Journal articles: '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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6

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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7

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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10

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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11

Kon, Misaki, Kazumichi Kobayashi, and Masao Watanabe. "Liquid temperature dependence of kinetic boundary condition at vapor–liquid interface." International Journal of Heat and Mass Transfer 99 (August 2016): 317–26. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.03.088.

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12

Besse, Christophe, Saja Borghol, Thierry Goudon, Ingrid Lacroix-Violet, and Jean-Paul Dudon. "Hydrodynamic Regimes, Knudsen Layer, Numerical Schemes: Definition of Boundary Fluxes." Advances in Applied Mathematics and Mechanics 3, no. 5 (October 2011): 519–61. http://dx.doi.org/10.4208/aamm.10-m1041.

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AbstractWe propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime. The typical example we discuss is the derivation of the Euler system from the BGK equation. The boundary condition relies on the analysis of boundary layers formation that accounts from the fact that the incoming kinetic flux might be far from the thermodynamic equilibrium.

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13

Frankel, M. L., and V. Roytburd. "Finite-dimensional attractors for a free boundary problem with a kinetic condition." Applied Mathematics Letters 15, no. 1 (January 2002): 83–87. http://dx.doi.org/10.1016/s0893-9659(01)00097-0.

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14

Shen, Sheng, Gang Chen, Robert M. Crone, and Manuel Anaya-Dufresne. "A kinetic-theory based first order slip boundary condition for gas flow." Physics of Fluids 19, no. 8 (August 2007): 086101. http://dx.doi.org/10.1063/1.2754373.

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15

Neustupa, Tomáš, and Ondřej Winter. "ON THE SENSITIVITY OF THE NONLINEAR TERM IN THE OUTFLOW BOUNDARY CONDITION." Acta Polytechnica 61, SI (February 10, 2021): 117–21. http://dx.doi.org/10.14311/ap.2021.61.0117.

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This paper studies the artificial outflow boundary condition for the Navier-Stokes system. This type of condition is widely used and it is therefore very important to study its influence on a numerical solution of the corresponding boundary-value problem. We particularly focus on the role of the coefficient in front of the nonlinear term in the boundary condition on the outflow. The influence of this term is examined numerically, comparing the obtained results in a close neighbourhood of the outflow. The numerical experiment is carried out for a fluid flow through the channel with so called sudden extension. Presented numerical results are obtained by means of the OpenFOAM toolbox. They confirm that the kinetic energy of the flow in the channel can be controlled by means of the proposed boundary condition.

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Ren, Junjie, Ping Guo, and Zhaoli Guo. "Rectangular Lattice Boltzmann Equation for Gaseous Microscale Flow." Advances in Applied Mathematics and Mechanics 8, no. 2 (April 2014): 306–30. http://dx.doi.org/10.4208/aamm.2014.m672.

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AbstractThe lattice Boltzmann equation (LBE) is considered as a promising approach for simulating flows of liquid and gas. Most of LBE studies have been devoted to regular square LBE and few works have focused on the rectangular LBE in the simulation of gaseous microscale flows. In fact, the rectangular LBE, as an alternative and efficient method, has some advantages over the square LBE in simulating flows with certain computational domains of large aspect ratio (e.g., long micro channels). Therefore, in this paper we expand the application scopes of the rectangular LBE to gaseous microscale flow. The kinetic boundary conditions for the rectangular LBE with a multiple-relaxation-time (MRT) collision operator, i.e., the combined bounce-back/specular-reflection (CBBSR) boundary condition and the discrete Maxwell's diffuse-reflection (DMDR) boundary condition, are studied in detail. We observe some discrete effects in both the CBBSR and DMDR boundary conditions for the rectangular LBE and present a reasonable approach to overcome these discrete effects in the two boundary conditions. It is found that the DMDR boundary condition for the square MRT-LBE can not realize the real fully diffusive boundary condition, while the DMDR boundary condition for the rectangular MRT-LBE with the grid aspect ratio a≠1 can do it well. Some numerical tests are implemented to validate the presented theoretical analysis. In addition, the computational efficiency and relative difference between the rectangular LBE and the square LBE are analyzed in detail. The rectangular LBE is found to be an efficient method for simulating the gaseous microscale flows in domains with large aspect ratios.

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17

Dillman, Charles J., Tricia A. Murray, and Robert A. Hintermeister. "Biomechanical Differences of Open and Closed Chain Exercises with Respect to the Shoulder." Journal of Sport Rehabilitation 3, no. 3 (August 1994): 228–38. http://dx.doi.org/10.1123/jsr.3.3.228.

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Confusion of the terms open and closed kinetic chain and scarcity of research comparing kinetic chain exercises that have similar mechanics and loading prompted this case study. Exercises were classified by the boundary condition of the distal segment and presence of an external load. Classifications included a fixed boundary condition with an external load (FEL), a movable boundary with an external load (MEL), and a movable boundary with no external load (MNL). It was hypothesized that if the direction and mass of loading in MEL and FEL exercises were similar, the electromyographic activity of the primary muscle groups involved would be comparable. Muscular activity was monitored from six shoulder muscles during one MNL, four MEL, and five FEL exercises. The results indicated that MEL and FEL exercises having similar biomechanics produced comparable muscular activity. Evaluation and selection of exercises for patients should be based upon mechanics and loading that achieve appropriate muscle activity.

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18

GUAN, ZHICHENG, and XU-JIA WANG. "Critical exponent in a Stefan problem with kinetic condition." European Journal of Applied Mathematics 8, no. 5 (October 1997): 525–32. http://dx.doi.org/10.1017/s0956792597003215.

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In this paper we deal with the one-dimensional Stefan problemut−uxx =s˙(t)δ(x−s(t)) in ℝ ;× ℝ+, u(x, 0) =u0(x)with kinetic condition s˙(t)=f(u) on the free boundary F={(x, t), x=s(t)}, where δ(x) is the Dirac function. We proved in [1] that if [mid ]f(u)[mid ][les ]Meγ[mid ]u[mid ] for some M>0 and γ∈(0, 1/4), then there exists a global solution to the above problem; and the solution may blow up in finite time if f(u)[ges ] Ceγ1[mid ]u[mid ] for some γ1 large. In this paper we obtain the optimal exponent, which turns out to be √2πe. That is, the above problem has a global solution if [mid ]f(u)[mid ][les ]Meγ[mid ]u[mid ] for some γ∈(0, √2πe), and the solution may blow up in finite time if f(u)[ges ] Ce√2πe[mid ]u[mid ].

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Mao, X., H. M. Blackburn, and S. J. Sherwin. "Optimal inflow boundary condition perturbations in steady stenotic flow." Journal of Fluid Mechanics 705 (March 1, 2012): 306–21. http://dx.doi.org/10.1017/jfm.2012.58.

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AbstractWe determine optimal inflow boundary perturbations to steady flow through a straight inflexible tube with a smooth axisymmetric stenosis at a bulk-flow Reynolds number $\mathit{Re}= 400$, for which the flow is asymptotically stable. The perturbations computed produce an optimal gain, i.e. kinetic energy in the domain at a given time horizon normalized by a measure of time-integrated energy on the inflow boundary segment. We demonstrate that similarly to the optimal initial condition problem, the gain can be interpreted as the leading singular value of the forward linearized operator that evolves the boundary conditions to the final state at a fixed time. In this investigation we restrict our attention to problems where the temporal profile of the perturbations examined is a product of a Gaussian bell and a sinusoid, whose frequency is selected to excite axial wavelengths similar to those of the optimal initial perturbations in the same geometry. Comparison of the final state induced by the optimal boundary perturbation with that induced by the optimal initial condition demonstrates a close agreement for the selected problem. Previous works dealing with optimal boundary perturbation considered a prescribed spatial structure and computed an optimal temporal variation of a wall-normal velocity component, whereas in this paper we consider the problem of a prescribed temporal structure and compute the optimal spatial variation of velocity boundary conditions over a one-dimensional inflow boundary segment. The methodology is capable of optimizing boundary perturbations in general non-parallel two- and three-dimensional flows.

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Jambunathan, Revathi, and Deborah A. Levin. "A Self-Consistent Open Boundary Condition for Fully Kinetic Plasma Thruster Plume Simulations." IEEE Transactions on Plasma Science 48, no. 3 (March 2020): 610–30. http://dx.doi.org/10.1109/tps.2020.2968887.

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21

Wu, Lei, and Henning Struchtrup. "Assessment and development of the gas kinetic boundary condition for the Boltzmann equation." Journal of Fluid Mechanics 823 (June 21, 2017): 511–37. http://dx.doi.org/10.1017/jfm.2017.326.

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Gas–surface interactions play important roles in internal rarefied gas flows, especially in micro-electro-mechanical systems with large surface area to volume ratios. Although great progress has been made to solve the Boltzmann equation, the gas kinetic boundary condition (BC) has not been well studied. Here we assess the accuracy of the Maxwell, Epstein and Cercignani–Lampis BCs, by comparing numerical results of the Boltzmann equation for the Lennard–Jones potential to experimental data on Poiseuille and thermal transpiration flows. The four experiments considered are: Ewart et al. (J. Fluid Mech., vol. 584, 2007, pp. 337–356), Rojas-Cárdenas et al. (Phys. Fluids, vol. 25, 2013, 072002) and Yamaguchi et al. (J. Fluid Mech., vol. 744, 2014, pp. 169–182; vol. 795, 2016, pp. 690–707), where the mass flow rates in Poiseuille and thermal transpiration flows are measured. This requires that the BC has the ability to tune the effective viscous and thermal slip coefficients to match the experimental data. Among the three BCs, the Epstein BC has more flexibility to adjust the two slip coefficients, and hence for most of the time it gives good agreement with the experimental measurements. However, like the Maxwell BC, the viscous slip coefficient in the Epstein BC cannot be smaller than unity but the Cercignani–Lampis BC can. Therefore, we propose to combine the Epstein and Cercignani–Lampis BCs to describe gas–surface interaction. Although the new BC contains six free parameters, our approximate analytical expressions for the viscous and thermal slip coefficients provide useful guidance to choose these parameters.

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Zhao, Xinran, and Mehrdad Massoudi. "Flow of granular materials with slip boundary condition: A continuum–kinetic theory approach." Applied Mathematics and Computation 242 (September 2014): 518–27. http://dx.doi.org/10.1016/j.amc.2014.05.093.

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23

Kamali, R., A. Kharazmi, and M. Akbari. "A Kinetic Theory-Based First-Order Slip Boundary Condition for Gas Micro/Nano-Flows with Heat Transfer." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224, no. 11 (April 27, 2010): 2390–95. http://dx.doi.org/10.1243/09544062jmes2182.

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A kinetic theory-based first-order slip boundary condition for micro/nano-gas flows with heat transfer is presented analytically using the Chapman—Enskog solution of the Boltzmann equation. This slip model is investigated by studying heat transfer for laminar Newtonian fluid in a Poiseuille flow. The problem is solved for two different thermal boundary conditions, namely, constant heat flux and constant wall temperature with different Knudsen numbers. The interactive effects of the Knudsen number on the Nusselt numbers are determined analytically, and for both cases, the temperature profile and the Nusselt number are compared with previous published results.

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EL GHANI, NAJOUA. "ASYMPTOTIC ANALYSIS FOR A VLASOV–NAVIER–STOKES SYSTEM IN A BOUNDED DOMAIN." Journal of Hyperbolic Differential Equations 07, no. 02 (June 2010): 191–210. http://dx.doi.org/10.1142/s0219891610002098.

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This article is devoted to the asymptotic analysis of a Vlasov–Navier–Stokes system in dimension two, and treat general initial data with finite mass, energy and entropy. The limit problem is the Navier–Stokes system with non-constant density. The convergence result is proved in a bounded domain of ℝ2with a homogeneous Dirichlet boundary condition on the fluid velocity field and Maxwell boundary condition on the kinetic distribution function, while the proof relies on a relative entropy method.

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Pereira, Gerald G. "Numerical Modelling of Reactive Flows through Porous Media." Geosciences 12, no. 4 (March 28, 2022): 153. http://dx.doi.org/10.3390/geosciences12040153.

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We consider a lattice Boltzmann (LB) model to solve the coupled Navier–Stokes and advection–diffusion equation with reactive boundary conditions at the interface between fluid and solid domains. The reactive boundary condition results in the position of the boundary changing continuously, and so boundary nodes may be partially filled with fluid at any instant. We develop the LB boundary conditions for both the velocity and concentration fields in the presence of partially filled boundary nodes and then validate this algorithm on some test cases—the Stefan problem for diffusion-dominated dissolution and kinetic-dominated dissolution. It is shown that the developed model agrees well with analytic results, so that they can be used for more general boundaries of arbitrary shape. Numerical simulations in three dimensions are then carried out on demonstration problems at various Peclet numbers to elucidate the transport mechanisms and their influence on solid grain dissolution.

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Onishi, Yoshimoto. "The spherical-droplet problem of evaporation and condensation in a vapour-gas mixture." Journal of Fluid Mechanics 163 (February 1986): 171–94. http://dx.doi.org/10.1017/s0022112086002264.

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The behaviour of a binary mixture of a vapour and an inert gas around the spherical condensed-phase droplet is studied analytically using kinetic theory. By the singular-perturbation method, the linearized Boltzmann equation of B–G–K type is first solved for problems with spherical symmetry under the diffusive boundary condition when the Knudsen number of the problem is small. The macroscopic equations and the appropriate boundary conditions in the form of the temperature and partial-pressure jumps on the interface between the droplet and the gas phase, which enable us to treat the problems at the level of ordinary fluid dynamics, are derived together with the Knudsen-layer structure formed near the interface. Then the velocity, temperature and pressure fields around the droplet are explicitly obtained, as well as the mass, heat and energy flows from it. The results obtained are capable of describing the transition from the diffusion-control to the kinetic-control mechanism in the mass-transfer process. The negative-temperature-gradient phenomenon, a common phenomenon for pure-vapour cases (absence of inert gas), is also possible, manifesting itself more easily as the kinetic-control mechanism becomes prevalent and the critical condition for its existence is given. The present analysis could be applied to other problems with spherical symmetry as well.

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Le, Nam TP, Nam H. Tran, Thoai N. Tran, and Toan T. Tran. "New slip boundary condition in high-speed rarefied gas flow simulations." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 234, no. 3 (November 6, 2019): 840–56. http://dx.doi.org/10.1177/0954410019886955.

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In this paper, we propose a new slip boundary condition in hypersonic gas flow simulations. It is derived by considering the Langmuir isotherm adsorption into the Kaniadarkis et al. model of the kinetic theory of gas. Moreover, the motion of the adsorbed molecules over the surface (i.e. surface diffusion) is considered for the calculation of the mean free path in new slip condition. Three aerodynamic configurations are selected for evaluating new slip condition such as (1) the sharp-leading-edge flat plate, (2) circular cylinder in cross-flow, and (3) the sharp 25°–55° biconic cases. Hypersonic gas flows have the Mach number ranging from 6.1 to 15.6, and the working gases are argon and nitrogen. The simulation results show that new slip condition predicts better slip velocity than the Maxwell slip condition and gives good agreement with the direct simulation Monte-Carlo data for all cases considered in the present work.

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Lu, Guo Yun, and Shan Yuan Zhang. "Elastic-Plastic Dynamic Response of the Tube with Free Boundary Condition Subjected to Impact." Key Engineering Materials 340-341 (June 2007): 263–68. http://dx.doi.org/10.4028/www.scientific.net/kem.340-341.263.

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Some experimental results of the free-free tubes laterally impacted by the missile were given and the finite element program LS-DYNA was used to simulate this dynamic response process. The instantaneous deformation of the circular shell given by experiments and computer simulation were compared and discussed. It can be seen that when the impact occur the local dents firstly appear at the beginning of impact. With time increase, the depth of the dents increase, the scope of the deformation of the tube wall is enlarged; the total stiffness of the cross-section of the tube is weaken and decreases at the impact point, the beam-like bending deformation take place and the rigid-body translations occur. Through the computer simulation the exchanged energy between the missile and the tube were acquired. The impact energy of the missile is transferred to internal energy and kinetic energy of the tube. The ratio of the internal energy with the kinetic energy of the tube is great for the weakness rigidity of the tube wall, which is opposite to that of a free-free beam. This research made us deeply understand the character of the response when studying the elastic-plastic behavior of the free circular shell under intense dynamic loading.

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Germider, O. V., and V. N. Popov. "A collocation method for the Williams equation with Chebyshev polynomials." Journal of Physics: Conference Series 2056, no. 1 (October 1, 2021): 012005. http://dx.doi.org/10.1088/1742-6596/2056/1/012005.

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Abstract The linearized problem of gas flow in plane channel with infinite walls has been solved in the kinetic approximation. The flow in the channel is caused by a constant pressure gradient parallel to the walls of the channel. The Williams equation has been used as a basic equation, and the boundary condition has been set in terms of the diffuse reflection model. The collocation method for Chebyshev polynomials has been applied to construct the solution of the equation of Williams with the given boundary conditions. The mass flux of the gas in the channel has been calculated.

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Ren, Junjie, Shengzhen Wang, and Xiaoxue Liu. "A modified lattice Boltzmann model for microcylindrical Couette gas flows." Physica Scripta 97, no. 8 (June 27, 2022): 085201. http://dx.doi.org/10.1088/1402-4896/ac7910.

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Abstract We develop an axisymmetric lattice Boltzmann (LB) model to simulate microcylindrical Couette gas flows (MCGF) in the slip regime and transition regime, respectively. A kinetic boundary scheme in the cylindrical coordinate system is proposed to fulfill the second-order slip boundary condition at the cylindrical wall. To consider the effect of the Knudsen layers for transition flows, local effective Knudsen numbers are introduced into the kinetic boundary scheme and relaxation time. Numerical tests are executed to acquire the velocity distributions of the time-independent and time-dependent MCGF. Comparisons with the analytical solution and direct Monte Carlo data are also implemented. The simulation results demonstrate that the developed LB model can successfully acquire the velocity distribution of the MCGF with an intermediate Knudsen number in the transition regime.

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Sanchez, Richard, and Lahbib Bourhrara. "Existence Result for the Kinetic Neutron Transport Problem with a General Albedo Boundary Condition." Transport Theory and Statistical Physics 40, no. 2 (September 2011): 69–84. http://dx.doi.org/10.1080/00411450.2011.596607.

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Kon, Misaki, Kazumichi Kobayashi, and Masao Watanabe. "Kinetic boundary condition in vapor–liquid two-phase system during unsteady net evaporation/condensation." European Journal of Mechanics - B/Fluids 64 (July 2017): 81–92. http://dx.doi.org/10.1016/j.euromechflu.2016.12.001.

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Бурмашева, Н. В., Е. А. Ларина, and Е. Ю. Просвиряков. "ТЕЧЕНИЕ ТИПА КУЭТТА С УЧЕТОМ ИДЕАЛЬНОГО СКОЛЬЖЕНИЯ НА КОНТАКТЕ С ТВЕРДОЙ ПОВЕРХНОСТЬЮ." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 74 (2021): 79–94. http://dx.doi.org/10.17223/19988621/74/9.

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On the basis of a system of hydrodynamic equations, the unidirectional steady flow of a viscous incompressible fluid in a horizontal extended layer is studied. The solution to the governing equations is discovered in a distinguished class of functions that are linear in coordinates. The contact of the fluid with a lower hydrophobic solid boundary is described by the Navierslip condition. At the upper boundary of the layer, the temperature and pressure fields are assumed to be given, and a zero shear stress is specified. The system of boundary conditions is redefined due to the fact that all conditions for velocities are assigned as their derivatives. Zero flow rate is taken as an additional condition. The obtained exact solution to the boundary value problem is the only possible polynomial solution. The highest (eighth) degree of polynomials corresponds to a solution for background pressure. Analysis of the solution shows that it can describe a multiple stratification of kinetic-force fields. Since the analysis is carried out in a general form (without specifying physical constants that uniquely identify the fluid under study), the obtained results are applicable to viscous fluids of different nature.

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Kwon, T. H., and C. S. Kim. "Modeling and Numerical Analysis of Compression Molding of Three-Dimensional Thin Parts With Curing Process." Journal of Engineering Materials and Technology 117, no. 3 (July 1, 1995): 239–54. http://dx.doi.org/10.1115/1.2804536.

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A numerical modeling is proposed for the simulation of flow, heat transfer, and reaction kinetics during the compression molding of three-dimensional thin parts. A nonisothermal, non-Newtonian model including the kinetic equation for a curing mechanism of thermosetting materials is implemented in a computer program, and a finite element method is used to simulate a preheating, a filling, and a post-heating stage during the entire compression molding process. As a more rigorous approach, a moving boundary condition due to the drag motion of an upper mold of a nonplanar shape or due to an apparent slip phenomena of particle filled materials is introduced into the present modeling, resulting in a new governing equation and the corresponding finite element formulation. Verifications of the analysis program were performed with a simple geometry for the Newtonian and non-Newtonian isothermal cases, in which the numerical results are found to be in good agreement with theoretical results. Effects of the moving boundary condition and processing conditions, such as thickness of compression molded parts, mold closing velocity and the preheating stage on overall compression molding processing, are numerically investigated. Numerical results for a car fender are also presented as an example of industrial applications.

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Guo, Wenqiang, and Guoxiang Hou. "Three-Dimensional Simulations of Anisotropic Slip Microflows Using the Discrete Unified Gas Kinetic Scheme." Entropy 24, no. 7 (June 30, 2022): 907. http://dx.doi.org/10.3390/e24070907.

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The specific objective of the present work study is to propose an anisotropic slip boundary condition for three-dimensional (3D) simulations with adjustable streamwise and spanwise slip length by the discrete unified gas kinetic scheme (DUGKS). The present boundary condition is proposed based on the assumption of nonlinear velocity profiles near the wall instead of linear velocity profiles in a unidirectional steady flow. Moreover, a 3D corner boundary condition is introduced to the DUGKS to reduce the singularities. Numerical tests validate the effectiveness of the present method, which is more accurate than the bounce-back and specular reflection slip boundary condition in the lattice Boltzmann method. It is of significance to study the lid-driven cavity flow due to its applications and its capability in exhibiting important phenomena. Then, the present work explores, for the first time, the effects of anisotropic slip on the two-sided orthogonal oscillating micro-lid-driven cavity flow by adopting the present method. This work will generate fresh insight into the effects of anisotropic slip on the 3D flow in a two-sided orthogonal oscillating micro-lid-driven cavity. Some findings are obtained: The oscillating velocity of the wall has a weaker influence on the normal velocity component than on the tangential velocity component. In most cases, large slip length has a more significant influence on velocity profiles than small slip length. Compared with pure slip in both top and bottom walls, anisotropic slip on the top wall has a greater influence on flow, increasing the 3D mixing of flow. In short, the influence of slip on the flow field depends not only on slip length but also on the relative direction of the wall motion and the slip velocity. The findings can help in better understanding the anisotropic slip effect on the unsteady microflow and the design of microdevices.

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DALLASTON, MICHAEL C., and SCOTT W. McCUE. "Corner and finger formation in Hele-Shaw flow with kinetic undercooling regularisation." European Journal of Applied Mathematics 25, no. 6 (August 4, 2014): 707–27. http://dx.doi.org/10.1017/s0956792514000230.

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We examine the effect of a kinetic undercooling condition on the evolution of a free boundary in Hele-Shaw flow, in both bubble and channel geometries. We present analytical and numerical evidence that the bubble boundary is unstable and may develop one or more corners in finite time, for both expansion and contraction cases. This loss of regularity is interesting because it occurs regardless of whether the less viscous fluid is displacing the more viscous fluid, or vice versa. We show that small contracting bubbles are described to leading order by a well-studied geometric flow rule. Exact solutions to this asymptotic problem continue past the corner formation until the bubble contracts to a point as a slit in the limit. Lastly, we consider the evolving boundary with kinetic undercooling in a Saffman-Taylor channel geometry. The boundary may either form corners in finite time, or evolve to a single long finger travelling at constant speed, depending on the strength of kinetic undercooling. We demonstrate these two different behaviours numerically. For the travelling finger, we present results of a numerical solution method similar to that used to demonstrate the selection of discrete fingers by surface tension. With kinetic undercooling, a continuum of corner-free travelling fingers exists for any finger width above a critical value, which goes to zero as the kinetic undercooling vanishes. We have not been able to compute the discrete family of analytic solutions, predicted by previous asymptotic analysis, because the numerical scheme cannot distinguish between solutions characterised by analytic fingers and those which are corner-free but non-analytic.

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Kavokin, A. A., I. H. Kazmi, and B. Munir. "Computational Model of Phase Transformations in Thermo-Chemical Cathodes Using Kinetic Approach." Key Engineering Materials 510-511 (May 2012): 9–14. http://dx.doi.org/10.4028/www.scientific.net/kem.510-511.9.

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The paper presents the results of modeling of the processes of phases transformations occurring in cathode of plasmatron with zirconium insertion. Model describes temperature and liquid-solid phase transformation in cathode considering kinetics of transformation in accordance with a state diagram. The comparison between one-dimensional mathematical models was exploited for estimation of the kinetics coefficient. First model is based on well-known heat equation with Stefans condition on the free boundary between liquid and solid phases [. The standard analytical self-similar solution for two-phase case is applied. In the second model, for heat equation instead of Stefans conditions, differential equations of kinetics are used.

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Echouchene, Fraj, Thamraa Al-shahrani, and Hafedh Belmabrouk. "Analysis of Temperature-Jump Boundary Conditions on Heat Transfer for Heterogeneous Microfluidic Immunosensors." Sensors 21, no. 10 (May 18, 2021): 3502. http://dx.doi.org/10.3390/s21103502.

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The objective of the current study is to analyze numerically the effect of the temperature-jump boundary condition on heterogeneous microfluidic immunosensors under electrothermal force. A three-dimensional simulation using the finite element method on the binding reaction kinetics of C-reactive protein (CRP) was performed. The kinetic reaction rate was calculated with coupled Laplace, Navier−Stokes, energy, and mass diffusion equations. Two types of reaction surfaces were studied: one in the form of a disc surrounded by two electrodes and the other in the form of a circular ring, one electrode is located inside the ring and the other outside. The numerical results reveal that the performance of a microfluidic biosensor is enhanced by using the second design of the sensing area (circular ring) coupled with the electrothermal force. The improvement factor under the applied ac field 15 Vrms was about 1.2 for the first geometry and 3.6 for the second geometry. Furthermore, the effect of temperature jump on heat transfer rise and response time was studied. The effect of two crucial parameters, viz. Knudsen number (Kn) and thermal accommodation coefficient (σT) with and without electrothermal effect, were analyzed for the two configurations.

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Chu, Su-Kuan, Chen-Te Ma, and Chih-Hung Wu. "Two-dimensional dilaton gravity theory and lattice Schwarzian theory." International Journal of Modern Physics A 34, no. 29 (October 20, 2019): 1950176. http://dx.doi.org/10.1142/s0217751x19501768.

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We report a holographic study of a two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the cases of nonvanishing and vanishing cosmological constants. Our result shows that the boundary theory of the two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the case of nonvanishing cosmological constants is the Schwarzian term coupled to a dilaton field, while for the case of vanishing cosmological constant, a theory does not have a kinetic term. We also include the higher derivative term [Formula: see text], where [Formula: see text] is the scalar curvature that is coupled to a dilaton field. We find that the form of the boundary theory is not modified perturbatively. Finally, we show that a lattice holographic picture is realized up to the second-order perturbation of boundary cutoff [Formula: see text] under a constant boundary dilaton field and the nonvanishing cosmological constant by identifying the lattice spacing [Formula: see text] of a lattice Schwarzian theory with the boundary cutoff [Formula: see text] of the two-dimensional dilaton gravity theory.

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HILHORST, D., F. ISSARD-ROCH, and J. M. ROQUEJOFFRE. "Large time behavior of the solutions to a one-dimensional Stefan problem with a kinetic condition at the free boundary." European Journal of Applied Mathematics 15, no. 3 (June 2004): 297–313. http://dx.doi.org/10.1017/s095679250400556x.

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We consider a Stefan problem with a kinetic condition at the free boundary and prove the convergence of the solution as $t$ tends to infinity either to a travelling wave solution or to a self-similar solution. The key idea is to transform this problem into a problem for a single nonlocal parabolic equation which admits a comparison principle.

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Ma, Xuan, and Fuli He. "The initial boundary value problem for the Vlasov–Poisson–Fokker–Planck system." Journal of Mathematical Physics 63, no. 9 (September 1, 2022): 091506. http://dx.doi.org/10.1063/5.0095310.

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This paper is devoted to the initial boundary value problem of the Vlasov–Poisson–Fokker–Planck system in a bounded domain. The global existence of a unique strong solution and its exponential convergence rate to the equilibrium state are proved under the specular reflection boundary condition. The proof is based on an elementary energy method and the [Formula: see text] theory developed by Guo et al. [Arch. Ration. Mech. Anal. 236(3), 1389–1454 (2020)] for kinetic models.

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Kobayashi, Kazumichi, Shingo Mouri, Yusuke Watanabe, Masao Watanabe, and Shigeo Fujikawa. "Evaporation and Condensation Coefficients of Methanol at Room Temperature, and Consideration of Kinetic Boundary Condition." Netsu Bussei 27, no. 1 (2014): 9–14. http://dx.doi.org/10.2963/jjtp.27.9.

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Błazik-Borowa, Ewa. "The influence of boundary condition functions on the quality of the solution and its sensitivity to coefficients of k-ε turbulence models." Budownictwo i Architektura 8, no. 1 (June 13, 2011): 015–26. http://dx.doi.org/10.35784/bud-arch.2255.

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The paper is devoted to the problem of boundary conditions influence on the quality of the solution obtained with use of k-ε turbulence models. There are calculation results for different boundary conditions and two methods: standard k-ε and RNG k-ε in the paper. The flow parameters obtained from the calculation are compared with our own measurement results. Moreover, the influence of input data on the inflow edge on sensitivity coefficients is shown and analysed in the paper. The research is performed for components of velocity and turbulence kinetic energy.

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Li, Simon SW, and Daniel HK Chow. "Modified electromyography-assisted optimization approach for predicting lumbar spine loading while walking with backpack loads." Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 234, no. 5 (February 13, 2020): 527–33. http://dx.doi.org/10.1177/0954411920906243.

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This study modified an electromyography-assisted optimization approach for predicting lumbar spine loading while walking with backpack loads. The modified-electromyography-assisted optimization approach eliminated the electromyography measurement at maximal voluntary contraction and adopted a linear electromyography–force relationship. Moreover, an optimal lower boundary condition for muscle gain was introduced to constrain the trunk muscle co-activation. Anthropometric information of 10 healthy young men as well as their kinematic, kinetic, and electromyography data obtained while walking with backpack loads were used as inputs in this study. A computational algorithm was used to find and analyse the sensitivity of the optimal lower boundary condition for achieving minimum deviation of the modified-electromyography-assisted optimization approach from the electromyography-assisted optimization approach for predicting lumbosacral joint compression force. Results validated that the modified-electromyography-assisted optimization approach (at optimal lower boundary condition of 0.92) predicted on average, a non-significant deviation in peak lumbosacral joint compression force of −18 N, a standard error of 9 N, and a root mean square difference in force profile of 73.8 N. The modified-electromyography-assisted optimization approach simplified the experimental process by eliminating the electromyography measurement at maximal voluntary contraction and provided comparable estimations for lumbosacral joint compression force that is also applicable to patients or individuals having difficulty in performing the maximal voluntary contraction activity.

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Li, Hang, Yong Hong Liu, Ya Zhou Wang, and Jian Ming Ma. "Numerical Simulation of Flow around Cylinder Using the Lattice Boltzmann Method Based on Guo Boundary Condition." Key Engineering Materials 474-476 (April 2011): 422–27. http://dx.doi.org/10.4028/www.scientific.net/kem.474-476.422.

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In this paper, the lattice Boltzmann Method is applied to simulate incompressible steady flow around a cylinder. The simulation model is based on D2Q9 lattice model and Guo boundary condition. Different Reynolds number and cylinder position in the flow field is considered to acquire corresponding velocity, vorticity, pressure and kinetic energy. The conclusions demonstrated in this paper could be useful for the project like construction of ocean platform, cooling tower or high chimney and so on.

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Cao, J., G. Ahmadi, and M. Massoudi. "Gravity granular flows of slightly frictional particles down an inclined bumpy chute." Journal of Fluid Mechanics 316 (June 10, 1996): 197–221. http://dx.doi.org/10.1017/s002211209600050x.

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Gravity-driven granular flow of slightly frictional particles down an inclined, bumpy chute is studied. A modified kinetic model which includes the frictional energy loss effects is used, and the boundary conditions for a bumpy wall with small friction are derived by ensuring the balance of momentum and energy. At the free surface, the condition of vanishing of the solid volume fraction is used. The mean velocity, the fluctuation kinetic energy and the solid volume fraction profiles are evaluated. It is shown that steady granular gravity flow down a bumpy frictional chute could be achieved at arbitrary inclination angles. The computational results also show that the slip velocity may vary considerably depending on the granular layer height, the surface boundary roughness, the friction coefficient and the inclination angles. The model predictions are compared with the existing experimental and simulation data, and good agreement is observed. In particular, the model can well predicate the features of the variation of solid volume fraction and fluctuation energy profiles for different particle–wall friction coefficients and wall roughnesses.

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Goruleva, L. S., and E. Yu Prosviryakov. "Unidirectional steady-state inhomogeneous Couette flow with a quadratic velocity profile along a horizontal coordinate." Diagnostics, Resource and Mechanics of materials and structures, no. 3 (June 2022): 47–60. http://dx.doi.org/10.17804/2410-9908.2022.3.047-060.

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The paper presents an exact solution to the boundary value problem describing the steady-state unidirectional flow of a viscous incompressible fluid. The fluid moves in an infinite horizontal strip (infinite fluid layer). The fulfillment of the no-slip condition is postulated at the lower boundary of the viscous fluid layer. At the upper boundary, which is assumed to be rigid, non-uniform velocity distribution is specified. The deformation of the free boundary is neglected due to the use of the rigid-lid boundary condition. The exact solution to the equations of the hydrodynamics of incompressible fluids automatically satisfies the continuity equation (the incompressibility equation). The velocity function is harmonic in this case. The simplest exact solution satisfying the Laplace equation is constructed, which takes into account the features of the velocity field along the transverse (vertical) coordinate and one of the longitudinal (horizontal) coordinates. The paper analyzes the topological properties of the velocity field, the tangential stress field, the vorticity vector, specific kinetic energy, and specific helicity.

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KOBAYASHI, Kazumichi, Misaki KON, Kotaro OHASHI, and Masao WATANABE. "J053025 Numerical Simulation for Kinetic Boundary Condition at a Vapor-Liquid Interface Based Enskog-Vlasov Equation." Proceedings of Mechanical Engineering Congress, Japan 2013 (2013): _J053025–1—_J053025–4. http://dx.doi.org/10.1299/jsmemecj.2013._j053025-1.

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ISHIYAMA, Tatsuya, Takeru YANO, and Shigeo FUJIKAWA. "Molecular Dynamics Study on Kinetic Boundary Condition at a Vapor-Liquid Interface in a Nonequilibrium State." Proceedings of the JSME annual meeting 2004.2 (2004): 369–70. http://dx.doi.org/10.1299/jsmemecjo.2004.2.0_369.

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ISHIYAMA, Tatsuya, Takeru YANO, and Shigeo FUJIKAWA. "Molecular Dynamics Simulation on Kinetic Boundary Condition at an Interface between Vapor and its Condensed Phase." Proceedings of the Fluids engineering conference 2003 (2003): 96. http://dx.doi.org/10.1299/jsmefed.2003.96.

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Journal articles on the topic 'Kinetic Boundary Condition'

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