Academic literature on the topic 'Oscillating boundary domains'
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Journal articles on the topic "Oscillating boundary domains"
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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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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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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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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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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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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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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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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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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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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.
Full textDissertations / Theses on the topic "Oscillating boundary domains"
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Zebiri, Boubakr. "Étude numérique des interactions onde de choc / couche limite dans les tuyères propulsives Shock-induced flow separation in an overexpanded supersonic planar nozzle A parallel high-order compressible flows solver with domain decomposition method in the generalized curvilinear coordinates system Analysis of shock-wave unsteadiness in conical supersonic nozzles." Thesis, Normandie, 2020. http://www.theses.fr/2020NORMIR06.
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La nécessité d’une meilleure compréhension du mécanisme d’entrainement pour l’instabilité à basse fréquence observée dans un écoulement dans une tuyère sur-détendue a été discutée. Le caractère instable de l’onde de choc/couche limite reste un défi pratique important pour les problèmes des écoulements dans les tuyères. De plus, pour une couche limite turbulente incidente donnée, ce type d’écoulement présente généralement des mouvements de choc à basse fréquence plus élevées qui sont moins couplés aux échelles de temps de la turbulence en amont. Cela peut être bon du point de vue d’un expérimentateur, en raison de difficultés à mesurer des fréquences plus élevées, mais c’est plus difficile d’un point de vue calcul numérique en raison de la nécessité d’obtenir des séries temporelles plus longues pour résoudre les mouvements à basse fréquence. En excellent accord avec les résultats expérimentaux, une série de calcul LES de très longue durée a été réalisée, il a été clairement démontré l’existence de mouvements énergétiques à basse fréquence et à large bande près du point de séparation. Des efforts particuliers ont été faits pour éviter tout forçage à basse fréquence en amont, et il a été explicitement démontré que les oscillations de choc à basse fréquence observées n’étaient pas liées à la génération de turbulence d’entrée, excluant la possibilité d’un artefact numérique. Différentes méthodes d’analyse spectrales, et en décomposition en mode dynamique ont été utilisées pour montrer que les échelles de temps impliquées dans un tel mécanisme sont environ deux ordres de grandeur plus grandes que les échelles de temps impliquées dans la turbulence de la couche limite, ce qui est cohérent avec les mouvements de basse fréquence observés. En outre, ces échelles de temps se sont avérées être fortement modulées par la quantité de flux inversé à l’intérieur de la bulle de séparation. Ce scénario peut, en principe, expliquer à la fois l’instabilité des basses fréquences et sa nature à large bandeThe need for a better understanding of the driving mechanism for the observed low-frequency unsteadiness in an over-expanded nozzle flows was discussed. The unsteady character of the shock wave/boundary layer remains an important practical challenge for the nozzle flow problems. Additionally, for a given incoming turbulent boundary layer, this kind of flow usually exhibits higher low-frequency shock motions which are less coupled from the timescales of the incoming turbulence. This may be good from an experimenter’s point of view, because of the difficulties in measuring higher frequencies, but it is more challenging from a computational point of view due to the need to obtain long time series to resolve low-frequency movements. In excellent agreement with the experimental findings, a very-long LES simulation run was carried out to demonstrate the existence of energetic broadband low-frequency motions near the separation point. Particular efforts were done in order to avoid any upstream low-frequency forcing, and it was explicitly demonstrated that the observed low-frequency shock oscillations were not connected with the inflow turbulence generation, ruling out the possibility of a numerical artefact. Different methods of spectral analysis and dynamic mode decomposition have been used to show that the timescales involved in such a mechanism are about two orders of magnitude larger than the time scales involved in the turbulence of the boundary layer, which is consistent with the observed low-frequency motions. Furthermore, those timescales were shown to be strongly modulated by the amount of reversed flow inside the separation bubble. This scenario can, in principle, explain both the low-frequency unsteadiness and its broadband nature
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Aiyappan, S. "Unfolding Operators in Various Oscillatory Domains : Homogenization of Optimal Control Problems." Thesis, 2017. http://etd.iisc.ac.in/handle/2005/3696.
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In this thesis, we study homogenization of optimal control problems in various oscillatory domains. Specifically, we consider four types of domains given in Figure 1 below.
Figure 1: Oscillating Domains
The thesis is organized into six chapters. Chapter 1 provides an introduction to our work and the rest of the thesis. The main contributions of the thesis are contained in Chapters 2-5. Chapter 6 presents the conclusions of the thesis and possible further directions. A brief description of our work (Chapters 2-5) follows:
Chapter 2: Asymptotic behaviour of a fourth order boundary optimal control problem with Dirichlet boundary data posed on an oscillating domain as in Figure 1(A) is analyzed. We use the unfolding operator to study the asymptotic behavior of this problem.
Chapter 3: Homogenization of a time dependent interior optimal control problem on a branched structure domain as in Figure 1(B) is studied. Here we pose control on the oscillating interior part of the domain. The analysis is carried out by appropriately defined unfolding operators suitable for this domain. The optimal control is characterized using various unfolding operators defined at each branch of every level.
Chapter 4: A new unfolding operator is developed for a general oscillating domain as in Figure 1(C). Homogenization of a non-linear elliptic problem is studied using this new un-folding operator. Using this idea, homogenization of an optimal control problem on a circular oscillating domain as in Figure 1(D) is analyzed.
Chapter 5: Homogenization of a non-linear optimal control problem posed on a smooth oscillating domain as in Figure 1(C) is studied using the unfolding operator.
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Aiyappan, S. "Unfolding Operators in Various Oscillatory Domains : Homogenization of Optimal Control Problems." Thesis, 2017. http://etd.iisc.ernet.in/2005/3696.
Full textAbstract:
In this thesis, we study homogenization of optimal control problems in various oscillatory domains. Specifically, we consider four types of domains given in Figure 1 below.
Figure 1: Oscillating Domains
The thesis is organized into six chapters. Chapter 1 provides an introduction to our work and the rest of the thesis. The main contributions of the thesis are contained in Chapters 2-5. Chapter 6 presents the conclusions of the thesis and possible further directions. A brief description of our work (Chapters 2-5) follows:
Chapter 2: Asymptotic behaviour of a fourth order boundary optimal control problem with Dirichlet boundary data posed on an oscillating domain as in Figure 1(A) is analyzed. We use the unfolding operator to study the asymptotic behavior of this problem.
Chapter 3: Homogenization of a time dependent interior optimal control problem on a branched structure domain as in Figure 1(B) is studied. Here we pose control on the oscillating interior part of the domain. The analysis is carried out by appropriately defined unfolding operators suitable for this domain. The optimal control is characterized using various unfolding operators defined at each branch of every level.
Chapter 4: A new unfolding operator is developed for a general oscillating domain as in Figure 1(C). Homogenization of a non-linear elliptic problem is studied using this new un-folding operator. Using this idea, homogenization of an optimal control problem on a circular oscillating domain as in Figure 1(D) is analyzed.
Chapter 5: Homogenization of a non-linear optimal control problem posed on a smooth oscillating domain as in Figure 1(C) is studied using the unfolding operator.
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Renjith, T. "Homogenization of PDEs on oscillating boundary domains with L1 data and optimal control problems." Thesis, 2023. https://etd.iisc.ac.in/handle/2005/6084.
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This thesis comprehensively studies the homogenization of partial differential equations (PDEs) and optimal control problems with oscillating coefficients in oscillating domains. After the introduction, the thesis is divided into two parts. In part I, we consider problems in oscillating circular domains with three chapters(chapters 1-3), whereas in part II(chapters 4-5), we deal with domains having oscillations in low dimensions.
The first chapter investigates the homogenization of a second-order elliptic PDE with oscillating coefficients in a circular oscillating boundary domain. By using the polar form of the differential equations and a polar unfolding operator, we consider the general type of oscillations and study the asymptotic behavior of the renormalized solution of the PDE with a source term in $L^1$.
The second chapter examines the homogenization of an elliptic variational form with oscillating coefficients in a circular domain that is highly oscillating itself. The source term is in $L^1$, and we take into account the non-uniform ellipticity that arises due to the highly oscillating boundary, rapidly oscillating coefficient, and the oscillating part made up of highly contrasting materials.
The third chapter focuses on the homogenization of optimal control problems governed by second-order semi-linear elliptic PDEs with matrix coefficients in a circular domain. The cost functionals considered are of general energy type and may have different oscillating matrix coefficients than the constrained PDEs. We prove the existence of well-defined limit problems and derive explicit expressions for the limiting coefficient matrices.
The fourth chapter extends the study to an $n$-dimensional domain with an oscillating boundary that oscillates in $m$ directions, where $1\leq m < n$. This is a relatively unexplored area in the literature, and we show that in this case, the limit problem has derivatives in all non-oscillating directions, or $n-m$. Specifically, we study the homogenization of an elliptic PDE in such a domain with $L^1$ data. Our work expands upon previous research and could have potential applications in various fields.
The fifth chapter investigates the homogenization of optimal control problems governed by second-order semi-linear elliptic PDEs with matrix coefficients in a low-dimensional oscillating domain. The cost functionals considered are of general energy type and may have different oscillating matrix coefficients than the constrained PDEs. We prove the existence of well-defined limit problems and derive explicit expressions for the limiting coefficient matrices. We show that, in this case, the limit problem has derivatives in all non-oscillating directions. Our results show that the limiting cost functional's coefficient matrix is a combination of the original cost functional's and constrained PDE's coefficient matrices.
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Ravi, Prakash *. "Homogenization of Optimal Control Problems in a Domain with Oscillating Boundary." Thesis, 2013. http://etd.iisc.ac.in/handle/2005/2807.
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Mathematical theory of homogenization of partial differential equations is relatively a new area of research (30-40 years or so) though the physical and engineering applications were well known. It has tremendous applications in various branches of engineering and science like : material science ,porous media, study of vibrations of thin structures, composite materials to name a few. There are at present various methods to study homogenization problems (basically asymptotic analysis) and there is a vast amount of literature in various directions. Homogenization arise in problems with oscillatory coefficients, domain with large number of perforations, domain with rough boundary and so on. The latter one has applications in fluid flow which is categorized as oscillating boundaries.
In fact ,in this thesis, we consider domains with oscillating boundaries. We plan to study to homogenization of certain optimal control problems with oscillating boundaries. This thesis contains 6 chapters including an introductory Chapter 1 and future proposal Chapter 6. Our main contribution contained in chapters 2-5. The oscillatory domain under consideration is a 3-dimensional cuboid (for simplicity) with a large number of pillars of length O(1) attached on one side, but with a small cross sectional area of order ε2 .As ε0, this gives a geometrical domain with oscillating boundary. We also consider 2-dimensional oscillatory domain which is a cross section of the above 3-dimensional domain.
In chapters 2 and 3, we consider the optimal control problem described by the Δ operator with two types of cost functionals, namely L2-cost functional and Dirichlet cost functional. We consider both distributed and boundary controls. The limit analysis was carried by considering the associated optimality system in which the adjoint states are introduced. But the main contribution in all the different cases(L2 and Dirichlet cost functionals, distributed and boundary controls) is the derivation of error estimates what is known as correctors in homogenization literature. Though there is a basic test function, one need to introduce different test functions to obtain correctors. Introducing correctors in homogenization is an important aspect of study which is indeed useful in the analysis, but important in numerical study as well.
The setup is the same in Chapter 4 as well. But here we consider Stokes’ Problem and study asymptotic analysis as well as corrector results. We obtain corrector results for velocity and pressure terms and also for its adjoint velocity and adjoint pressure. In Chapter 5, we consider a time dependent Kirchhoff-Love equation with the same domain with oscillating boundaries with a distributed control. The state equation is a fourth order hyperbolic type equation with associated L2-cost functional. We do not have corrector results in this chapter, but the limit cost functional is different and new. In the earlier chapters the limit cost functional were of the same type.
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Ravi, Prakash *. "Homogenization of Optimal Control Problems in a Domain with Oscillating Boundary." Thesis, 2013. http://hdl.handle.net/2005/2807.
Full textAbstract:
Mathematical theory of homogenization of partial differential equations is relatively a new area of research (30-40 years or so) though the physical and engineering applications were well known. It has tremendous applications in various branches of engineering and science like : material science ,porous media, study of vibrations of thin structures, composite materials to name a few. There are at present various methods to study homogenization problems (basically asymptotic analysis) and there is a vast amount of literature in various directions. Homogenization arise in problems with oscillatory coefficients, domain with large number of perforations, domain with rough boundary and so on. The latter one has applications in fluid flow which is categorized as oscillating boundaries.
In fact ,in this thesis, we consider domains with oscillating boundaries. We plan to study to homogenization of certain optimal control problems with oscillating boundaries. This thesis contains 6 chapters including an introductory Chapter 1 and future proposal Chapter 6. Our main contribution contained in chapters 2-5. The oscillatory domain under consideration is a 3-dimensional cuboid (for simplicity) with a large number of pillars of length O(1) attached on one side, but with a small cross sectional area of order ε2 .As ε0, this gives a geometrical domain with oscillating boundary. We also consider 2-dimensional oscillatory domain which is a cross section of the above 3-dimensional domain.
In chapters 2 and 3, we consider the optimal control problem described by the Δ operator with two types of cost functionals, namely L2-cost functional and Dirichlet cost functional. We consider both distributed and boundary controls. The limit analysis was carried by considering the associated optimality system in which the adjoint states are introduced. But the main contribution in all the different cases(L2 and Dirichlet cost functionals, distributed and boundary controls) is the derivation of error estimates what is known as correctors in homogenization literature. Though there is a basic test function, one need to introduce different test functions to obtain correctors. Introducing correctors in homogenization is an important aspect of study which is indeed useful in the analysis, but important in numerical study as well.
The setup is the same in Chapter 4 as well. But here we consider Stokes’ Problem and study asymptotic analysis as well as corrector results. We obtain corrector results for velocity and pressure terms and also for its adjoint velocity and adjoint pressure. In Chapter 5, we consider a time dependent Kirchhoff-Love equation with the same domain with oscillating boundaries with a distributed control. The state equation is a fourth order hyperbolic type equation with associated L2-cost functional. We do not have corrector results in this chapter, but the limit cost functional is different and new. In the earlier chapters the limit cost functional were of the same type.
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Sardar, Bidhan Chandra. "Study of Optimal Control Problems in a Domain with Rugose Boundary and Homogenization." Thesis, 2016. http://etd.iisc.ac.in/handle/2005/2883.
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Mathematical theory of partial differential equations (PDEs) is a pretty old classical area with wide range of applications to almost every branch of science and engineering. With the advanced development of functional analysis and operator theory in the last century, it became a topic of analysis. The theory of homogenization of partial differential equations is a relatively new area of research which helps to understand the multi-scale phenomena which has tremendous applications in a variety of physical and engineering models, like in composite materials, porous media, thin structures, rapidly oscillating boundaries and so on. Hence, it has emerged as one of the most interesting and useful subject to study for the last few decades both as a theoretical and applied topic.
In this thesis, we study asymptotic analysis (homogenization) of second-order partial differential equations posed on an oscillating domain. We consider a two dimensional oscillating domain (comb shape type) consisting of a fixed bottom region and an oscillatory (rugose) upper region. We introduce optimal control problems for the Laplace equation. There are mainly two types of optimal control problems; namely distributed control and boundary control. For distributed control problems in the oscillating domain, one can apply control on the oscillating part or on the fixed part and similarly for boundary control problem (control on the oscillating boundary or on the fixed part the boundary). We consider all the four cases, namely distributed and boundary controls both on the oscillating part and away from the oscillating part.
The present thesis consists of 8 chapters. In Chapter 1, a brief introduction to homogenization and optimal control is given with relevant references. In Chapter 2, we introduce the oscillatory domain and define the basic unfolding operators which will be used throughout the thesis. Summary of the thesis is given in Chapter 3 and future plan in Chapter 8. Our main contribution is contained in Chapters 4-7.
In chapters 4 and 5, we study the asymptotic analysis of optimal control problems namely distributed and boundary controls, respectively, where the controls act away from the oscillating part of the domain. We consider both L2 cost functional as well as Dirichlet (gradient type) cost functional. We derive homogenized problem and introduce the limit optimal control problems with appropriate cost functional. Finally, we show convergence of the optimal solution, optimal state and associate adjoint solution. Also convergence of cost-functional.
In Chapter 6, we consider the periodic controls on the oscillatory part together with Neumann condition on the oscillating boundary. One of the main contributions is the characterization of the optimal control using unfolding operator. This characterization is new and also will be used to study the limiting analysis of the optimality system.
Chapter 7 deals with the boundary optimal control problem, where the control is applied through Neumann boundary condition on the oscillating boundary with a suitable scaling parameter. To characterize the optimal control, we introduce boundary unfolding operators which we consider as a novel approach. This characterization is used in the limiting analysis. In the limit, we obtain two limit problems according to the scaling parameters. In one of the limit optimal control problem, we observe that it contains three controls namely; a distributed control, a boundary control and an interface control.
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Sardar, Bidhan Chandra. "Study of Optimal Control Problems in a Domain with Rugose Boundary and Homogenization." Thesis, 2016. http://hdl.handle.net/2005/2883.
Full textAbstract:
Mathematical theory of partial differential equations (PDEs) is a pretty old classical area with wide range of applications to almost every branch of science and engineering. With the advanced development of functional analysis and operator theory in the last century, it became a topic of analysis. The theory of homogenization of partial differential equations is a relatively new area of research which helps to understand the multi-scale phenomena which has tremendous applications in a variety of physical and engineering models, like in composite materials, porous media, thin structures, rapidly oscillating boundaries and so on. Hence, it has emerged as one of the most interesting and useful subject to study for the last few decades both as a theoretical and applied topic.
In this thesis, we study asymptotic analysis (homogenization) of second-order partial differential equations posed on an oscillating domain. We consider a two dimensional oscillating domain (comb shape type) consisting of a fixed bottom region and an oscillatory (rugose) upper region. We introduce optimal control problems for the Laplace equation. There are mainly two types of optimal control problems; namely distributed control and boundary control. For distributed control problems in the oscillating domain, one can apply control on the oscillating part or on the fixed part and similarly for boundary control problem (control on the oscillating boundary or on the fixed part the boundary). We consider all the four cases, namely distributed and boundary controls both on the oscillating part and away from the oscillating part.
The present thesis consists of 8 chapters. In Chapter 1, a brief introduction to homogenization and optimal control is given with relevant references. In Chapter 2, we introduce the oscillatory domain and define the basic unfolding operators which will be used throughout the thesis. Summary of the thesis is given in Chapter 3 and future plan in Chapter 8. Our main contribution is contained in Chapters 4-7.
In chapters 4 and 5, we study the asymptotic analysis of optimal control problems namely distributed and boundary controls, respectively, where the controls act away from the oscillating part of the domain. We consider both L2 cost functional as well as Dirichlet (gradient type) cost functional. We derive homogenized problem and introduce the limit optimal control problems with appropriate cost functional. Finally, we show convergence of the optimal solution, optimal state and associate adjoint solution. Also convergence of cost-functional.
In Chapter 6, we consider the periodic controls on the oscillatory part together with Neumann condition on the oscillating boundary. One of the main contributions is the characterization of the optimal control using unfolding operator. This characterization is new and also will be used to study the limiting analysis of the optimality system.
Chapter 7 deals with the boundary optimal control problem, where the control is applied through Neumann boundary condition on the oscillating boundary with a suitable scaling parameter. To characterize the optimal control, we introduce boundary unfolding operators which we consider as a novel approach. This characterization is used in the limiting analysis. In the limit, we obtain two limit problems according to the scaling parameters. In one of the limit optimal control problem, we observe that it contains three controls namely; a distributed control, a boundary control and an interface control.
Book chapters on the topic "Oscillating boundary domains"
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Maz’ya, Vladimir, Serguei Nazarov, and Boris A. Plamenevskij. "Elliptic Boundary Value Problems with Rapidly Oscillating Coefficients." In Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains, 211–35. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8432-7_7.
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Gómez, D., S. A. Nazarov, and E. Pérez. "Spectral Stiff Problems in Domains with a Strongly Oscillating Boundary." In Integral Methods in Science and Engineering, 159–72. Boston: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8238-5_15.
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Arrieta, José M., and Manuel Villanueva-Pesqueira. "Fast and Slow Boundary Oscillations in a Thin Domain." In Advances in Differential Equations and Applications, 13–22. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06953-1_2.
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"4. Asymptotic Analysis of Optimal Neumann Boundary Control Problem in Domain with Boundary Oscillation for Elliptic Equation with Exponential Non-Linearity." In Approximation Methods in Optimization of Nonlinear Systems, 116–63. De Gruyter, 2019. http://dx.doi.org/10.1515/9783110668520-005.
Full textConference papers on the topic "Oscillating boundary domains"
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Li, Hui, Hao Lizhu, Huilong Ren, and Xiaobo Chen. "Zero Speed Rankine-Kelvin Hybrid Method With a Cylinder Control Surface." In ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/omae2015-41565.
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The solution of hydrodynamic problem with forward speed still has some well-known problems such as high oscillation and slow convergence of the wave term when using a moving and oscillating source as the Green function. Recently, Ten and Chen (2010) has come up with a new method to benefit the merits of both the Rankine source and moving and oscillating source by taking a hemisphere as the control surface which separates the fluid region into two domains, but some troubles have been induced in the process of solution. Therefore, in this paper, a cylindrical surface instead of a hemisphere is selected to be the control surface to make the solution easy, and in this method, the control surface isn’t divided into panels. In the interior domain near the ship, the Rankin Green function is used to simplify the calculation. In the exterior domain some distance from the ship, there is no panels representing the free surface by using the Green function which satisfy the free surface boundary condition. The whole fluid region matches by the condition that the velocity potentials and their normal derivatives in the interior domain and exterior domain are equal on the control surface separately. In this paper, we have validated the Rankine-Kelvin hybrid method is applicable by adopting it to solve the zero speed problem in this work.
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Ji, Shanhong, and Feng Liu. "Computation of Flutter of Turbomachinery Cascades Using a Parallel Unsteady Navier-Stokes Code." In ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/98-gt-043.
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A quasi-three-dimensional multigrid Navier-Stokes solver on single and multiple passage domains is presented for solving unsteady flows around oscillating turbine and compressor blades. The conventional “direct store” method is used for applying the phase-shifted periodic boundary condition over a single blade passage. A parallel version of the solver using the Message Passing Interface (MPI) standard is developed for multiple passage computations. In the parallel multiple passage computations, the phase-shifted periodic boundary condition is converted to simple in-phase periodic condition. Euler and Navier-Stokes solutions are obtained for unsteady flows through an oscillating turbine cascade blade row with both the sequential and the parallel code. It is found that the parallel code offers almost linear speedup with multiple CPUs. In addition, significant improvement is achieved in convergence of the computation to a periodic unsteady state in the parallel multiple passage computations due to the use of in-phase periodic boundary conditions as compared to that in the single passage computations with phase-lagged periodic boundary conditions via the “direct store” method. The parallel Navier-Stokes code is also used to calculate the flow through an oscillating compressor cascade. Results are compared with experimental data and computations by other authors.
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Abdulrasool, Ali A., and Yongho Lee. "A DNS Study on Roughness-Induced Transition in Oscillating Pipe Flow by Employing Overset Methodology." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-12300.
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Abstract In this paper, we model a circular pipe with wavy inner wall, for the purpose of studying the role of surface roughness in a purely oscillating flow. Overset-grid technique is utilized for two combined flow domains, and the interpolation process within the shared zone is validated with the exact laminar flow solution for long-time oscillation. Direct numerical simulations are performed at different flow conditions, taking advantage of the overlapping capability of the spectral element method. All simulations begin with zero initial conditions, and periodic boundary conditions are applied at the two ends of the pipe with different roughness heights. The internal pipe roughness modeled by the overset meshes operates as a triggering mechanism for transition to turbulence, and the critical Reynolds number based on the Stokes thickness and the centerline velocity amplitude is determined to be 223.5 at the Stokes number of 10. The results confirm that the periodic turbulence bursts react to the presence of the roughness with different levels of turbulence intensity among the four Stokes numbers presented herein. Additionally, friction losses are calculated and compared with three cases of the existing experimental results for smooth and rough walls.
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Daily, D. J., and S. L. Thomson. "A Study of Vocal Fold Vibration Using a Slightly Compressible Fluid Domain." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-10628.
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During human voice production, air forced from the lungs through the larynx induces vibration of the vocal folds. Computational models of this coupled fluid-solid system have traditionally utilized an incompressible fluid domain. However, studies have shown that coupling of tracheal acoustics with vocal fold dynamics is significant. Further, in the absence of compressibility, some models fail to achieve self-sustained vibration. This presentation discusses a slightly compressible airflow model, fully coupled with a vocal fold tissue model, as a possible substitute for the traditional incompressible approach. The derivation and justification of the slightly compressible fluid model are discussed. Results are reported of a study of the nature of the coupling between the fluid and vocal fold regions for both slightly compressible and incompressible fluid domains using a commercial fluid-solid finite element package. Three different types of inlet boundary conditions, including constant pressure, constant velocity, and moving wall, are explored. The incompressible and slightly compressible models with the three boundary conditions are compared with each other and with experimental data obtained using synthetic self-oscillating vocal fold models. The results are used to validate the slightly compressible flow model as well as to explore candidate boundary conditions for vocal fold vibration simulations.
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Shadloo, Mostafa Safdari, Amir Zainali, and Mehmet Yildiz. "Fluid-Structure Interaction Simulation by Smoothed Particle Hydrodynamics." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-31137.
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In this article, a modified SPH algorithm is proposed to solve Fluid-Structure Interaction (FSI) problems including fluid flow in interaction with compatible structures under a large deformation. To validate the current algorithm against available data in literature, we consider two important benchmark cases; namely, an oscillating elastic beam and dam breaking problems. The proposed algorithm is based on the elimination of the intermediate data transfer steps between the fluid and the solid structures, whereby resulting in an easy and time-saving simulation method. With the test application studied, we were able to prove the ability of the modified SPH method for solving of fluid and solid domains monolithically without the need to define an interfacial boundary condition or any additional steps to simulate the deformation of an elastic dam. Numerical results suggest that upon choosing correct SPH parameters such as smoothing function, and lengths, as well as coefficients for artificial viscosity and artificial stress, one can obtain results in satisfactorily agreement with numerical findings of earlier works.
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Sayar, Ersin. "Boiling Heat Transfer From an Oscillated Water Column Through a Porous Domain: A Simplified Thermodynamic Analysis." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-66901.
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Heat transfer in an oscillating water column in the transition regime of pool boiling to bubbly flow is investigated experimentally and theoretically. Forced oscillations are applied to water via a frequency controlled dc motor and a piston-cylinder device. Heat transfer is from the electrically heated inner surface to the reciprocating flow. The heat transfer in the oscillating fluid column is altered by using stainless steel scrap metal layers (made off open-cell discrete cells) which produces a porous medium within the system. The effective heat transfer mechanism is enhanced and it is due to the hydrodynamic mixing of the boundary layer and the core flow. In oscillating flow, the hydrodynamic lag between the core flow and the boundary layer flow is somehow significant. At low actuation frequencies and at low heat fluxes, heat transfer is restricted in the single phase flows. The transition regime of pool boiling to bubbly flow is proposed to be a remedy to the stated limitation. The contribution by the pool boiling on heat transfer appears to be the dominant mechanism for the selected low oscillation amplitudes and frequencies. Accordingly the regime is a transition from pool boiling to bubbly flow. Nucleate-bubbly flow boiling in oscillating flow is also investigated using a simplified thermodynamic analysis. According to the experimental results, bubbles induce highly efficient heat transfer mechanisms. Experimental study proved that the heater surface temperature is the dominant parameter affecting heat transfer. At greater actuation frequencies saturated nucleate pool boiling ceases to exist. Actuation frequency becomes important in that circumstances. The present investigation has possible applications in moderate sized wicked heat pipes, boilers, compact heat exchangers and steam generators.
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Charrayre, François, Christophe Peyrard, Michel Benoit, and Aurélien Babarit. "A Coupled Methodology for Wave-Body Interactions at the Scale of a Farm of Wave Energy Converters Including Irregular Bathymetry." In ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/omae2014-23457.
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Knowledge of the wave perturbation caused by an array of Wave Energy Converters (WEC) is of great concern, in particular for estimating the interaction effects between the various WECs and determining the modification of the wave field at the scale of the array, as well as possible influence on the hydrodynamic conditions in the surroundings. A better knowledge of these interactions will also allow a more efficient layout for future WEC farms. The present work focuses on the interactions of waves with several WECs in an array. Within linear wave theory and in frequency domain, we propose a methodology based on the use of a BEM (Boundary Element Method) model (namely Aquaplus) to solve the radiation-diffraction problem locally around each WEC, and to combine it with a model based on the mild slope equation at the scale of the array. The latter model (ARTEMIS software) solves the Berkhoff’s equation in 2DH domains (2 dimensional code with a z-dependence), considering irregular bathymetries. In fact, the Kochin function (a far field approximation) is used to propagate the perturbations computed by Aquaplus into Artemis, which is well adapted for a circular wave representing the perturbation of an oscillating body. This approximation implies that the method is only suitable for well separated devices. A main advantage of this coupling technique is that Artemis can deal with variable bathymetry. It is important when the wave farm is in shallow water or in nearshore areas. The methodology used for coupling the two models, with the underlying assumptions is detailed first. Validations test-cases are then carried out with simple bodies (namely heaving vertical cylinders) to assess the accuracy and efficiency of the coupling scheme. These tests also allow to analyze and to quantify the magnitude of the interactions between the WECs inside the array.
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Nihei, Yasunori, Takeshi Kinoshita, and Weiguang Bao. "Non-Linear Wave Forces Acting on a Body of Arbitrary Shape Slowly Oscillating in Waves." In ASME 2005 24th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2005. http://dx.doi.org/10.1115/omae2005-67486.
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In the present study, non-linear wave loads such as the wave drift force, wave drift damping and wave drift added mass, acting on a moored body is evaluated based on the potential theory. The body is oscillating at a low frequency under the non-linear excitation of waves. The problem of interaction between the low-frequency oscillation of the body and ambient wave fields is considered. A moving coordinate frame following the low frequency motion is adopted. Two small parameters, which measure the wave slope and the frequency of slow oscillations (compared with the wave frequency) respectively, are used in the perturbation analysis. So obtained boundary value problems for each order of potentials are solved by means of the hybrid method. The fluid domain is divided into two regions by an virtual circular cylinder surrounding the body. Different approaches, i.e. boundary element method and eigen-function expansion, are applied to these two regions. Calculated nonlinear wave loads are compared to the semi-analytical results to validate the present method.
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Ceci, A. "High-fidelity simulation of shock-wave/boundary layer interactions." In Aerospace Science and Engineering. Materials Research Forum LLC, 2023. http://dx.doi.org/10.21741/9781644902677-57.
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Abstract. We perform direct numerical simulations of impinging shock-boundary layer interaction on a flat plate, in which the shock is not orthogonal to the boundary layer flow. The analysis relies on an idealized configuration, where a spanwise flow component is used to introduce the effect of the sweep angle between a statistically two-dimensional boundary layer and the shock. A quantitative comparison is carried out between the swept case and the corresponding unswept one, and the effect of the domain spanwise width is examined. The analysis reveals that, while the time-averaged swept flow characteristics are basically unaffected by the choice of the domain width, the spectral dynamics of the flow dramatically changes with it. For very narrow domains, a pure two-dimensional, low-frequency component can be detected, which resembles the low-frequency oscillation of the unswept case. The present work is also devoted to compare the performance of Digital Filtering (DF) and Recycling-Rescaling methods (RR) in reaching an equilibrium state for the Direct Numerical Simulation (DNS) of a turbulent boundary layer. We performed two sets of DNS of supersonic and hypersonic boundary layers, based on previous numerical studies. It is found that, overall, the RR method is the most appropriate choice, to quickly reach a correct trend of the wall pressure fluctuations, whereas the DF method is more capable in obtain small deviations of the skin friction coefficient with respect to the benchmark.
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Thomas, Jeffrey P., Earl H. Dowell, and Kenneth C. Hall. "A Harmonic Balance Approach for Modeling Three-Dimensional Nonlinear Unsteady Aerodynamics and Aeroelasticity." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-32532.
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Presented is a frequency domain harmonic balance (HB) technique for modeling nonlinear unsteady aerodynamics of three-dimensional transonic inviscid flows about wing configurations. The method can be used to model efficiently nonlinear unsteady aerodynamic forces due to finite amplitude motions of a prescribed unsteady oscillation frequency. When combined with a suitable structural model, aeroelastic (fluid-structure), analyses may be performed at a greatly reduced cost relative to time marching methods to determine the limit cycle oscillations (LCO) that may arise. As a demonstration of the method, nonlinear unsteady aerodynamic response and limit cycle oscillation trends are presented for the AGARD 445.6 wing configuration. Computational results based on the inviscid flow model indicate that the AGARD 445.6 wing configuration exhibits only mildly nonlinear unsteady aerodynamic effects for relatively large amplitude motions. Furthermore, and most likely a consequence of the observed mild nonlinear aerodynamic behavior, the aeroelastic limit cycle oscillation amplitude is predicted to increase rapidly for reduced velocities beyond the flutter boundary. This is consistent with results from other time-domain calculations. Although not a configuration that exhibits strong LCO characteristics, the AGARD 445.6 wing nonetheless serves as an excellent example for demonstrating the HB/LCO solution procedure.