes equations is replaced by an algebraic equation with temperature differences. In the continuum flow regime, the new gas dynamic equations automatically recover the standard Navier–Stokes equations. The current gas dynamic equations are natural extension of the Navier–Stokes equations to the near continuum flow regime and can be used for near continuum flow study.

APA, Harvard, Vancouver, ISO, and other styles

20

Liu, Chi-Min. "Another Approach to the Extended Stokes’ Problems for the Oldroyd-B Fluid." ISRN Applied Mathematics 2012 (June 25, 2012): 1–12. http://dx.doi.org/10.5402/2012/274914.

Full text

Abstract:

The extended Stokes problems, which study the flow suddenly driven by relatively moving half-planes, are reexamined for the Oldroyd-B fluid. This topic has been studied (Liu, 2011) by applying the series expansion to calculate the inverse Laplace transform. The derived solution was correct but tough to perform the calculation due to the series expansion of infinite terms. Herein another approach, the contour integration, is applied to calculate the inversion. Moreover, the Heaviside unit step function is included into the boundary condition to ensure the consistence between boundary and initial conditions. Mathematical methods used herein can be applied to other fluids for the extended Stokes’ problems.

APA, Harvard, Vancouver, ISO, and other styles

21

Wang, C. Y. "Stokes Flow Through a Transversely Finned Channel." Journal of Fluids Engineering 119, no. 1 (March 1, 1997): 110–14. http://dx.doi.org/10.1115/1.2819095.

Full text

Abstract:

The efficient method of eigenfunction expansion and point match is used to solve the Stokes flow through a channel with transverse fins. Both in-phase and staggered fins are considered. Streamlines and resistances are found in terms of fin height and fin spacing. Extrapolating to large spacings, the added resistances due to a single pair of aligned fins and that of a single fin in a channel are obtained.

APA, Harvard, Vancouver, ISO, and other styles

22

Dassios, George, and Panayiotis Vafeas. "On the Spheroidal Semiseparation for Stokes Flow." Research Letters in Physics 2008 (February 13, 2008): 1–4. http://dx.doi.org/10.1155/2008/135289.

Full text

Abstract:

Many heat and mass transport problems involve particle-fluid systems, where the assumption of Stokes flow provides a very good approximation for representing small particles embedded within a viscous, incompressible fluid characterizing the steady, creeping flow. The present work is concerned with some interesting practical aspects of the theoretical analysis of Stokes flow in spheroidal domains. The stream function ψ, for axisymmetric Stokes flow, satisfies the well-known equation E4ψ=0. Despite the fact that in spherical coordinates this equation admits separable solutions, this property is not preserved when one seeks solutions in the spheroidal geometry. Nevertheless, defining some kind of semiseparability, the complete solution for ψ in spheroidal coordinates has been obtained in the form of products combining Gegenbauer functions of different degrees. Thus, the general solution is represented in a full-series expansion in terms of eigenfunctions, which are elements of the space kerE2 (separable solutions), and in terms of generalized eigenfunctions, which are elements of the space kerE4 (semiseparable solutions). In this work we revisit this aspect by introducing a different and simpler way of representing the aforementioned generalized eigenfunctions. Consequently, additional semiseparable solutions are provided in terms of the Gegenbauer functions, whereas the completeness is preserved and the full-series expansion is rewritten in terms of these functions.

APA, Harvard, Vancouver, ISO, and other styles

23

Šprlák, Michal. "Generalized geoidal estimators for deterministic modifications of spherical Stokes' function." Contributions to Geophysics and Geodesy 40, no. 1 (January 1, 2010): 45–64. http://dx.doi.org/10.2478/v10126-010-0003-7.

Full text

Abstract:

Generalized geoidal estimators for deterministic modifications of spherical Stokes' function Stokes' integral, representing a surface integral from the product of terrestrial gravity data and spherical Stokes' function, is the theoretical basis for the modelling of the local geoid. For the practical determination of the local geoid, due to restricted knowledge and availability of terrestrial gravity data, this has to be combined with the global gravity model. In addition, the maximum degree and order of spherical harmonic coefficients in the global gravity model is finite. Therefore, modifications of spherical Stokes' function are used to obtain faster convergence of the spherical harmonic expansion. Decomposition of Stokes' integral and modifications of Stokes' function have been studied by many geodesists. In this paper, the proposed deterministic modifications of spherical Stokes' function are generalized. Moreover, generalized geoidal estimators, when the Stokes' integral is decomposed in to spectral and frequency domains, are introduced. Higher derivatives of spherical Stokes' function and their numerical stability are discussed. Filtering and convergence properties for deterministic modifications of the spherical Stokes' function in the form of a remainder of the Taylor polynomial are studied as well.

APA, Harvard, Vancouver, ISO, and other styles

24

Pileckas, Konstantin, and Alicija Raciene. "Non-stationary Navier–Stokes equations in 2D power cusp domain." Advances in Nonlinear Analysis 10, no. 1 (January 1, 2021): 982–1010. http://dx.doi.org/10.1515/anona-2020-0164.

Full text

Abstract:

Abstract The initial boundary value problem for the non-stationary Navier-Stokes equations is studied in 2D bounded domain with a power cusp singular point O on the boundary. The case of the boundary value with a nonzero flow rate is considered. In this case there is a source/sink in O and the solution necessary has infinite energy integral. In the first part of the paper the formal asymptotic expansion of the solution near the singular point is constructed. The justification of the asymptotic expansion and the existence of a solution are proved in the second part of the paper.

APA, Harvard, Vancouver, ISO, and other styles

25

Hoang, Luan T., and Vincent R. Martinez. "Asymptotic expansion in Gevrey spaces for solutions of Navier–Stokes equations." Asymptotic Analysis 104, no. 3-4 (September 7, 2017): 167–90. http://dx.doi.org/10.3233/asy-171429.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Çamliyurt, Güher, and Igor Kukavica. "A local asymptotic expansion for a solution of the Stokes system." Evolution Equations and Control Theory 5, no. 4 (October 2016): 647–59. http://dx.doi.org/10.3934/eect.2016023.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Kweon, Jae Ryong. "A Singular Expansion of Solution for a Regularized Compressible Stokes System." Annales Henri Poincaré 5, no. 1 (February 2004): 169–88. http://dx.doi.org/10.1007/s00023-004-0164-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Mansour, Kamyar. "Using stokes expansion for natural convection inside a two-dimensional cavity." Fluid Dynamics Research 12, no. 1 (July 1993): 1–33. http://dx.doi.org/10.1016/0169-5983(93)90102-g.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Wu, Xiaonan, and Jicheng Jin. "A finite element method for Stokes equation using discrete singularity expansion." Computer Methods in Applied Mechanics and Engineering 194, no. 1 (January 2005): 83–101. http://dx.doi.org/10.1016/j.cma.2004.06.012.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Aubin, Christopher A., and Rolf J. Ryham. "Stokes flow for a shrinking pore." Journal of Fluid Mechanics 788 (December 23, 2015): 228–45. http://dx.doi.org/10.1017/jfm.2015.699.

Full text

Abstract:

We consider a sphere with a circular pore embedded in an unbounded viscous fluid, where the rim of the pore moves in such a way that the radius of the sphere is constant. Away from the pore, the surface area stretches or compresses uniformly. An exact form for the axisymmetric velocity field which describes the quasi-static motion of the bulk fluid is calculated. The resulting dissipation function yields an analytical value for the aqueous drag coefficient for the sphere with a shrinking pore. Additionally, we examine the small hole and small angle limits, which converge to the unsteady flow for the expansion of a hole in a plane wall, and for the contraction of a circular disk.

APA, Harvard, Vancouver, ISO, and other styles

31

Milos, Frank S., Andreas Acrivos, and John Kim. "Steady flow past sudden expansions at large Reynolds number. II. Navier–Stokes solutions for the cascade expansion." Physics of Fluids 30, no. 1 (1987): 7. http://dx.doi.org/10.1063/1.866062.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Chuvakhov, P. V., and I. V. Egorov. "Numerical Simulation of Disturbance Evolution in the Supersonic Boundary Layer over an Expansion Corner." Fluid Dynamics 56, no. 5 (September 2021): 645–56. http://dx.doi.org/10.1134/s0015462821050025.

Full text

Abstract:

Abstract— The linear and nonlinear stages of disturbance development in the supersonic boundary layer over a 10° expansion corner is investigated numerically within the framework of Navier—Stokes equations for Mach number 3. The effect of sudden flow expansion on the disturbance evolution is analyzed. The flow stabilization effect observable in the aerodynamic experiment is also discussed.

APA, Harvard, Vancouver, ISO, and other styles

33

Joshi, N., and C. J. Lustri. "Stokes phenomena in discrete Painlevé I." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2177 (May 2015): 20140874. http://dx.doi.org/10.1098/rspa.2014.0874.

Full text

Abstract:

In this study, we consider the asymptotic behaviour of the first discrete Painlevé equation in the limit as the independent variable becomes large. Using an asymptotic series expansion, we identify two types of solutions which are pole-free within some sector of the complex plane containing the positive real axis. Using exponential asymptotic techniques, we determine Stokes phenomena effects present within these solutions, and hence the regions in which the asymptotic series expression is valid. From a careful analysis of the switching behaviour across Stokes lines, we find that the first type of solution is uniquely defined, while the second type contains two free parameters, and that the region of validity may be extended for appropriate choice of these parameters.

APA, Harvard, Vancouver, ISO, and other styles

34

Khuri, S. A. "Biorthogonality condition for axisymmetric stokes flow in spherical geometries." International Journal of Mathematics and Mathematical Sciences 23, no. 10 (2000): 711–15. http://dx.doi.org/10.1155/s0161171200002891.

Full text

Abstract:

We derive the biorthogonality condition for axisymmetric Stokes flow in a region between two concentric spheres. This biorthogonality condition is a property satisfied by the eigenfunctions and adjoint eigenfunctions, which is needed to compute the coefficients of the eigenfunction expansion solution of the corresponding creeping flow problem.

APA, Harvard, Vancouver, ISO, and other styles

35

Pileckas, Konstantin, and Alicija Raciene. "Non-stationary Navier–Stokes equations in 2D power cusp domain." Advances in Nonlinear Analysis 10, no. 1 (January 1, 2021): 1011–38. http://dx.doi.org/10.1515/anona-2020-0165.

Full text

Abstract:

Abstract The initial boundary value problem for the non-stationary Navier-Stokes equations is studied in 2D bounded domain with a power cusp singular point O on the boundary. We consider the case where the boundary value has a nonzero flux over the boundary. In this case there is a source/sink in O and the solution necessary has infinite energy integral. In the first part of the paper the formal asymptotic expansion of the solution near the singular point was constructed. In this, second part, the constructed asymptotic decomposition is justified, i.e., existence of the solution which is represented as the sum of the constructed asymptotic expansion and a term with finite energy norm is proved. Moreover, it is proved that the solution represented in this form is unique.

APA, Harvard, Vancouver, ISO, and other styles

36

Wang, Yan, Zi-Chen Deng, and Wei-Peng Hu. "Symplectic Exact Solution for Stokes Flow in the Thin Film Coating Applications." Mathematical Problems in Engineering 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/151470.

Full text

Abstract:

The symplectic analytical method is introduced to solve the problem of the stokes flow in the thin film coating applications. Based on the variational principle, the Lagrangian function of the stokes flow is established. By using the Legendre transformation, the dual variables of velocities and the Hamiltonian function are derived. Considering velocities and stresses as the basic variables, the equations of stokes flow problems are transformed into Hamiltonian system. The method of separation of variables and expansion of eigenfunctions are developed to solve the governing equations in Hamiltonian system, and the analytical solutions of the stokes flow are obtained. Several numerical simulations are carried out to verify the analytical solutions in the present study and discuss the effects of the driven lids of the square cavity on the dynamic behavior of the flow structure.

APA, Harvard, Vancouver, ISO, and other styles

37

KING, J. R., and S. J. CHAPMAN. "Asymptotics beyond all orders and Stokes lines in nonlinear differential-difference equations." European Journal of Applied Mathematics 12, no. 4 (August 2001): 433–63. http://dx.doi.org/10.1017/s095679250100434x.

Full text

Abstract:

A technique for calculating exponentially small terms beyond all orders in singularly perturbed difference equations is presented. The approach is based on the application of a WKBJ-type ansatz to the late terms in the naive asymptotic expansion and the identification of Stokes lines, and is closely related to the well-known Stokes line smoothing phenomenon in linear ordinary differential equations. The method is illustrated by application to examples and the results extended to time-dependent differential-difference problems.

APA, Harvard, Vancouver, ISO, and other styles

38

Balser, W. "A Laurent-type expansion for solutions of Stokes' equation in sectorial regions." Analysis Mathematica 24, no. 1 (December 1998): 15–30. http://dx.doi.org/10.1007/bf02771071.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Shail, R. "On the asymptotic expansion of certain functions arising in multiphase Stokes flows." Quarterly Journal of Mechanics and Applied Mathematics 52, no. 3 (September 1, 1999): 419–40. http://dx.doi.org/10.1093/qjmam/52.3.419.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Kukavica, Igor, and Ednei Reis. "Asymptotic expansion for solutions of the Navier–Stokes equations with potential forces." Journal of Differential Equations 250, no. 1 (January 2011): 607–22. http://dx.doi.org/10.1016/j.jde.2010.08.016.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Ku, Hwar-Ching, and Dimitri Hatziavramidis. "Solutions of the two-dimensional Navier-Stokes equations by Chebyshev expansion methods." Computers & Fluids 13, no. 1 (January 1985): 99–113. http://dx.doi.org/10.1016/0045-7930(85)90035-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Truong, Nguyen Ngoc, and Tran Van Nhac. "Determination of the constant W_o for local geoid of Vietnam and it’s systematic deviation from the global geoid." Tạp chí Khoa học và Công nghệ biển 17, no. 4B (December 15, 2017): 138–44. http://dx.doi.org/10.15625/1859-3097/17/4b/13001.

Full text

Abstract:

Constant Wo, defining the geoid, has important applications in the area of physical geodesy. With the development of artificial Earth satellite, constant Wo for the global geoid approximating the oceans on Earth can be calculated from an expansion of spherical harmonics - Stokes constants determined by observation of perturbations in artificial satellite’s orbits. However, the Stokes constants are limited, therefore the geoid constant Wo could not be calculated for local geoid (state geoid) from the mentioned expansion of spherical harmonics. In this paper, we present a method to determine the constant Wo for local geoid of Vietnam, using generalized Bruns formula and Neyman boundary problem. The initial data used are Faye gravity anomalies surveyed on land and sea of Southern Vietnam. The constant Wo is then used to calculate the systematic deviation of the local geoid of Vietnam from the global geoid EGM - 96.

APA, Harvard, Vancouver, ISO, and other styles

43

Fischer, T. M., G. C. Hsiao, and W. L. Wendland. "On two-dimensional slow viscous flows past obstacles in a half-plane." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 104, no. 3-4 (1986): 205–15. http://dx.doi.org/10.1017/s0308210500019181.

Full text

Abstract:

SynopsisWe consider a cylinder with arbitrary cross section moving in a viscous incompressible fluid parallel to a plane wall. Formal asymptotic expansions of the solution for small Reynolds numbers are constructed by using boundary integral equations of the first kind. In contrast to the problem without a wall, we show that there exists a unique solution to the zeroth order problem. However, the problem considered here is still singular in the sense that we find the Stokes paradox in the next higher order problem. A justification of the formal asymptotic expansion for the first two terms is established rigorously.

APA, Harvard, Vancouver, ISO, and other styles

44

He, Shi Hua, Li Xiang Zhang, and Liang Cao. "End Effects of Symplectic Solution to Stokes Flow in a Rectangular Cavity." Applied Mechanics and Materials 166-169 (May 2012): 3258–64. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.3258.

Full text

Abstract:

The end effects of symplectic direct solution to Stokes flow in a rectangular cavity are considered. Based on establishing the dual equations for Stokes flow in Hamilton system, the non-zero eigenvalues and their eigensolutions for an anti-symmetric problem were obtained. Expanding the solutions of dual equations by non-zero eigensolutions and determining the expansion coefficients by the end boundary conditions, the decay tendency and interaction mechanism of end effects were discussed and the end boundary errors were investigated. The resultant velocity caused by tangentially driving lid is gradually decayed along the longitudinal direction of cavity. The more number of the expansion items are superposed, the more accurate the solutions are. The smaller the depth-to-width ratios are, the stronger the interference between the end velocities is. The error of ends moving in the same directions is bigger than that in opposite directions.

APA, Harvard, Vancouver, ISO, and other styles

45

Pierson, Willard J. "Oscillatory Third-Order Perturbation Solutions for Sums of Interacting Long-Crested Stokes Waves on Deep Water." Journal of Ship Research 37, no. 04 (December 1, 1993): 354–83. http://dx.doi.org/10.5957/jsr.1993.37.4.354.

Full text

Abstract:

Oscillatory third-order perturbation solutions for sums of interacting long-crested Stokes waves on deep water are obtained. A third-order perturbation expansion of the nonlinear free boundary value problem, defined by the coupled Bernoulli equation and kinematic boundary condition evaluated at the free surface, is solved by replacing the exponential term in the potential function by its series expansion and substituting the equation for the free surface into it. There are second-order changes in the frequencies of the first-order terms at third order. The waves have a Stokes-like form when they are high. The phase speeds are a function of the amplitudes and wave numbers of all of the first-order terms. The solutions are illustrated. A preliminary experiment at the United States Naval Academy is described. Some applications to sea keeping are bow submergence and slamming, capsizing in following seas and bending moments.

APA, Harvard, Vancouver, ISO, and other styles

46

Venturi, D., X. Wan, R. Mikulevicius, B. L. Rozovskii, and G. E. Karniadakis. "Wick–Malliavin approximation to nonlinear stochastic partial differential equations: analysis and simulations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2158 (October 8, 2013): 20130001. http://dx.doi.org/10.1098/rspa.2013.0001.

Full text

Abstract:

Approximating nonlinearities in stochastic partial differential equations (SPDEs) via the Wick product has often been used in quantum field theory and stochastic analysis. The main benefit is simplification of the equations but at the expense of introducing modelling errors. In this paper, we study the accuracy and computational efficiency of Wick-type approximations to SPDEs and demonstrate that the Wick propagator, i.e. the system of equations for the coefficients of the polynomial chaos expansion of the solution, has a sparse lower triangular structure that is seemingly universal, i.e. independent of the type of noise. We also introduce new higher-order stochastic approximations via Wick–Malliavin series expansions for Gaussian and uniformly distributed noises, and demonstrate convergence as the number of expansion terms increases. Our results are for diffusion, Burgers and Navier–Stokes equations, but the same approach can be readily adopted for other nonlinear SPDEs and more general noises.

APA, Harvard, Vancouver, ISO, and other styles

47

Nemes, Gergő. "Error bounds and exponential improvements for the asymptotic expansions of the gamma function and its reciprocal." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145, no. 3 (June 2015): 571–96. http://dx.doi.org/10.1017/s0308210513001558.

Full text

Abstract:

In 1994 Boyd derived a resurgence representation for the gamma function, exploiting the 1991 reformulation of the method of steepest descents by Berry and Howls. Using this representation, he was able to derive a number of properties of the asymptotic expansion for the gamma function, including explicit and realistic error bounds, the smooth transition of the Stokes discontinuities and asymptotics for the late coefficients. The main aim of this paper is to modify Boyd’s resurgence formula, making it suitable for deriving better error estimates for the asymptotic expansions of the gamma function and its reciprocal. We also prove the exponentially improved versions of these expansions complete with error terms. Finally, we provide new (formal) asymptotic expansions for the coefficients appearing in the asymptotic series and compare their numerical efficacy with the results of earlier authors.

APA, Harvard, Vancouver, ISO, and other styles

48

Ahlkrona, J., N. Kirchner, and P. Lötstedt. "Accuracy of the zeroth and second order shallow ice approximation – numerical and theoretical results." Geoscientific Model Development Discussions 6, no. 3 (August 7, 2013): 4281–325. http://dx.doi.org/10.5194/gmdd-6-4281-2013.

Full text

Abstract:

Abstract. In ice sheet modelling, the Shallow Ice Approximation (SIA) and Second Order Shallow Ice Approximation (SOSIA) schemes are approaches to approximate the solution of the full Stokes equations governing ice sheet dynamics. This is done by writing the solution to the full Stokes equations as an asymptotic expansion in the aspect ratio ε, i.e. the quotient between a characteristic height and a characteristic length of the ice sheet. SIA retains the zeroth order terms and SOSIA the zeroth, first, and second order terms in the expansion. Here, we evaluate the order of accuracy of SIA and SOSIA by numerically solving a two dimensional model problem for different values of ε, and comparing the solutions with a finite element solution of the full Stokes equations obtained from Elmer/Ice. The SIA and SOSIA solutions are also derived analytically for the model problem. For decreasing ε, the computed errors in SIA and SOSIA decrease, but not always in the expected way. Moreover, they depend critically on a parameter introduced to avoid singularities in Glen's flow law in the ice model. This is because the assumptions behind the SIA and SOSIA neglect a thick, high viscosity boundary layer near the ice surface. The sensitivity to the parameter is explained by the analytical solutions.

APA, Harvard, Vancouver, ISO, and other styles

49

Paris, R. B. "The Stokes phenomenon associated with the Hurwitz zeta function ζ( s , a )." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2053 (January 8, 2005): 297–304. http://dx.doi.org/10.1098/rspa.2004.1395.

Full text

Abstract:

We examine the exponentially improved asymptotic expansion of the Hurwitz zeta function ζ ( s , a ) for large complex values of a , with s regarded as a parameter. It is shown that an infinite number of subdominant exponential terms switch on across the Stokes lines arg a = ± ½ π .

APA, Harvard, Vancouver, ISO, and other styles

50

Panasenko, Grigori P. "Asymptotic expansion of the solution of Navier-Stokes equation in a tube structure." Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy 326, no. 12 (January 1998): 867–72. http://dx.doi.org/10.1016/s1251-8069(99)80041-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Journal articles on the topic 'Stokes expansion'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles