Relevant bibliographies by topics / Kinetic Boundary Condition

Academic literature on the topic 'Kinetic Boundary Condition'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Kinetic Boundary Condition"

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Karimov, F., T. N. Lam, and A. A. Yushkanov. "About boundary conditions for kinetic equations in metal." Journal of Physics: Conference Series 2056, no. 1 (October 1, 2021): 012019. http://dx.doi.org/10.1088/1742-6596/2056/1/012019.

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Abstract Boundary conditions for kinetic equations describing the dynamics of electrons in the metal were analyzed. The boundary condition of the Fuchs and the boundary condition of Soffer were considered. The Andreev conditions for almost tangential moving electrons were taken into account. It is shown that the Soffer boundary condition does not satisfy this condition. The boundary condition was proposed that satisfies the Andreev condition. It is shown that this boundary condition passes in the limiting case into the mirror–diffuse Fuchs boundary condition.
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Choi, Young-Pil, and Jinwook Jung. "Asymptotic analysis for a Vlasov–Fokker–Planck/Navier–Stokes system in a bounded domain." Mathematical Models and Methods in Applied Sciences 31, no. 11 (October 2021): 2213–95. http://dx.doi.org/10.1142/s0218202521500482.

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We study an asymptotic analysis of a coupled system of kinetic and fluid equations. More precisely, we deal with the nonlinear Vlasov–Fokker–Planck equation coupled with the compressible isentropic Navier–Stokes system through a drag force in a bounded domain with the specular reflection boundary condition for the kinetic equation and homogeneous Dirichlet boundary condition for the fluid system. We establish a rigorous hydrodynamic limit corresponding to strong noise and local alignment force. The limiting system is a type of two-phase fluid model consisting of the isothermal Euler system and the compressible Navier–Stokes system. Our main strategy relies on the relative entropy argument based on the weak–strong uniqueness principle. For this, we provide a global-in-time existence of weak solutions for the coupled kinetic-fluid system. We also show the existence and uniqueness of strong solutions to the limiting system in a bounded domain with the kinematic boundary condition for the Euler system and Dirichlet boundary condition for the Navier–Stokes system.
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Yang, Xiang Long, Zhong Wei Huang, and Lei Yang. "The Effect of Boundary Conditions on Simulation of Horizontally Homogeneous Atmospheric Boundary Layer." Applied Mechanics and Materials 204-208 (October 2012): 4490–94. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.4490.

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The Influence of six kinds of combinations of different boundary conditions on the maintenance of homogeneity of atmospheric boundary layer in computational wind engineering was investigated. The inlet condition was applied by either prescribing velocity and turbulent quantities or using a periodic boundary. The top boundary condition includes symmetry, prescribing velocity and turbulent quantities, constant static pressure and applying driving shear stress. Numerical results show that the stream-wise velocity and the turbulent dissipation rate are almost immune to boundary conditions, but the turbulent kinetic energy is affected by boundary conditions dramatically. Best maintenance can be obtained by using periodic boundary condition at inlet and outlet and applying driving shear stress on the top of the domain.
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Deng, Shijin, Weike Wang, and Shih-Hsien Yu. "Bifurcation on boundary data for linear broadwell model with conservative boundary condition." Journal of Hyperbolic Differential Equations 11, no. 03 (September 2014): 603–19. http://dx.doi.org/10.1142/s0219891614500179.

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We study a simple kinetic model with a conservative boundary condition which resembles the Maxwell diffuse boundary condition for the Boltzmann equation. We use a streamlined approach to construct the global pointwise structure of the full boundary data from the imposed boundary condition. Our estimates are strong enough to conclude the bifurcation in terms of the coefficients of the Broadwell model and the speed of the physical boundary.
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Jin, Jiaxin, and Chanwoo Kim. "Damping of Kinetic Transport Equation with Diffuse Boundary Condition." SIAM Journal on Mathematical Analysis 54, no. 5 (October 2022): 5524–50. http://dx.doi.org/10.1137/21m1455358.

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Visintin, A. "Stefan problem with a kinetic condition at the free boundary." Annali di Matematica Pura ed Applicata 146, no. 1 (December 1986): 97–122. http://dx.doi.org/10.1007/bf01762361.

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Dewynne, J. N., S. D. Howison, J. R. Ockendon, and Weiqing Xie. "Asymptotic behavior of solutions to the Stefan problem with a kinetic condition at the free boundary." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 31, no. 1 (July 1989): 81–96. http://dx.doi.org/10.1017/s0334270000006494.

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AbstractWe study the large time behaviour of the free boundary for a one-phase Stefan problem with supercooling and a kinetic condition u = −ε|⋅ṡ| at the free boundary x = s(t). The problem is posed on the semi-infinite strip [0,∞) with unit Stefan number and bounded initial temperature ϕ(x) ≤ 0, such that ϕ → −1 − δ as x → ∞, where δ is constant. Special solutions and the asymptotic behaviour of the free boundary are considered for the cases ε ≥ 0 with δ negative, positive and zero, respectively. We show that, for ε > 0, the free boundary is asymptotic to , δt/ε if < δ > 0 respectively, and that when δ = 0 the large time behaviour of the free boundary depends more sensitively on the initial temperature. We also give a brief summary of the corresponding results for a radially symmetric spherical crystal with kinetic undercooling and Gibbs-Thomson conditions at the free boundary.
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Dong, Hongjie, Yan Guo, and Timur Yastrzhembskiy. "Kinetic Fokker-Planck and Landau equations with specular reflection boundary condition." Kinetic and Related Models 15, no. 3 (2022): 467. http://dx.doi.org/10.3934/krm.2022003.

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<p style='text-indent:20px;'>We establish existence of finite energy weak solutions to the kinetic Fokker-Planck equation and the linear Landau equation near Maxwellian, in the presence of specular reflection boundary condition for general domains. Moreover, by using a method of reflection and the <inline-formula><tex-math id="M1">\begin{document}$ S_p $\end{document}</tex-math></inline-formula> estimate of [<xref ref-type="bibr" rid="b7">7</xref>], we prove regularity in the kinetic Sobolev spaces <inline-formula><tex-math id="M2">\begin{document}$ S_p $\end{document}</tex-math></inline-formula> and anisotropic Hölder spaces for such weak solutions. Such <inline-formula><tex-math id="M3">\begin{document}$ S_p $\end{document}</tex-math></inline-formula> regularity leads to the uniqueness of weak solutions.</p>
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Chen, You, Chang Shu, Yu Sun, Li Ming Yang, and Yan Wang. "A diffuse interface IBM for compressible flows with Neumann boundary condition." International Journal of Modern Physics B 34, no. 14n16 (April 10, 2020): 2040070. http://dx.doi.org/10.1142/s0217979220400706.

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The recently proposed boundary condition-enforced immersed boundary-gas kinetic flux solver (IB-GKFS) is a new approach for simulation of compressible flows with curved and moving boundaries. In the previous application of IB-GKFS, only the Dirichlet boundary condition is considered, which cannot be applied directly to the Neumann boundary condition. In this paper, an auxiliary layer of Lagrangian points is introduced to tackle Neumann boundary condition. Two test cases, including flow around a circular cylinder and flow around a NACA0012 airfoil, are carried out for validation. The results obtained by the present scheme are compared with the reference data available in the literature. Good agreements are achieved, which indicate that the developed method can effectively simulate the compressible flow with Neumann boundary condition.
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Weiqing, Xie. "The Stefan Problem with a Kinetic Condition at the Free Boundary." SIAM Journal on Mathematical Analysis 21, no. 2 (March 1990): 362–73. http://dx.doi.org/10.1137/0521020.

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Dissertations / Theses on the topic "Kinetic Boundary Condition"

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Maini, Deepak. "VOF Based Multiphase Lattice Boltzmann Method Using Explicit Kinematic Boundary Conditons at the Interface." Thesis, Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/16240.

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A VOF based multiphase Lattice Boltzmann method that explicitly prescribes kinematic boundary conditions at the interface is developed. The advantage of the method is the direct control over the surface tension value. The details of the numerical method are presented. The Saffman instability, Taylor instability, and flow of deformable suspensions in a channel are used as example-problems to demonstrate the accuracy of the method. The method allows for relatively large viscosity and density ratios.
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Leibold, Jan [Verfasser], and M. [Akademischer Betreuer] Hochbruck. "A unified error analysis for the numerical solution of nonlinear wave-type equations with application to kinetic boundary conditions / Jan Leibold ; Betreuer: M. Hochbruck." Karlsruhe : KIT-Bibliothek, 2021. http://d-nb.info/1229514643/34.

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Chabane, Adam. "Modélisation des transferts de masse et de chaleur au voisinage de parois réactives : applications à l’oxydation de composés carbonés pour le post-traitement." Thesis, Université Paris-Saclay (ComUE), 2015. http://www.theses.fr/2015SACLC028/document.

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La crise environnementale a conduit l’industrie automobile à faire face à des contraintes croissantes tandis que les limitations drastiques de polluants entrent en vigueur. Afin de réduire les émissions polluantes issues de la combustion, l’une des solutions adoptées est de post-traiter les fumées à l’aide de systèmes de post-traitement catalytique à l’image du catalyseur 3 voies (TWC) pour les moteurs à essence ou le catalyseur d’oxydation (DOC)pour les moteurs diesel. Ces appareils présentent une structure en nid d’abeille constituée d’un réseau de canaux à l’échelle millimétrique appelés monolithes et dont les parois intérieures sont recouvertes d’une fine couche de métal précieux aux propriétés catalytiques. Les polluants sont transformés via l’interaction entre les molécules présentes dans la phase gaz et les sites actifs du métal précieux. Etant donné les conditions laminaires d’écoulement au sein des monolithes, un mélange faible et une diffusion moléculaire limitée peuvent être rencontrés au voisinage de la paroi réactive. Le taux de conversion des polluants peut être alors insuffisant pour des conditions opératoires données. Dans le but d’optimiser les transferts,des obstacles peuvent être introduits par déformation mécanique des parois du canal catalytique au cours du processus de fabrication.Les simulations numériques peuvent contribuer à l’émergence de solutions innovantes basées sur une compréhension et une maitrise profonde des phénomènes sous-jacents. Afin d’atteindre cet objectif, le premier élément clé a été de formuler et d’intégrer dans le code de dynamique des fluides AVBP une approche numérique combinant d’une part des conditions aux limites dédiées à la prise en compte de parois réactives,et d’autre part, la résolution de la cinétique chimique gaz et surface via un solveur d’EDP.L’approche a permis la prise en compte de la cinétique détaillée et l’interaction entre la phase gaz et les parois réactives. L’outil développé a été validé en premier lieu à l’aide de calculs de réacteurs hétérogènes zéro-dimensionnels. Les résultats ont montré un parfait accord avec le solveur de référence SENKIN. L’approche a été validée ensuite en l’appliquant à la simulation de deux canaux réactifs aux parois planes et en comparant les résultats numériques aux résultats expérimentaux de Dogwiler et al. L’approche développée s’est révélée être capable de reproduire les principales caractéristiques de la combustion catalytique pour différents points de fonctionnement. Enfin, l’outil développé a été appliqué à l’étude de l’impact de l’introduction d’obstacles pariétaux sur les taux de conversion des systèmes catalytiques. Les résultats ont permis d’ouvrir des perspectives très intéressantes quant à la contribution de la CFD2D et de la chimie hétérogène détaillée à l’optimisation du design des systèmes de post traitement catalytique. En particulier, l’étude de l’influence des obstacles pariétaux a montré que le design de la géométrie des monolithes constitue un fort potentiel d’optimisation de l’efficacité des systèmes de conversion catalytique et ce, à moindre coût grâce à une utilisation optimisée du métal précieux rendue possible par une meilleure interaction entre l'écoulement, les réactions chimiques dans la phase gaz et la paroi réactive
The environmental emergency has led automotive industry to deal with growing constraints as drastic regulations of pollutant emissions are emerging. In order to reduce emissions resulting from the combustion process, one of the solution adopted is to post process pollutants by the means of catalytic after-treatment systems such as three-way converters (TWC) for gasoline applications oroxidation catalysts (DOC) for Diesel applications. These devices present a honeycomb shape which consists in a grid of millimeter-scale narrow channels called monoliths whose interior wall are coated with precious metals presenting catalytic properties.Pollutants are converted through the chemical interaction involving gas-phase molecules and active precious metal sites. Given the laminar flow encountered within these monoliths, weak mixing and molecular diffusion could occur near the catalytic walls. Pollutant conversion rates may therefore prove insufficient for certain operating conditions. In order to promote transfers, obstacles could be introduced by mechanically deforming the channel wall during the manufacturing process. Numerical simulations can contribute to the emergence of innovative technologies based on a profound understanding and mastering of the underlying phenomena that simulation allows. In order to achieve this goal, a first key element was the formulation and integration into the AVBP CFD code of a numerical approach combining specific boundary conditions for reactive walls and ODE solvers for the gas phase and surface chemistry.The approach allowed to account for detailed kinetics and the interplay between the reactive surface and the gas-phase. The resulting tool was first validated using a zero-dimensional heterogeneous reactor computations. The results were shown to perfectly match the ones obtained with the reference kinetic solver SENKIN.Furthermore, the approach was then validated by applying it to the simulation of two planar reactive channel flows, and comparing the predictions with experimental findings of Dogwiler et al.. The developed approach proved to be able of reproducing main features of the catalytic combustion observed for different operating points. Finally, the developed tool was applied to explore the impact of introducing wall obstacles on the conversion rate of catalytic devices. The resulting findings have proved to open very interesting perspectives for contributing to the optimization of the design of catalytic converters using 2D CFD and detailed heterogeneous chemistry. In particular, the study of the impact of wall obstacles indicates the potential for contributing to further increase the efficiency of catalytic converters via the design of monolith geometries that would allow a more efficient and thus less costly usage of Pt-coating as a consequence of optimized interactions between the gas flow, gas phase chemistry and surface chemistry
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Albert, Francisca [Verfasser]. "Identification of kinematic boundary conditions triggering removal of material in tectonically erosive margins : Insight from scaled physical experiments / Francisca Albert." Berlin : Freie Universität Berlin, 2014. http://d-nb.info/1068191414/34.

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Albert, Francisca [Verfasser]. "Identification of kinematic boundary conditions triggering removal of material in tectonically erosive margins : insight from scaled physical experiments / Francisca Albert. Deutsches GeoForschungsZentrum GFZ." Potsdam : Deutsches GeoForschungsZentrum GFZ, 2013. http://d-nb.info/1041525230/34.

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Jolley, Kenny. "Multiscale methods for nanoengineering." Thesis, University of Leicester, 2009. http://hdl.handle.net/2381/7809.

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This thesis is presented in two sections. Two different multiscale models are developed in order to increase the computational speed of two well known atomistic algorithms, Molecular Dynamics (MD) and Kinetic Monte Carlo (KMC). In Section I, the MD method is introduced. Following this, a multiscale method of linking an MD simulation of heat conduction to a finite element (FE) simulation is presented. The method is simple to implement into a conventional MD code and is independent of the atomistic model employed. This bridge between the FE and MD simulations works by ensuring that energy is conserved across the FE/MD boundary. The multiscale simulation allows for the investigation of large systems which are beyond the range of MD. The method is tested extensively in the steady state and transient regimes, and is shown to agree with well with large scale MD and FE simulations. Furthermore, the method removes the artificial boundary effects due to the thermostats and hence allows exact temperatures and temperature gradients to be imposed on to an MD simulation. This allows for better study of temperature gradients on crystal defects etc. In Section II, the KMC method is introduced. A continuum model for the KMC method is presented and compared to the standard KMC model of surface diffusion. This method replaces the many discrete back and forth atom jumps performed by a standard KMC algorithm with a single flux that can evolve in time. Elastic strain is then incorporated into both algorithms and used to simulate atom deposition upon a substrate by Molecular Beam Epitaxy. Quantum dot formation due to a mismatch in the lattice spacing between a substrate and a deposited film is readily observed in both models. Furthermore, by depositing alternating layers of substrate and deposit, self-organised quantum dot super-lattices are observed in both models.
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Мартинюк, Петро Миколайович, П. Н. Мартынюк, and P. M. Martyniuk. "Математичне моделювання консолідації грунтів з урахуванням техногенного впливу та комплексу фізико-хімічних процесів." Thesis, Тернопільський національний технічний університет ім. Івана Пулюя, 2015. http://elartu.tntu.edu.ua/handle/123456789/5477.

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Робота виконана на кафедрі прикладної математики Національного університету водного господарства та природокористування (м. Рівне) Міністерства освіти і науки України.Захист відбувся у 2015 р. на засіданні спеціалізованої вченої ради Д58.052.01 у Тернопільському національному технічному університеті імені Івана Пулюя за адресою: 46001, м. Тернопіль, вул. Білогірська, 50, навчальний корпус 10, конференцзала. З дисертацією можна ознайомитися у науково-технічній бібліотеці Тернопільського національного технічного університету імені Івана Пулюя за адресою: 46001, м. Тернопіль, вул. Руська, 56.
В дисертації побудовано нові математичні моделі взаємних процесів фільтраційної консолідації та фільтраційного руйнування гетерогенних пористих середовищ з урахуванням впливу одночасно функціонуючих процесів переносу тепла та солей, хімічних масообмінних процесів, фізичних процесів просідання та розмиву ґрунту, багатофракційної контактної суфозії, наявності зосереджених шляхів фільтрації. Узагальнено закон Дарсі-Герсеванова руху рідин в деформівних пористих середовищах на основі формалізації дії фізичних законів та явищ термічного та хімічного осмосів, залежності параметрів фільтрації від теплового та хімічного станів пористого середовища, нелінійної залежності коефіцієнта фільтрації від функції самих надлишкових напорів. Враховано явище термічного розширення фаз ґрунту. Побудовано математичні моделі та досліджено процеси фільтраційної консолідації ґрунтів з тонкими напівпроникними включеннями (включення із природних ґрунтів, які мають властивості напівпроникних мембран). Запропоновано в умовах спряження використати ступінь ідеальності напівпроникного включення. Виведено кінематичні граничні умови на рухомих межах області ґрунту з урахуванням: просідань, як результату консолідації; розмиву ґрунту фільтраційним потоком; просідань, як результату багатофракційної контактної суфозії. Для дослідження отриманих нелінійних крайових задач розвинуто та ефективно використано потужні сіткові та безсіткові чисельні методи. На основі розроблених алгоритмів створено програмне забезпечення та проведено серію чисельних експериментів.
В диссертации важная научно-прикладная проблема математического моделирования взаимосвязанных процессов фильтрационной консолидации и фильтрационного разрушения гетерогенных пористых сред рассмотрена в новой неклассической постановке, которая до сих пор не рассматривалась, и связана с изменением химического и теплового состояния пористой среды. Посредством формализации действия физических законов учтены комплексные нелинейные взаимные влияния и зависимости физико-химических и техногенных процессов в пористых средах, к которым относятся грунты. В частности, процессов фильтрационной консолидации, тепло-солепереноса, фильтрационного разрушения пористых сред, более детально – контактного размыва, наличия сосредоточенных путей фильтрации и многофракционной контактной суффозии, химических гетерогенных масообменных процессов, явлений ползучести скелета пористой среды, а также её проседаний в процессе уплотнения. Показано, что существенная нелинейность и топологическая сложность не позволяют рассматривать взаимные влияния и зависимости как обычную суперпозицию отдельно взятых явлений и процессов, а поэтому математическое моделирование указанных явлений и процессов, их взаимодействия должно носить комплексный и системный характер. В диссертации выведены кинематические граничные условия: на верхней подвижной границе пористой среды для учета и прогнозирования величины проседаний при исследованиях консолидации грунтов; на границе размыва грунта фильтрационным потоком для прогнозирования величины зоны размыва и ее эволюции во времени при исследованиях совместимых процессов фильтрационной консолидации и контактного размыва грунтов; на верхней подвижной границе массива грунта в случае исследования совместных процессов фильтрационной консолидации и многофракционной контактной суффозии. Усовершенствован закон Дарси-Герсеванова движения жидкостей в деформируемых гетерогенных пористых средах. Комплексно учтены явления термического и химического осмоса, зависимости параметров фильтрации от теплового и химического состояний грунта, а также нелинейная зависимость коэффициента фильтрации от функции самых избыточных напоров. Впервые учтено явление термического расширения фаз грунта в уравнениях неразрывной при построении математических моделей фильтрационной консолидации гетерогенной пористой среды. Учтено влияние техногенных факторов при исследовании консолидации слоистых грунтов (природная неоднородность или случай постепенного строительства грунтового сооружения). Также исследованы процессы фильтрационной консолидации грунтов с тонкими полупроницаемыми включениями (включение из природных грунтов, которые имеют свойства полупроницаемых мембран). Предложено в условие сопряжения неидеального контакта для концентрации порового солевого раствора на данном включении внести «поправочный коэффициент», который с физической точки зрения означает степень идеальности полупроницаемого включения. Полученные результаты влияния полупроницаемого включения на фильтрационную консолидацию массива грунта в условиях присутствия техногенных факторов качественно согласовываются с наблюдением аномальных напоров и их перепадов в природных неоднородных геологических формациях. В диссертационном исследовании впервые удалось математически смоделировать это явление через использование в условиях сопряжения степени идеальности полупроницаемого включения. Полученные данные свидетельствуют об адекватности построенной математической модели естественным процессам. Получили дальнейшее развитие и эффективно использованы известные численные методы для отыскания приближенных решений соответствующих нелинейных краевых задач. В частности, это методы конечных разностей, конечных элементов и бессеточный метод радиальных базисных функций. Для численного решения нелинейных краевых задач в пространственном случае и в областях с подвижными границами адаптирован метод радиальных базисных функций. Для некоторых задач проведено сравнение приближенных решений, найденых разными численными методами. В целом, учет явлений тепло-солепереноса способствует более быстрому рассеиванию поля избыточных напоров в области возле дренированных границ и замедлению такого рассеивания в областях возле непроницаемых границ. Длительное воздействие техногенных факторов в областях дренированных границ приводит к переходу грунта в переуплотненное состояние (напоры становятся меньшими нуля). Такое состояние нельзя считать стабилизированным. Ведь прекращение действия техногенных факторов приведет к всасыванию поровой жидкости, а отсюда к набуханию грунта, что, в свою очередь, может вызывать неравномерные деформации его поверхности. Неравномерность полей температуры и концентрации химических веществ в поровой жидкости вызывает неравномерное оседание грунтовой поверхности. В диссертации, посредством численных экспериментов, установлены степени влияния каждого из факторов отдельно и в целом. Данные, полученные из компьютерного моделирования взаимных процессов фильтрационной консолидации и фильтрационного разрушения грунтов, засвидетельствовали возможность значительного влияния техногенных факторов на результаты прогнозных расчетов. Глубина и длина области размыва могут увеличиться на 34%-72% в зависимости от условий.
The thesis deals with the new mathematical models of mutual filtration consolidation process and filtration destruction of heterogeneous porous media (for example, soil) taking into account the effect of simultaneously operating processes of heat and salt transfer, chemical mass exchange processes, physical processes of soil subsidence and erosion, a multi-fraction contact suffusion, the presence of concentrated flow paths. Darcy-Gersevanov’s law of the fluid movement in deformable porous media was improved basing on the formalization of physical laws and phenomena of thermal and chemical osmosis, dependence of filtration parameters on the thermal and chemical state of the porous medium, nonlinear dependence of the filtration coefficient on the excessive pressures function. The phenomenon of thermal expansion of the soil phases was considered. Mathematical models were built and the processes of soils filtration consolidation with thin semi-permeable inclusions (natural soils inclusions that have properties of semi-permeable membranes) were investigated. In conjugation conditions it was proposed to use the ideality degree of semi-permeable inclusion. The kinematic boundary conditions on the moving boundaries of the soil domain were deduced taking into account the subsidence as a result of consolidation; soil erosion by flow path; subsidence as a result of multi-fraction contact suffusion. Powerful mesh and meshfree numerical methods were developed and used effectively to investigate the obtained nonlinear boundary value problems. Software was created on the basis of developed algorithms and a series of numerical experiments were done.
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Ghosh, Ashis Kumar. "Robust Least Squares Kinetic Upwind Method For Inviscid Compressible Flows." Thesis, 1996. http://etd.iisc.ernet.in/handle/2005/1570.

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Caputa, J. P. "Boundary conditions for vapor-solid interfaces in the context of vapor phase crystal growth by physical methods." Thesis, 2010. http://hdl.handle.net/1828/3620.

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Non-equilibrium boundary conditions based upon kinetic theory and linear irreversible thermodynamics are applied to the interface kinetics in vapor crystal growth of unitary and binary materials. These are compared to equilibrium boundary conditions in a simple, 1D closed ampoule physical vapor transport model. It is found that in cases where the diffusive impedance is negligible and when system pressure is low, surface kinetics play an important role in limiting the mass transport. In cases where diffusion is the dominant transport impedance, and/or when the pressure in the system is high, the kinetic impedances at the interfaces are negligible, as impedances due to diffusion and latent heat transport at the interfaces become more significant. The non-equilibrium boundary conditions are dependent upon the sticking coefficient of the surface. An experiment to estimate the sticking coefficient on solid surfaces is proposed. The non-equilibrium theory also predicts significant temperature jumps at the interfaces.
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Taheri, Bonab Peyman. "Macroscopic description of rarefied gas flows in the transition regime." Thesis, 2010. http://hdl.handle.net/1828/3018.

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The fast-paced growth in microelectromechanical systems (MEMS), microfluidic fabrication, porous media applications, biomedical assemblies, space propulsion, and vacuum technology demands accurate and practical transport equations for rarefied gas flows. It is well-known that in rarefied situations, due to strong deviations from the continuum regime, traditional fluid models such as Navier-Stokes-Fourier (NSF) fail. The shortcoming of continuum models is rooted in nonequilibrium behavior of gas particles in miniaturized and/or low-pressure devices, where the Knudsen number (Kn) is sufficiently large. Since kinetic solutions are computationally very expensive, there has been a great desire to develop macroscopic transport equations for dilute gas flows, and as a result, several sets of extended equations are proposed for gas flow in nonequilibrium states. However, applications of many of these extended equations are limited due to their instabilities and/or the absence of suitable boundary conditions. In this work, we concentrate on regularized 13-moment (R13) equations, which are a set of macroscopic transport equations for flows in the transition regime, i.e., Kn≤1. The R13 system provides a stable set of equations in Super-Burnett order, with a great potential to be a powerful CFD tool for rarefied flow simulations at moderate Knudsen numbers. The goal of this research is to implement the R13 equations for problems of practical interest in arbitrary geometries. This is done by transformation of the R13 equations and boundary conditions into general curvilinear coordinate systems. Next steps include adaptation of the transformed equations in order to solve some of the popular test cases, i.e., shear-driven, force-driven, and temperature-driven flows in both planar and curved flow passages. It is shown that inexpensive analytical solutions of the R13 equations for the considered problems are comparable to expensive numerical solutions of the Boltzmann equation. The new results present a wide range of linear and nonlinear rarefaction effects which alter the classical flow patterns both in the bulk and near boundary regions. Among these, multiple Knudsen boundary layers (mechanocaloric heat flows) and their influence on mass and energy transfer must be highlighted. Furthermore, the phenomenon of temperature dip and Knudsen paradox in Poiseuille flow; Onsager's reciprocity relation, two-way flow pattern, and thermomolecular pressure difference in simultaneous Poiseuille and transpiration flows are described theoretically. Through comparisons it is shown that for Knudsen numbers up to 0.5 the compact R13 solutions exhibit a good agreement with expensive solutions of the Boltzmann equation.
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Books on the topic "Kinetic Boundary Condition"

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Sensitivity of combustion-acoustic instabilities to boundary conditions for premixed gas turbinecombustors. [Washington, DC]: National Aeronautics and Space Administration, 1995.

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Escudier, Marcel. Kinematic description of fluids in motion and approximations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198719878.003.0006.

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In this chapter some of the terminology and simplifications which enable us to begin to describe and analyse practical fluid-flow problems are introduced. The terms ‘fluid particle’ and ‘streamline’ are defined. The principle of conservation of mass applied to steady one-dimensional flow through a streamtube of varying cross-sectional area resulted in the continuity equation. This important equation relates mass flowrate ṁ, volumetric flowrate Q̇, average fluid velocity V̄, fluid density ρ‎, and cross-sectional area A: m = ρ‎ Q̇ = ρ‎AV̅ = constant. For a constant-density fluid this result shows that fluid velocity increases if the cross-sectional area decreases, and vice versa. The no-slip boundary condition, a consequence of which is the boundary layer, is introduced.
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Book chapters on the topic "Kinetic Boundary Condition"

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Wu, Lei. "Accuracy of Kinetic Boundary Condition." In Rarefied Gas Dynamics, 195–207. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-2872-7_11.

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Fujikawa, Shigeo, Takeru Yano, and Masao Watanabe. "Kinetic Boundary Condition at the Interface." In Heat and Mass Transfer, 19–69. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-18038-5_2.

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Bazaliy, B. V., and S. P. Degtyarev. "The Classical Stefan Problem as the Limit Case of the Stefan Problem with a Kinetic Condition at the Free Boundary." In Free Boundary Problems in Continuum Mechanics, 83–90. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-8627-7_9.

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Aoki, K., and Y. Sone. "Gas Flows Around the Condensed Phase with Strong Evaporation or Condensation — Fluid Dynamic Equation and Its Boundary Condition on the Interface and Their Application —." In Advances in Kinetic Theory and Continuum Mechanics, 43–54. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-50235-4_5.

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Sekhar, P. Chandra, A. K. Ghosh, and S. M. Deshpande. "Development of a New Higher Order Kinetic Boundary Condition and a New Algorithm for Moving Grid Using q-LSKUM." In Computational Fluid Dynamics 2000, 723–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56535-9_110.

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Rebosio, F., A. Widenhorn, B. Noll, and M. Aigner. "Analysis of the Effects of Wall Boundary Conditions and Detailed Kinetics on the Simulation of a Gas Turbine Model Combustor Under Very Lean Conditions." In High Performance Computing in Science and Engineering '11, 229–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-23869-7_18.

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"Kinematic boundary conditions." In Hydrodynamics of Ship Propellers, 42–45. Cambridge University Press, 1993. http://dx.doi.org/10.1017/cbo9780511624254.005.

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"Realistic Kinetic Boundary Conditions at Surfaces." In Rarefied Gas Dynamics: Experimental Techniques and Physical Systems, 554–62. Washington DC: American Institute of Aeronautics and Astronautics, 1994. http://dx.doi.org/10.2514/5.9781600866302.0554.0562.

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Kraus, Eric B., and Joost A. Businger. "Atmospherically Forced Perturbations in the Oceans." In Atmosphere-Ocean Interaction. Oxford University Press, 1995. http://dx.doi.org/10.1093/oso/9780195066180.003.0011.

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Kinetic energy flows almost exclusively downward, from the atmosphere into the ocean. The upward flux of energy is thermal, and that will be the topic of our concluding chapter. In the present chapter, we shall deal with the effects of kinetic energy inputs into the ocean. Although this requires some discussion of the different types of oceanic perturbations, our treatment of these topics is necessarily brief and incomplete. We are not concerned with details of the motion pattern in the deeper ocean or with processes involving friction and non-adiabatic mixing in the interior. These processes are essential for an understanding of ocean circulations. They are treated in general oceanographic textbooks and in many monographs that deal specifically with these subjects. Surface stress and air pressure variations produce surface wind waves along with a variety of other wave forms. Most of these waves are relatively slow, with periods that can be measured in hours, days, or even years. The amplitude of internal gravity waves in the oceans is often much larger than that of surface waves and their wavelengths tend to be in the kilometer range. The square of the amplitude-wavenumber product is usually a very small quantity. This makes first order approximations appropriate for many purposes. It justifies use of the hydrostatic approximation and of the linear equations as a basis for the following discussion. To do so, it is necessary to represent the unspecified forcing terms on the right-hand side of those equations in a linearized form. An algorithm for the inclusion of the various atmospheric inputs as a linearized boundary condition in the equations of motion for the ocean is discussed in Section 7.1. Section 7.2 describes a two-layer ocean model. Systems of this type are convenient for the conceptual consideration of atmosphere-ocean interactions, because the wind affects the ocean primarily through action upon the surface mixed-layer. Internal waves, the topic of Section 7.3, are ubiquitous both in the ocean and in the atmosphere. Essentially, sea surface gravity waves can be viewed as internal waves at the interface between two fluids of very unequal density.
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"Plane Strain Problems with Continuous Kinematic Boundary Conditions." In Problems of Technological Plasticity, 315–56. Elsevier, 1994. http://dx.doi.org/10.1016/b978-0-444-81646-7.50018-x.

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Conference papers on the topic "Kinetic Boundary Condition"

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Sugimoto, Hiroshi, and Kenjiro Amakawa. "Effect of kinetic boundary condition on the thermal transpiration coefficient." In PROCEEDINGS OF THE 29TH INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4902625.

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Qazi Zade, Azad, Metin Renksizbulut, and Jacob Friedman. "Boundary Conditions for Multi-Component Slip-Flows Based on the Kinetic Theory of Gases." In ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2008. http://dx.doi.org/10.1115/icnmm2008-62178.

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General temperature-jump, velocity-slip, and concentration-jump conditions on solid surfaces in rarefied multi-component gas flows are developed using the kinetic theory of gases. The presented model provides general boundary conditions which can be simplified according to the problem under consideration. In some limiting cases, the results of the current work are compared to the previously available and widely used boundary conditions reported in the literature. The details of the mathematical procedure are also provided to give a better insight about the physical importance of each term in the slip/jump boundary conditions. Also the disagreements between previously reported results are investigated to arrive at the most proper expressions for the slip/jump boundary conditions. The temperature-jump boundary condition is also modified to handle polyatomic gas flows unlike previously reported studies which were mostly concerned with monatomic gases.
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Durocher, Antoine, Jiayi Wang, Gilles Bourque, and Jeffrey M. Bergthorson. "Impact of Boundary Condition and Kinetic Parameter Uncertainties on NOx Predictions in Methane-Air Stagnation Flame Experiments." In ASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/gt2021-59404.

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Abstract A comprehensive understanding of uncertainty sources in experimental measurements is required to develop robust thermochemical models for use in industrial applications. Due to the complexity of the combustion process in gas turbine engines, simpler flames are generally used to study fundamental combustion properties and measure concentrations of important species to validate and improve modelling. Stable, laminar flames have increasingly been used to study nitrogen oxide (NOx) formation in lean-to-rich compositions in low-to-high pressures to assess model predictions and improve accuracy to help develop future low-emissions systems. They allow for non-intrusive diagnostics to measure sub-ppm concentrations of pollutant molecules, as well as important precursors, and provide well-defined boundary conditions to directly compare experiments with simulations. The uncertainties of experimentally-measured boundary conditions and the inherent kinetic uncertainties in the nitrogen chemistry are propagated through one-dimensional stagnation flame simulations to quantify the relative importance of the two sources and estimate their impact on predictions. Measurements in lean, stoichiometric, and rich methane-air flames are used to investigate the production pathways active in those conditions. Various spectral expansions are used to develop surrogate models with different levels of accuracy to perform the uncertainty analysis for 15 important reactions in the nitrogen chemistry and the 6 boundary conditions (ϕ, Tin, uin, du/dzin, Tsurf, P) simultaneously. After estimating the individual parametric contributions, the uncertainty of the boundary conditions are shown to have a relatively small impact on the prediction of NOx compared to kinetic uncertainties in these laboratory experiments. These results show that properly calibrated laminar flame experiments can, not only provide validation targets for modelling, but also accurate indirect measurements that can later be used to infer individual kinetic rates to improve thermochemical models.
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Jambunathan, Revathi, and Deborah Levin. "A New Self-Consistent Boundary Condition for Modeling of Plasma Plume Evolution Using a Fully Kinetic Pic Approach." In 2018 IEEE International Conference on Plasma Science (ICOPS). IEEE, 2018. http://dx.doi.org/10.1109/icops35962.2018.9575757.

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Ishiyama, Tatsuya, Takeru Yano, and Shigeo Fujikawa. "Determination of Condensation Coefficient and Boundary Condition for Kinetic Theory of Gases by Molecular Dynamics Simulations of Evaporation of Argon Into Vacuum." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45021.

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Molecular dynamics simulations at liquid-vapor equilibrium condition and evaporation condition into vacuum were carried out to investigate the boundary condition for the kinetic theory of gases. The determination method for condensation coefficient α consistent with the kinetic theory is also proposed. It was found that α for argon at an equilibrium state is close to unity near the triple point temperature of the bulk liquid, and decreases gradually as the temperature rises. The velocity distribution of molecules evaporating into vacuum becomes nearly half-Maxwellian near the triple point temperature, and is deformed as the temperature rises.
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Walla, Nicholas J., Vitalis Anisiuba, Armin K. Silaen, Alexandra Anderson, Joseph Grogan, and Chenn Q. Zhou. "Boundary Conditions for Modeling of a Lead Reverberatory Furnace." In ASME 2022 Heat Transfer Summer Conference collocated with the ASME 2022 16th International Conference on Energy Sustainability. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/ht2022-81206.

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Abstract The use of lead reverberatory furnaces is a common part of the lead recycling process, wherein a solid feed material comprising various lead compounds is directly exposed to combustive and radiative heat sources to melt the feed material and produce lead product. Furnace design decisions ranging from burner inputs to burner placement and furnace shape are difficult to trial without risking costly losses in productivity. The use of modern computational fluid dynamics approaches can allow for more-accurate modeling of the reverberatory furnace process. A steady state simulation of the reverberatory furnace has been created for this purpose. The direct modeling of the melting and smelting reactions is bypassed as this effort would be very computationally expensive and require detailed kinetic data, a large portion of which is unknown. However, as these reactions are largely endothermic, their influence on the overall temperature profile of the furnace cannot be ignored and is critical to both validation and usefulness of the model. To this end, a multi-variable artificial heat sink boundary condition has been placed on several key boundary surfaces within the furnace for the purpose of representing the heat consumption caused by the melting and smelting reactions. This boundary condition is tuned through parameter adjustment in the base study until the temperature profile matches sample data taken from furnace operation measurements.
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Ishiyama, Tatsuya. "Molecular dynamics study on the evaporation part of the kinetic boundary condition at the interface between water and water vapor." In RAREFIED GAS DYNAMICS: 24th International Symposium on Rarefied Gas Dynamics. AIP, 2005. http://dx.doi.org/10.1063/1.1941584.

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Kryukov, A. P., and A. K. Yastrebov. "Vapor Condensation at Sudden Contact With Cold Liquid in Non-Equilibrium Conditions." In 2010 14th International Heat Transfer Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ihtc14-22625.

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Condensation of saturated vapor at sudden contact with cold liquid was studied with use of numerical solution of the Boltzmann kinetic equation. Results were obtained for both constant and variable temperature of liquid. In the first case vapor condensation becomes stationary after very small time; in the second one this process can not be stationary due to used model of heat transfer in liquid. Possibility of use of stationary kinetic correlations was estimated. For both cases results of numerical solution are in good agreement with correlation proposed by D.A. Labuntsov and A.P. Kryukov. Therefore, this correlation can be used as non-equilibrium boundary condition at solution of applied problems.
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Nacer, M. Hadj, Pierre Perrier, and Irina Graur. "Mass Flow Rate Measurement Through Rectangular Microchannels for Large Knudsen Number Range." In ASME 2011 9th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2011. http://dx.doi.org/10.1115/icnmm2011-58167.

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The mass flow rate through microchannels with rectangular cross section is measured for the wide Knudsen number range (0.0025–26.2) in isothermal steady conditions. The experimental technique called ‘Constant Volume Method’ is used for the measurements. This method consists of measuring the small pressure variations in the tanks upstream and downstream of the microchannel. The measurements of the mass flow rate are carried out for three gases (Helium, Nitrogen and Argon). The microchannel internal surfaces are covered with a thin layer of gold with mean roughness Ra = 0.87nm (RMS). The continuum approach (Navier-Stokes equations) with first order velocity slip boundary condition was used in the slip regime (Knudsen number varies from 0.0025 to 0.1) to obtain the experimental velocity slip and accommodation coefficients associated to the Maxwell kinetic boundary condition. In the transitional and near free molecular regimes the linearized kinetic BGK model was used to calculate numerically the mass flow rate. From the comparison of the numerical and measured values of the mass flow rate the accommodation coefficient was also deduced.
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Darbandi, Masoud, and Shidvash Vakilipour. "Numerical Study of Flow and Heat in Long Micro and Nano Channels." In ASME 2008 First International Conference on Micro/Nanoscale Heat Transfer. ASMEDC, 2008. http://dx.doi.org/10.1115/mnht2008-52077.

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In this work, we extend a numerical tool capable of solving compressible and incompressible gas flows to study the momentum and heat transfer rates in micro/nano channels with high aspect ratio (L/H = 8000), where the compressibility effect is dominant. The constant heat flux thermal boundary condition is firstly applied at the wall. Next, the flow regime is extended to the early transition regime employing a high order slip velocity boundary condition based on the kinetic theory assumptions. The accuracy of the present results in the slip flow regimes is evaluated against other available theoretical and experimental results. The thermal and compressibility effects on the pressure and Knudsen number distribution are extensively studied along the channel at early transition regimes up to Kn = 0.5. Likely, this Knudsen is the highest one to be reached via applying the foregoing boundary conditions.
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Reports on the topic "Kinetic Boundary Condition"

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Richman, M. W. (Kinetic theory and boundary conditions for flows of highly inelastic spheres). Office of Scientific and Technical Information (OSTI), January 1991. http://dx.doi.org/10.2172/5667699.

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Richman, M. W. Kinetic theory and boundary conditions for flows of highly inelastic spheres. Office of Scientific and Technical Information (OSTI), January 1991. http://dx.doi.org/10.2172/6248822.

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Dorfman, S., W. Daughton, V. Roytershteyn, H. Ji, Y. Ren, and M. Yamada. Two-dimensional Fully Kinetic Simulations Of Driven Magnetic Reconnection With Boundary Conditions Relevant To The Magnetic Reconnection Experimen. Office of Scientific and Technical Information (OSTI), November 2008. http://dx.doi.org/10.2172/941511.

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Richman, M. [Kinetic theory and boundary conditions for highly inelastic spheres]. Quarterly progress report, July 1, 1993--September 30, 1993. Office of Scientific and Technical Information (OSTI), December 1993. http://dx.doi.org/10.2172/10117715.

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Richman, M. [Kinetic theory and boundary conditions for highly inelastic spheres]. Quarterly progress report, September 1, 1992--December 31, 1992. Office of Scientific and Technical Information (OSTI), December 1992. http://dx.doi.org/10.2172/10117951.

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Richman, M. [Kinetic theory and boundary conditions for highly inelastic spheres]. Quarterly progress report, April 1, 1993--June 30, 1993. Office of Scientific and Technical Information (OSTI), December 1993. http://dx.doi.org/10.2172/10117962.

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Richman, M. W. [Kinetic theory and boundary conditions for flows of highly inelastic spheres]. Quarterly progress report, October 1, 1991--December 31, 1991. Office of Scientific and Technical Information (OSTI), December 1991. http://dx.doi.org/10.2172/10141570.

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Richman, M. Kinetic theory and boundary conditions for flows of highly inelastic spheres. Quarterly progress report, January 1, 1994--March 31, 1994. Office of Scientific and Technical Information (OSTI), December 1994. http://dx.doi.org/10.2172/102298.

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Richman, M. Kinetic theory and boundary conditions for flows of highly inelastic spheres. Quarterly progress report, July 1, 1994--September 30, 1994. Office of Scientific and Technical Information (OSTI), December 1994. http://dx.doi.org/10.2172/102334.

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Richman, M. Kinetic theory and boundary conditions for flows of highly inelastic spheres. Quarterly progress report, April 1, 1995--June 30, 1995. Office of Scientific and Technical Information (OSTI), September 1995. http://dx.doi.org/10.2172/102338.

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