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Journal articles on the topic 'Oscillating boundary domains'

Author: Grafiati

Published: 6 September 2023

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1

Amirat, Youcef, Olivier Bodart, Gregory A. Chechkin, and Andrey L. Piatnitski. "Boundary homogenization in domains with randomly oscillating boundary." Stochastic Processes and their Applications 121, no. 1 (January 2011): 1–23. http://dx.doi.org/10.1016/j.spa.2010.08.011.

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2

Amirat, Youcef, Gregory A. Chechkin, and Rustem R. Gadyl’shin. "Spectral boundary homogenization in domains with oscillating boundaries." Nonlinear Analysis: Real World Applications 11, no. 6 (December 2010): 4492–99. http://dx.doi.org/10.1016/j.nonrwa.2008.11.023.

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3

Chechkin, Gregory A., Avner Friedman, and Andrey L. Piatnitski. "The Boundary-value Problem in Domains with Very Rapidly Oscillating Boundary." Journal of Mathematical Analysis and Applications 231, no. 1 (March 1999): 213–34. http://dx.doi.org/10.1006/jmaa.1998.6226.

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4

Aiyappan, S., A. K. Nandakumaran, and Ravi Prakash. "Semi-linear optimal control problem on a smooth oscillating domain." Communications in Contemporary Mathematics 22, no. 04 (April 1, 2019): 1950029. http://dx.doi.org/10.1142/s0219199719500299.

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We demonstrate the asymptotic analysis of a semi-linear optimal control problem posed on a smooth oscillating boundary domain in the present paper. We have considered a more general oscillating domain than the usual “pillar-type” domains. Consideration of such general domains will be useful in more realistic applications like circular domain with rugose boundary. We study the asymptotic behavior of the problem under consideration using a new generalized periodic unfolding operator. Further, we are studying the homogenization of a non-linear optimal control problem and such non-linear problems are limited in the literature despite the fact that they have enormous real-life applications. Among several other technical difficulties, the absence of a sufficient criteria for the optimal control is one of the most attention-grabbing issues in the current setting. We also obtain corrector results in this paper.

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5

Eger, V., O. A. Oleinik, and T. A. Shaposhnikova. "Homogenization of boundary value problems in domains with rapidly oscillating nonperiodic boundary." Differential Equations 36, no. 6 (June 2000): 833–46. http://dx.doi.org/10.1007/bf02754407.

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6

Feldman, William M. "Homogenization of the oscillating Dirichlet boundary condition in general domains." Journal de Mathématiques Pures et Appliquées 101, no. 5 (May 2014): 599–622. http://dx.doi.org/10.1016/j.matpur.2013.07.003.

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7

OULD-HAMMOUDA, AMAR, and RACHAD ZAKI. "Homogenization of a class of elliptic problems with nonlinear boundary conditions in domains with small holes." Carpathian Journal of Mathematics 31, no. 1 (2015): 77–88. http://dx.doi.org/10.37193/cjm.2015.01.09.

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We consider a class of second order elliptic problems in a domain of RN , N > 2, ε-periodically perforated by holes of size r(ε) , with r(ε)/ε → 0 as ε → 0. A nonlinear Robin-type condition is prescribed on the boundary of some holes while on the boundary of the others as well as on the external boundary of the domain, a Dirichlet condition is imposed. We are interested in the asymptotic behavior of the solutions as ε → 0. We use the periodic unfolding method introduced in [Cioranescu, D., Damlamian, A. and Griso, G., Periodic unfolding and homogenization, C. R. Acad. Sci. Paris, Ser. I, 335 (2002), 99–104]. The method allows us to consider second order operators with highly oscillating coefficients and so, to generalize the results of [Cioranescu, D., Donato, P. and Zaki, R., Asymptotic behavior of elliptic problems in perforated domains with nonlinear boundary conditions, Asymptot. Anal., Vol. 53 (2007), No. 4, 209–235].

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8

Pettersson, Irina. "Two-scale convergence in thin domains with locally periodic rapidly oscillating boundary." Differential Equations & Applications, no. 3 (2017): 393–412. http://dx.doi.org/10.7153/dea-2017-09-28.

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9

Zhuge, Jinping. "First-order expansions for eigenvalues and eigenfunctions in periodic homogenization." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 5 (March 20, 2019): 2189–215. http://dx.doi.org/10.1017/prm.2019.8.

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AbstractFor a family of elliptic operators with periodically oscillating coefficients, $-{\rm div}(A(\cdot /\varepsilon )\nabla )$ with tiny ε > 0, we comprehensively study the first-order expansions of eigenvalues and eigenfunctions (eigenspaces) for both the Dirichlet and Neumann problems in bounded, smooth and strictly convex domains (or more general domains of finite type). A new first-order correction term is introduced to derive the expansion of eigenfunctions in L2 or $H^1_{\rm loc}$. Our results rely on the recent progress on the homogenization of boundary layer problems.

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10

Piatnitski, A., and V. Rybalko. "Homogenization of boundary value problems for monotone operators in perforated domains with rapidly oscillating boundary conditions of fourier type." Journal of Mathematical Sciences 177, no. 1 (July 27, 2011): 109–40. http://dx.doi.org/10.1007/s10958-011-0450-3.

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11

Durante, Tiziana, Luisa Faella, and Carmen Perugia. "Homogenization and behaviour of optimal controls for the wave equation in domains with oscillating boundary." Nonlinear Differential Equations and Applications NoDEA 14, no. 5-6 (December 2007): 455–89. http://dx.doi.org/10.1007/s00030-007-3043-6.

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12

Guckenberger, Achim, and Stephan Gekle. "A boundary integral method with volume-changing objects for ultrasound-triggered margination of microbubbles." Journal of Fluid Mechanics 836 (December 19, 2017): 952–97. http://dx.doi.org/10.1017/jfm.2017.836.

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A variety of numerical methods exist for the study of deformable particles in dense suspensions. None of the standard tools, however, currently include volume-changing objects such as oscillating microbubbles in three-dimensional periodic domains. In the first part of this work, we develop a novel method to include such entities based on the boundary integral method. We show that the well-known boundary integral equation must be amended with two additional terms containing the volume flux through the bubble surface. We rigorously prove the existence and uniqueness of the solution. Our proof contains as a subset the simpler boundary integral equation without volume-changing objects (such as red blood cell or capsule suspensions) which is widely used but for which a formal proof in periodic domains has not been published to date. In the second part, we apply our method to study microbubbles for targeted drug delivery. The ideal drug delivery agent should stay away from the biochemically active vessel walls during circulation. However, upon reaching its target it should attain a near-wall position for efficient drug uptake. Though seemingly contradictory, we show that lipid-coated microbubbles in conjunction with a localized ultrasound pulse possess precisely these two properties. This ultrasound-triggered margination is due to hydrodynamic interactions between the red blood cells and the oscillating lipid-coated microbubbles which alternate between a soft and a stiff state. We find that the effect is very robust, existing even if the duration in the stiff state is more than three times lower than the opposing time in the soft state.

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13

Trefry, M. G., D. McLaughlin, G. Metcalfe, D. Lester, A. Ord, K. Regenauer-Lieb, and B. E. Hobbs. "On oscillating flows in randomly heterogeneous porous media." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1910 (January 13, 2010): 197–216. http://dx.doi.org/10.1098/rsta.2009.0186.

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The emergence of structure in reactive geofluid systems is of current interest. In geofluid systems, the fluids are supported by a porous medium whose physical and chemical properties may vary in space and time, sometimes sharply, and which may also evolve in reaction with the local fluids. Geofluids may also experience pressure and temperature conditions within the porous medium that drive their momentum relations beyond the normal Darcy regime. Furthermore, natural geofluid systems may experience forcings that are periodic in nature, or at least episodic. The combination of transient forcing, near-critical fluid dynamics and heterogeneous porous media yields a rich array of emergent geofluid phenomena that are only now beginning to be understood. One of the barriers to forward analysis in these geofluid systems is the problem of data scarcity. It is most often the case that fluid properties are reasonably well known, but that data on porous medium properties are measured with much less precision and spatial density. It is common to seek to perform an estimation of the porous medium properties by an inverse approach, that is, by expressing porous medium properties in terms of observed fluid characteristics. In this paper, we move toward such an inversion for the case of a generalized geofluid momentum equation in the context of time-periodic boundary conditions. We show that the generalized momentum equation results in frequency-domain responses that are governed by a second-order equation which is amenable to numerical solution. A stochastic perturbation approach demonstrates that frequency-domain responses of the fluids migrating in heterogeneous domains have spatial spectral densities that can be expressed in terms of the spectral densities of porous media properties.

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14

Durante, Danilo, and Riccardo Broglia. "A Residual Theorem Approach Applied to Stokes’ Problems with Generally Periodic Boundary Conditions including a Pressure Gradient Term." Mathematical Problems in Engineering 2018 (August 28, 2018): 1–16. http://dx.doi.org/10.1155/2018/1267689.

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The differential problem given by a parabolic equation describing the purely viscous flow generated by a constant or an oscillating motion of a boundary is the well-known Stokes’ problem. The one-dimensional equation is generally solved for unbounded or bounded domains; for the latter, either free slip (i.e., zero normal gradient) or no-slip (i.e., zero velocity) conditions are enforced on one boundary. Generally, the analytical strategy to solve these problems is based on finding the solutions of the Laplace-transformed (in time) equation and on inverting these solutions. In the present paper this problem is solved by making use of the residuals theorem; as it will be shown, this strategy allows achieving the solutions of First and Second Stokes’ problems in both infinite and finite depth. The extension to generally periodic boundaries with the presence of a periodic pressure gradient is also presented. This approach allows getting closed form solutions in the time domain in a rather fast and simple way. An ad hoc numerical algorithm, based on a finite difference approximation of the differential equation, has been developed to check the correctness of the analytical solutions.

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15

ter Heege, J. H., J. H. P. de Bresser, and C. J. Spiers. "Dynamic Recrystallization of Dense Polycrystalline NaCl: Dependence of Grain Size Distribution on Stress and Temperature." Materials Science Forum 467-470 (October 2004): 1187–92. http://dx.doi.org/10.4028/www.scientific.net/msf.467-470.1187.

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Only few models explain the development of a steady state grain size during dynamic recrystallization, and their microphysical basis is poorly understood. In this study, we investigate mechanical and microstructural data on dry and wet NaCl, deformed at a range of stresses and temperatures at elevated pressure, with the aim to evaluate the different models. The results show that dry NaCl continuously work hardens and shows evidence for recrystallization dominated by progressive subgrain rotation, while the wet material shows, at similar conditions, oscillating stressstrain behaviour and recrystallization dominated by grain boundary migration. Taking into account the distribution of grain size, deformation of wet NaCl is best described by flow laws based on composite grain size sensitive (GSS) solution-precipitation creep and grain size insensitive (GSI) dislocation creep. The recrystallized grain size data in wet NaCl can be modeled with the hypothesis that recrystallized grain size organises itself in the boundary between the GSS and GSS creep domains.

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16

Pinto Jr, E. A., M. Das N. Gomes, L. A. O. Rocha, E. D. dos Santos, and L. A. Isoldi. "EVALUATION OF STATIC PRESSURE BEHAVIOR IN AN OSCILLATING WATER COLUMN WAVE ENERGY CONVERTER." Revista de Engenharia Térmica 18, no. 1 (June 3, 2019): 36. http://dx.doi.org/10.5380/reterm.v18i1.67045.

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The international scenario of non-renewable resources scarcity coupled with increasing energy demand are incentives for the diversification of the world's energy matrix with a focus on renewable energy sources. Among these sources, energy from sea waves is especially attractive because its global resource is estimated around 2 TW, comparable to the average electrical power consumed worldwide each year. There are currently several technologies proposed for the sea wave energy conversion into electricity. Among them it stands out the Oscillating Water Column (OWC) converter, which basically consists of a hydropneumatic chamber and a turbine duct where a turbine is installed. Its chamber is opened below the sea water free surface while the turbine duct outlet is free to atmosphere. Inside the chamber the water free surface oscillating movement produced by the incident waves causes the air to flow through the turbine duct and to activate the turbine, so the OWC principle of operating can be approximated to a cylinder-piston system. Therefore, one of the methodologies used in the computational modeling to simulate the operating principle of this device is the Piston Methodology, which simplifies the problem analysis considering only the air flow through the OWC converter. Among the phenomena that occur within the OWC device, the static pressure behavior is arguably one of the most important because it is through it that it is possible to estimate the hydropneumatic power and the converter efficiency. Thus, the objective of this work is to evaluate the static pressure behavior within the OWC, using the Piston Methodology, by imposing a monochromatic wave boundary condition in an axisymmetric domain. Among the obtained results it was inferred that the static pressure, in this case, depends directly on the flow acceleration and it is strongly influenced by the vorticity generated in domains with a change of area.

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17

CHAPMAN, C. J. "Energy paths in edge waves." Journal of Fluid Mechanics 426 (January 10, 2001): 135–54. http://dx.doi.org/10.1017/s0022112000002184.

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In this paper the energy streamlines, energy paths, and energy streak lines in a steady or unsteady inhomogeneous acoustic field next to an unstable oscillating boundary, such as a vortex sheet or shear layer, are determined. The theory in the paper applies also to an evanescent wave produced by total internal reflection, and to any other type of edge wave, e.g. a coastally or topographically trapped wave in geophysical fluid dynamics. The idea of the paper is that energy velocity, i.e. energy flux divided by energy density, is defined at every point in space and time, not merely when averaged over a cycle. Integration of the ordinary differential equation for energy velocity as a function of position and time gives the energy paths. These paths are calculated explicitly, and are found to have starting and finishing directions very different from those of cycle-averaged paths. The paper discusses the physical significance of averaged and non-averaged energy paths, especially in relation to causality. Many energy paths have cusps, at which the energy velocity is instantaneously zero. The domain of influence of an arbitrary point on the boundary of a steady acoustic edge wave is shown to lie within 45° of a certain direction, in agreement with a known result on shear-layer instability in compressible flow. The results are consistent with flow visualization photographs of near-field jet noise. The method of the paper determines domains of influence and causality in any wave problem with an explicit solution, for example as represented by a Fourier integral.

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18

Li, Zele, Decheng Feng, Mohammad Noori, Dipanjan Basu, and Wael A. Altabey. "Dynamic response analysis of Euler–Bernoulli beam on spatially random transversely isotropic viscoelastic soil." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 236, no. 5 (January 6, 2022): 1037–52. http://dx.doi.org/10.1177/14644207211067442.

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A novel dynamic soil-structure interaction model is developed for analysis for Euler–Bernoulli beam rests on a spatially random transversely isotropic viscoelastic foundation subjected to moving and oscillating loads. The dynamic equilibrium equation of beam-soil system is established using the extended Hamilton's principle, and the corresponding partial differential equations describing the displacement of beam and soil and boundary conditions are further obtained by the variational principles. These partial differential equations are discretized in spatial and time domains and solved by the finite difference (FD) method. After the differential equations of beam and soil are discretized in the spatial domain, the implicit iterative scheme is used to solve the equations in the time domain. The solving result shows the FD method is effective and convenient for solving the differential equations of beam-soil system. The spring foundation model adopted the modified Vlasov model, which is a two-parameter model considering the compression and shear of soil. The advantage of the present foundation model is avoided estimating input parameters of the modified Vlasov model using prior knowledge. The present solution is verified by publishing solution and equivalent three-dimensional FE analysis. The present model produced an accurate, faster, and effective displacement response. A few examples are carried out to analyze the parameter variation influence for beam on spatially random transversely isotropic viscoelastic soil under moving loads.

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19

Cessi, Paola, and Pantxika Otheguy. "Oceanic Teleconnections: Remote Response to Decadal Wind Forcing." Journal of Physical Oceanography 33, no. 8 (August 1, 2003): 1604–17. http://dx.doi.org/10.1175/2400.1.

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Abstract The transhemispheric and interbasin response to time-dependent wind forcing localized in the Northern Hemisphere of a single basin is examined using the reduced-gravity shallow-water equations in domains of simple geometry. On decadal timescales, the pressure on the eastern boundary fluctuates synchronously in both hemispheres and thus communicates a signal to latitudes distant from the forcing. The signal then penetrates into the interior through westward radiation of Rossby waves. Associated with the eastern boundary pressure fluctuation is a time-dependent mass flux across the equator that, in a single basin, is balanced by a storage of mass in the unforced hemisphere. Two oceanic basins connected by a reentrant channel at the high-latitude edge of the Southern Hemisphere are then considered. Again the forcing is confined to the Northern Hemisphere of one basin only. In this geometry the time-dependent mass flux across the equator of the forced basin is not entirely balanced within the same basin, but induces a mass flux into the unforced basin, while the mass heaving within the periodic channel is negligible. This process is illustrated by considering winds oscillating at a period on the same order as the Rossby wave transit time in high latitudes. The interhemispheric and interbasin teleconnection is achieved by a combination of long Rossby waves and large-scale, low-frequency gravity waves forced by the Rossby signal. These disturbances share no characteristics of Kelvin waves; that is, they are not boundary trapped.

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20

Zhao, Jie, and Juan Wang. "Homogenization Problem in a Domain with Double Oscillating Boundary." Mathematical Problems in Engineering 2018 (October 21, 2018): 1–14. http://dx.doi.org/10.1155/2018/3746562.

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In this paper, we study the convergence of solutions for homogenization problems about the Poisson equation in a domain with double oscillating locally periodic boundary. Such a problem arises in the processing of devices with very small features. We utilize second-order Taylor expansion of boundary data in combination with boundary correctors to obtain the convergence rate in H1-norm. This work explores the domain with double oscillating boundary and also shows the influence of the amplitudes and periods of the oscillations to convergence rates of solutions.

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21

Natroshvili, David, Guram Sadunishvili, and Irine Sigua. "Some Remarks Concerning Jones Eigenfrequencies and Jones Modes." gmj 12, no. 2 (June 2005): 337–48. http://dx.doi.org/10.1515/gmj.2005.337.

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Abstract Three-dimensional fluid-solid interaction problems with regard for thermal stresses are considered. An elastic structure is assumed to be a bounded homogeneous isotropic body occupying a domain , where the thermoelastic four dimensional field is defined, while in the unbounded exterior domain there is defined the scalar (acoustic pressure) field. These two fields satisfy the differential equations of steady state oscillations in the corresponding domains along with the transmission conditions of special type on the interface ∂Ω±. We show that uniqueness of solutions strongly depends on the geometry of the boundary ∂Ω±. In particular, we prove that for the corresponding homogeneous transmission problem for a ball there exist infinitely many exceptional values of the oscillation parameter (Jones eigenfrequencies). The corresponding eigenvectors (Jones modes) are written explicitly. On the other hand, we show that if the boundary surface ∂Ω± contains two flat, non-parallel sub-manifolds then there are no Jones eigenfrequencies for such domains.

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22

Kupershtokh, A. L., E. V. Ermanyuk, and N. V. Gavrilov. "The Rupture of Thin Liquid Films Placed on Solid and Liquid Substrates in Gravity Body Forces." Communications in Computational Physics 17, no. 5 (May 2015): 1301–19. http://dx.doi.org/10.4208/cicp.2014.m340.

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AbstractThis paper presents a numerical and experimental study on hydrodynamic behavior of thin liquid films in rectangular domains. Three-dimensional computer simulations were performed using the lattice Boltzmann equation method (LBM). The liquid films laying on solid and liquid substrates are considered. The rupture of liquid films in computations is initiated via the thermocapillary (Marangoni) effect by applying an initial spatially localized temperature perturbation. The rupture scenario is found to depend on the shape of the temperature distribution and on the wettability of the solid substrate. For a wettable solid substrate, complete rupture does not occur: a residual thin liquid film remains at the substrate in the region of pseudo-rupture. For a non-wettable solid substrate, a sharp-peaked axisymmetric temperature distribution induces the rupture at the center of symmetry where the temperature is maximal. Axisymmetric temperature distribution with a flat-peaked temperature profile initiates rupture of the liquid film along a circle at some distance from the center of symmetry. The outer boundary of the rupture expands, while the inner liquid disk transforms into a toroidal figure and ultimately into an oscillating droplet.We also apply the LBM to simulations of an evolution of one or two holes in liquid films for two-layer systems of immiscible fluids in a rectangular cell. The computed patterns are successfully compared against the results of experimental visualizations. Both the experiments and the simulations demonstrate that the initially circular holes evolved in the rectangular cell undergoing drastic changes of their shape under the effects of the surface tension and gravity. In the case of two interacting holes, the disruption of the liquid bridge separating two holes is experimentally observed and numerically simulated.

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23

Ruan, Xiaozhou, and Andrew F. Thompson. "Bottom Boundary Potential Vorticity Injection from an Oscillating Flow: A PV Pump." Journal of Physical Oceanography 46, no. 11 (November 2016): 3509–26. http://dx.doi.org/10.1175/jpo-d-15-0222.1.

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AbstractOceanic boundary currents over the continental slope exhibit variability with a range of time scales. Numerical studies of steady, along-slope currents over a sloping bathymetry have shown that cross-slope Ekman transport can advect buoyancy surfaces in a bottom boundary layer (BBL) so as to produce vertically sheared geostrophic flows that bring the total flow to rest: a process known as buoyancy shutdown of Ekman transport or Ekman arrest. This study considers the generation and evolution of near-bottom flows due to a barotropic, oscillating, and laterally sheared flow over a slope. The sensitivity of the boundary circulation to changes in oscillation frequency ω, background flow amplitude, bottom slope, and background stratification is explored. When ω/f ≪ 1, where f is the Coriolis frequency, oscillations allow the system to escape from the steady buoyancy shutdown scenario. The BBL is responsible for generating a secondary overturning circulation that produces vertical velocities that, combined with the potential vorticity (PV) anomalies of the imposed barotropic flow, give rise to a time-mean, rectified, vertical eddy PV flux into the ocean interior: a “PV pump.” In these idealized simulations, the PV anomalies in the BBL make a secondary contribution to the time-averaged PV flux. Numerical results show the domain-averaged eddy PV flux increases nonlinearly with ω with a peak near the inertial frequency, followed by a sharp decay for ω/f > 1. Different physical mechanisms are discussed that could give rise to the temporal variability of boundary currents.

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24

Fyrillas, Marios M., and Andrew J. Szeri. "Dissolution or growth of soluble spherical oscillating bubbles." Journal of Fluid Mechanics 277 (October 25, 1994): 381–407. http://dx.doi.org/10.1017/s0022112094002806.

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A new theoretical formulation is presented for mass transport across the dynamic interface associated with a spherical bubble undergoing volume oscillations. As a consequence of the changing internal pressure of the bubble that accompanies volume oscillations, the concentration of the dissolved gas in the liquid at the interface undergoes large-amplitude oscillations. The convection-diffusion equations governing transport of dissolved gas in the liquid are written in Lagrangian coordinates to account for the moving domain. The Henry's law boundary condition is split into a constant and an oscillating part, yielding the smooth and the oscillatory problems respectively. The solution of the oscillatory problem is valid everywhere in the liquid but differs from zero only in a thin layer of the liquid in the neighbourhood of the bubble surface. The solution to the smooth problem is also valid everywhere in the liquid; it evolves via convection-enhanced diffusion on a slow timescale controlled by the Péclet number, assumed to be large. Both the oscillatory and smooth problems are treated by singular perturbation methods: the oscillatory problem by boundary-layer analysis, and the smooth problem by the method of multiple scales in time. Using this new formulation, expressions are developed for the concentration field outside a bubble undergoing arbitrary nonlinear periodic volume oscillations. In addition, the rate of growth or dissolution of the bubble is determined and compared with available experimental results. Finally, a new technique is described for computing periodically driven nonlinear bubble oscillations that depend on one or more physical parameters. This work extends a large body of previous work on rectified diffusion that has been restricted to the assumptions of infinitesimal bubble oscillations or of threshold conditions, or both. The new formulation represents the first self-consistent, analytical treatment of the depletion layer that accompanies nonlinear oscillating bubbles that grow via rectified diffusion.

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25

Ly, E., and J. Nakamichi. "Time-linearised transonic computations including entropy, vorticity and shock wave motion effects." Aeronautical Journal 107, no. 1077 (November 2003): 687–95. http://dx.doi.org/10.1017/s0001924000013555.

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Abstract The effect of small perturbations on steady nonlinear transonic small disturbance flowfields, in the context of two-dimensional flows governed by the general-frequency transonic small disturbance equation with nonreflecting far-field boundary conditions, is investigated. This paper presents a time-linearised time-domain solution method that includes effects due to the shock-generated entropy and vorticity and shock wave motions. The solution procedure correctly accounts for the small-amplitude shock wave motion due to small unsteady changes in the aerofoil boundary conditions, and correctly models a flowfield with embedded strong shock waves. Steady and first harmonic pressure distributions for the NACA 0003 aerofoil with a harmonically oscillating flap, and NACA 0012 aerofoil undergoing a sinusoidal pitching oscillation, are predicted and compared with the Euler results.

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26

Mozolyako, P. "Boundary oscillations of harmonic functions in Lipschitz domains." Collectanea Mathematica 68, no. 3 (July 1, 2016): 359–76. http://dx.doi.org/10.1007/s13348-016-0177-z.

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27

D’ Alessio, Gorizia, Arianna Pucci, Giulia Guida, and Francesca Casini. "Numerical study on the effects of groundwater table oscillation beneath the “Palazzaccio” courthouse in Rome." E3S Web of Conferences 382 (2023): 17006. http://dx.doi.org/10.1051/e3sconf/202338217006.

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This work aims to evaluate the settlement induced by the river Tiber groundwater table oscillations. A representative section of the subsoil beneath the courthouse “Palazzaccio”, close to the river in the city centre of Rome, is analysed via the finite element method with a fully coupled hydro-mechanicalmodel. The effects of wetting-drying cycles induced by the water table oscillation are accounted for by adopting the Barcelona Basic Model for the unsaturated layers, whose model parameters are calibrated using experimental results on saturated and unsaturated samples and literature data. The variation of the river Tiber level is reconstructed according to the “Tevere – Ripetta” hydrometric station records between 2005 and 2008, and it is applied as a boundary condition at the boundary of the model domain.

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28

BLANCHARD, DOMINIQUE, ANTONIO GAUDIELLO, and JACQUELINE MOSSINO. "HIGHLY OSCILLATING BOUNDARIES AND REDUCTION OF DIMENSION: THE CRITICAL CASE." Analysis and Applications 05, no. 02 (April 2007): 137–63. http://dx.doi.org/10.1142/s0219530507000924.

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In [4], the first two authors studied a nonlinear monotone problem in a multidomain composed of a part [Formula: see text], with a highly oscillating boundary, placed upon an asymptotically flat part of thickness hε. More precisely, [Formula: see text] is a "forest" of cylinders with fixed height and small cross section of size ε, distributed with ε-periodicity upon the flat domain. The analysis was achieved under the assumption εp/hε → 0 (p - 1 is the growth order of the operator at infinity), as ε tends to 0, and for rescaled external forces hε fε converging to 0 in the (rescaled) flat domain. In the present paper, we present the analysis under the assumption εp/hε → l, with l ∈ [0, +∞], and for general limit forces in the flat domain. When l ∈ ]0, +∞[, we show that a discontinuity in the Dirichlet transmission condition may occur between the limit domain filled by the oscillating boundary and the plate. This discontinuity is derived through solving a nonlinear problem (in general for a different monotone operator) in the unit cell of the oscillating boundary. When l = +∞, we show that a deterministic limit model may hardly be expected.

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29

Zhang, Yang, and Chunhua Zhou. "Reduction of Numerical Oscillations in Simulating Moving-Boundary Problems by the Local DFD Method." Advances in Applied Mathematics and Mechanics 8, no. 1 (December 21, 2015): 145–65. http://dx.doi.org/10.4208/aamm.2014.m590.

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AbstractIn this work, the hybrid solution reconstruction formulation proposed by Luo et al. [H. Luo, H. Dai, P. F. de Sousa and B. Yin, On the numerical oscillation of the direct-forcing immersed-boundary method for moving boundaries, Computers & Fluids, 56 (2012), pp. 61–76] for the finite-difference discretization on Cartesian meshes is implemented in the finite-element framework of the local domain-free discretization (DFD) method to reduce the numerical oscillations in the simulation of moving-boundary flows. The reconstruction formulation is applied at fluid nodes in the immediate vicinity of the immersed boundary, which combines weightly the local DFD solution with the specific values obtained via an approximation of quadratic polynomial in the normal direction to the wall. The quadratic approximation is associated with the no-slip boundary condition and the local simplified momentum equation. The weighted factor suitable for unstructured triangular and tetrahedral meshes is constructed, which is related to the local mesh intervals near the immersed boundary and the distances from exterior dependent nodes to the boundary. Therefore, the reconstructed solution can account for the smooth movement of the immersed boundary. Several numerical experiments have been conducted for two- and three-dimensional moving-boundary flows. It is shown that the hybrid reconstruction approach can work well in the finite-element context and effectively reduce the numerical oscillations with little additional computational cost, and the spatial accuracy of the original local DFD method can also be preserved.

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30

Podolskiy, A. V., and T. A. Shaposhnikova. "Homogenization of the boundary value problem for the poisson equation with rapidly oscillating nonlinear boundary conditions: space dimension n ≥ 3, critical case." Доклады Академии наук 485, no. 3 (May 21, 2019): 263–68. http://dx.doi.org/10.31857/s0869-56524853263-268.

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The homogenization of the Poisson equation in a bounded domain with rapidly oscillating boundary conditions specied on a part of the domain boundary is studied. A Neumann boundary condition alternates with an ε-periodically distributed nonlinear Robin condition involving the coefficient ε-β, where β ∈ R. The diameter of the boundary portions with a nonlinear Robin condition is of order O(εα), α > 1. A critical relation between the parameters α and β is considered

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31

Mossino, Jacqueline, and Ali Sili. "Limit behavior of thin heterogeneous domain with rapidly oscillating boundary." Ricerche di Matematica 56, no. 1 (June 2007): 119–48. http://dx.doi.org/10.1007/s11587-007-0009-2.

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32

Nakasato, Jean Carlos, and Marcone Corrêa Pereira. "The p-Laplacian in thin channels with locally periodic roughness and different scales*." Nonlinearity 35, no. 5 (May 5, 2022): 2474–512. http://dx.doi.org/10.1088/1361-6544/ac62e0.

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Abstract In this work we analyse the asymptotic behaviour of the solutions of the p-Laplacian equation with homogeneous Neumann boundary conditions posed in bounded thin domains as R ε = ( x , y ) ∈ R 2 : x ∈ ( 0 , 1 ) and 0 < y < ε G x , x / ε α for some α > 0. We take a smooth function G : ( 0 , 1 ) × R ↦ R , L-periodic in the second variable, which allows us to consider locally periodic oscillations at the upper boundary. The thin domain situation is established passing to the limit in the solutions as the positive parameter ɛ goes to zero and we determine the limit regime for three case: α < 1, α = 1 and α > 1.

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Mishra, Indira. "Homogenization of boundary optimal control problem." Electronic Journal of Differential Equations 2022, no. 01-87 (February 17, 2022): 12. http://dx.doi.org/10.58997/ejde.2022.12.

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In this article, we study the asymptotic behavior of solutions to some optimal control problems, governed by an elliptic boundary value problem with Robin boundary conditions in a periodically perforated domain. The coefficients of the differential operator in the state equation and in the cost-functional are rapidly oscillating. We also study the boundary homogenization of some optimal control problems.

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34

Blanchard, Dominique, Luciano Carbone, and Antonio Gaudiello. "Homogenization of a monotone problem in a domain with oscillating boundary." ESAIM: Mathematical Modelling and Numerical Analysis 33, no. 5 (September 1999): 1057–70. http://dx.doi.org/10.1051/m2an:1999134.

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35

Belyaev, A. G., A. L. Pyatnitskii, and G. A. Chechkin. "Averaging in a perforated domain with an oscillating third boundary condition." Sbornik: Mathematics 192, no. 7 (August 31, 2001): 933–49. http://dx.doi.org/10.1070/sm2001v192n07abeh000576.

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Fernández Bonder, Julián, Rafael Orive, and Julio D. Rossi. "The best Sobolev trace constant in a domain with oscillating boundary." Nonlinear Analysis: Theory, Methods & Applications 67, no. 4 (August 2007): 1173–80. http://dx.doi.org/10.1016/j.na.2006.07.005.

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Amirat, Y., and O. Bodart. "Boundary Layer Correctors for the Solution of Laplace Equation in a Domain with Oscillating Boundary." Zeitschrift für Analysis und ihre Anwendungen 20, no. 4 (2001): 929–40. http://dx.doi.org/10.4171/zaa/1052.

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Iwano, Kaoru. "Bloch Oscillations Due to Quantum Domain Breathing in One-Dimensional Electronic Photoinduced Phase Transitions." Applied Sciences 9, no. 12 (June 16, 2019): 2461. http://dx.doi.org/10.3390/app9122461.

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We theoretically predict a novel oscillation that will be observed during the dynamical processes of one-dimensional electronic photoinduced phase transitions. This oscillation is considered to be a breathing mode of a quantum domain of a photoinduced phase in the background of the initial phase. When the initial phase is sufficiently stable, being far apart from the phase boundary, the domain feels a constant attractive force depending on its size or the distance between the two domain walls. This fact allows an interpretation that this oscillation is essentially the same as a so-called Bloch oscillation seen for the Stark ladder.

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WANG, Q. X., and J. R. BLAKE. "Non-spherical bubble dynamics in a compressible liquid. Part 1. Travelling acoustic wave." Journal of Fluid Mechanics 659 (July 27, 2010): 191–224. http://dx.doi.org/10.1017/s0022112010002430.

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Micro-cavitation bubbles generated by ultrasound have wide and important applications in medical ultrasonics and sonochemistry. An approximate theory is developed for nonlinear and non-spherical bubbles in a compressible liquid by using the method of matched asymptotic expansions. The perturbation is performed to the second order in terms of a small parameter, the bubble-wall Mach number. The inner flow near the bubble can be approximated as incompressible at the first and second orders, leading to the use of Laplace's equation, whereas the outer flow far away from the bubble can be described by the linear wave equation, also for the first and second orders. Matching between the two expansions provides the model for the non-spherical bubble behaviour in a compressible fluid. A numerical model using the mixed Eulerian–Lagrangian method and a modified boundary integral method is used to obtain the evolving bubble shapes. The primary advantage of this method is its computational efficiency over using the wave equation throughout the fluid domain. The numerical model is validated against the Keller–Herring equation for spherical bubbles in weakly compressible liquids with excellent agreement being obtained for the bubble radius evolution up to the fourth oscillation. Numerical analyses are further performed for non-spherical oscillating acoustic bubbles. Bubble evolution and jet formation are simulated. Outputs also include the bubble volume, bubble displacement, Kelvin impulse and liquid jet tip velocity. Bubble behaviour is studied in terms of the wave frequency and amplitude. Particular attention is paid to the conditions if/when the bubble jet is formed and when the bubble becomes multiply connected, often forming a toroidal bubble. When subjected to a weak acoustic wave, bubble jets may develop at the two poles of the bubble surface after several cycles of oscillations. A resonant phenomenon occurs when the wave frequency is equal to the natural oscillation frequency of the bubble. When subjected to a strong acoustic wave, a vigorous liquid jet develops along the direction of wave propagation in only a few cycles of the acoustic wave.

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Simakov, Sergey T. "Initial and boundary value problems of internal gravity waves." Journal of Fluid Mechanics 248 (March 1993): 55–65. http://dx.doi.org/10.1017/s0022112093000680.

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The paper considers the generation of Boussinesq internal waves in the framework of the Green's function method. For certain domains it is shown how to construct Green's functions using the fundamental solution of the equation. The behaviour of the solution at large times for an impulsively started monochromatic point source is studied, attention being focused on the growth rate of the oscillation amplitude on the characteristic surfaces of the steady-oscillation equation which are emitted from the point source. In addition a simple extended source is considered, for which a focusing singularity phenomenon is shown to take place.

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Wong, L. H., and S. M. Calisal. "A Numerical Solution for Potential Flows Including the Effects of Vortex Shedding." Journal of Offshore Mechanics and Arctic Engineering 115, no. 2 (May 1, 1993): 111–15. http://dx.doi.org/10.1115/1.2920099.

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This paper reports on an attempt to include vortex shedding effects into potential flow calculations using the boundary element method. Significant computational advantages result because of the relatively simple approach to handling separation at the sharp edges while working only with the boundary values. A discrete vortex method was incorporated into a time domain boundary element algorithm for the numerical simulation of oscillating flow past a normal flat plate. Separation from a sharp edge results in the formation of a vortex sheet issuing from the edge. This vortex sheet is modeled by a series of discrete vortices introduced one at a time into the flow field at regular intervals. The motion of each vortex is traced over time using its convection velocity. As long as the Keulegan-Carpenter number is small enough, vortex shedding takes place close to the edge. The discrete vortex method can, in such cases, be looked upon as the inner region solution to the problem of normal oscillating flow past the flat plate. This inner region solution has to be matched with the outer potential flow solution. The combination of boundary element and discrete vortex methods provides this matching and at the same time does not require calculations inside the domain.

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Amirat, Youcef, Gregory A. Chechkin, and Rustem R. Gadyl'shin. "Asymptotics for eigenelements of Laplacian in domain with oscillating boundary: multiple eigenvalues." Applicable Analysis 86, no. 7 (July 2007): 873–97. http://dx.doi.org/10.1080/00036810701461238.

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Muthukumar, T., and K. Sankar. "Homogenization of the Stokes System in a Domain with an Oscillating Boundary." Multiscale Modeling & Simulation 20, no. 4 (December 5, 2022): 1361–93. http://dx.doi.org/10.1137/22m1474345.

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Muthukumar, T., Jean-Pierre Raymond, and K. Sankar. "Homogenization of parabolic equation in an evolving domain with an oscillating boundary." Journal of Mathematical Analysis and Applications 463, no. 2 (July 2018): 838–68. http://dx.doi.org/10.1016/j.jmaa.2018.03.063.

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Yoshida, Norio. "Forced oscillations of solutions of parabolic equations." Bulletin of the Australian Mathematical Society 36, no. 2 (October 1987): 289–94. http://dx.doi.org/10.1017/s0004972700026563.

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Moroz, I. P. "THE CORRECTING FUNCTIONS METHOD FOR SOLVING A BOUNDARY VALUE PROBLEM FOR THE AMBIPOLAR DIFFUSION EQUATION IN A DOMAIN WITH A CURVILINEAR BOUNDARIES." Journal of Numerical and Applied Mathematics, no. 2 (2022): 91–97. http://dx.doi.org/10.17721/2706-9699.2022.2.11.

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An approach for the ambipolar diffusion equation boundary value problem solving, which is posed in a two-dimensional domain with oscillating boundaries, is proposed. The construction of the solution of the model problem is based on the corresponding problem for a certain internal canonical majorant domain and the methodology for constructing the so-called corrective corrections based on the use of the perturbation theory elements. A feature of this problem is that it is not the problem equation or boundary conditions that are perturbed, but the region. And this leads to the construction of a fundamentally new solution structure.

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Wooyi, Young, and Hee-Chang Lim. "Synthetic Inflow GeneratorhavingVarious Oscillations." International Journal of Advance Research and Innovation 7, no. 1 (2019): 82–85. http://dx.doi.org/10.51976/ijari.711912.

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Large Eddy Simulation (LES), which has recently been developed and used for the climate local environment and turbulent boundary layer flow, can be applied for a variety of area. In particular, in order to achieve a faster performance, an artificial generation of inflow turbulent flowwould be necessary to make the faster convergence as well as to maintain the real turbulent flow in the calculation domain.In this study, the synthetic inflow generator has been developed based on spatial and temporal correlation functions, which have a form similar to an exponential function. This inflow data having various oscillationobtained by the synthetic inflow generator imposed into the inlet condition of LES simulation on a channel with smooth wall. In the result, fully developed turbulent boundary layer was successfully generated in the computational domain. In addition, the variation of oscillating inflow was taken into account to observe the effect of the fully developed turbulent boundary layer.

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48

Abdulle, Assyr, Doghonay Arjmand, and Edoardo Paganoni. "A parabolic local problem with exponential decay of the resonance error for numerical homogenization." Mathematical Models and Methods in Applied Sciences 31, no. 13 (November 2021): 2733–72. http://dx.doi.org/10.1142/s0218202521500603.

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This paper aims at an accurate and efficient computation of effective quantities, e.g. the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a micro–macro-coupling, where the macromodel describes the coarse scale behavior, and the micromodel is solved only locally to upscale the effective quantities, which are missing in the macromodel. The fact that the microproblems are solved over small domains within the entire macroscopic domain, implies imposing artificial boundary conditions on the boundary of the microscopic domains. A naive treatment of these artificial boundary conditions leads to a first-order error in [Formula: see text], where [Formula: see text] represents the characteristic length of the small scale oscillations and [Formula: see text] is the size of microdomain. This error dominates all other errors originating from the discretization of the macro and the microproblems, and its reduction is a main issue in today’s engineering multiscale computations. The objective of this work is to analyze a parabolic approach, first announced in A. Abdulle, D. Arjmand, E. Paganoni, C. R. Acad. Sci. Paris, Ser. I, 2019, for computing the homogenized coefficients with arbitrarily high convergence rates in [Formula: see text]. The analysis covers the setting of periodic microstructure, and numerical simulations are provided to verify the theoretical findings for more general settings, e.g. non-periodic microstructures.

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Aina, B., and S. Isa. "Influence of Heat Generation/Absorption on Mixed Convection Flow Behaviour in the Presence of Lorentz Forces in a Vertical Micro Circular Duct Having Time Periodic Boundary Conditions: Steady Periodic Regime." International Journal of Applied Mechanics and Engineering 25, no. 4 (December 1, 2020): 1–21. http://dx.doi.org/10.2478/ijame-2020-0046.

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AbstractThe problem of mixed convection flow of a heat generating/absorbing fluid in the presence existence of Lorentz forces in a vertical micro circular subjected to a periodic sinusoidal temperature change at the surface has been studied taking the first-order slip and jump effects into consideration. The research analysis is carried out by considering a fully developed parallel flow and steady periodic regime. The governing equations, together with the constraint equations which arise from the definition of mean velocity and temperature, are written in a dimensionless form and mapped into equations in the complex domain. One obtains two independent boundary value problems, which provide the mean value and the oscillating term of the velocity and temperature distributions. These boundary value problems are solved analytically. A parametric study of some of the physical parameters involved in the problem is conducted. The results of this research revealed that the magnetic field has a damping impact on the flow and results in decreases in fluid velocity for both air and water. Furthermore, the presence of the heat generation parameter is seen to enhance the temperature distribution and this is reflected as an increase in the magnitude of the oscillation dimensionless velocity, whereas in the presence of heat absorption a reversed trend occurs.

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Orchini, A., S. J. Illingworth, and M. P. Juniper. "Frequency domain and time domain analysis of thermoacoustic oscillations with wave-based acoustics." Journal of Fluid Mechanics 775 (June 25, 2015): 387–414. http://dx.doi.org/10.1017/jfm.2015.139.

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Many thermoacoustic systems exhibit rich nonlinear behaviour. Recent studies show that this nonlinear dynamics can be well captured by low-order time domain models that couple a level set kinematic model for a laminar flame, the $G$-equation, with a state-space realization of the linearized acoustic equations. However, so far the $G$-equation has been coupled only with straight ducts with uniform mean acoustic properties, which is a simplistic configuration. In this study, we incorporate a wave-based model of the acoustic network, containing area and temperature variations and frequency-dependent boundary conditions. We cast the linear acoustics into state-space form using a different approach from that in the existing literature. We then use this state-space form to investigate the stability of the thermoacoustic system, both in the frequency and time domains, using the flame position as a control parameter. We observe frequency-locked, quasiperiodic and chaotic oscillations. We identify the location of Neimark–Sacker bifurcations with Floquet theory. We also find the Ruelle–Takens–Newhouse route to chaos with nonlinear time series analysis techniques. We highlight important differences between the nonlinear response predicted by the frequency domain and the time domain methods. This reveals deficiencies with the frequency domain technique, which is commonly used in academic and industrial studies of thermoacoustic systems. We then demonstrate a more accurate approach based on continuation analysis applied to time domain techniques.

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