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Relevant bibliographies by topics / Discrete Boltzmann equation

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Academic literature on the topic 'Discrete Boltzmann equation'

Author: Grafiati

Published: 14 March 2023

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Journal articles on the topic "Discrete Boltzmann equation"

1

Simonis, Stephan, Martin Frank, and Mathias J. Krause. "On relaxation systems and their relation to discrete velocity Boltzmann models for scalar advection–diffusion equations." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2175 (June 22, 2020): 20190400. http://dx.doi.org/10.1098/rsta.2019.0400.

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The connection of relaxation systems and discrete velocity models is essential to the progress of stability as well as convergence results for lattice Boltzmann methods. In the present study we propose a formal perturbation ansatz starting from a scalar one-dimensional target equation, which yields a relaxation system specifically constructed for its equivalence to a discrete velocity Boltzmann model as commonly found in lattice Boltzmann methods. Further, the investigation of stability structures for the discrete velocity Boltzmann equation allows for algebraic characterizations of the equilibrium and collision operator. The methods introduced and summarized here are tailored for scalar, linear advection–diffusion equations, which can be used as a foundation for the constructive design of discrete velocity Boltzmann models and lattice Boltzmann methods to approximate different types of partial differential equations. This article is part of the theme issue ‘Fluid dynamics, soft matter and complex systems: recent results and new methods’.

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QU, KUN, CHANG SHU, and JINSHENG CAI. "DEVELOPING LBM-BASED FLUX SOLVER AND ITS APPLICATIONS IN MULTI-DIMENSION SIMULATIONS." International Journal of Modern Physics: Conference Series 19 (January 2012): 90–99. http://dx.doi.org/10.1142/s2010194512008628.

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In this paper, a new flux solver was developed based on a lattice Boltzmann model. Different from solving discrete velocity Boltzmann equation and lattice Boltzmann equation, Euler/Navier-Stokes (NS) equations were solved in this approach, and the flux at the interface was evaluated with a compressible lattice Boltzmann model. This method combined lattice Boltzmann method with finite volume method to solve Euler/NS equations. The proposed approach was validated by some simulations of one-dimensional and multi-dimensional problems.

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Hekmat, Mohamad Hamed, and Masoud Mirzaei. "Development of Discrete Adjoint Approach Based on the Lattice Boltzmann Method." Advances in Mechanical Engineering 6 (January 1, 2014): 230854. http://dx.doi.org/10.1155/2014/230854.

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The purpose of this research is to present a general procedure with low implementation cost to develop the discrete adjoint approach for solving optimization problems based on the LB method. Initially, the macroscopic and microscopic discrete adjoint equations and the cost function gradient vector are derived mathematically, in detail, using the discrete LB equation. Meanwhile, for an elementary case, the analytical evaluation of the macroscopic and microscopic adjoint variables and the cost function gradients are presented. The investigation of the derivation procedure shows that the simplicity of the Boltzmann equation, as an alternative for the Navier-Stokes (NS) equations, can facilitate the process of extracting the discrete adjoint equation. Therefore, the implementation of the discrete adjoint equation based on the LB method needs fewer attempts than that of the NS equations. Finally, this approach is validated for the sample test case, and the results gained from the macroscopic and microscopic discrete adjoint equations are compared in an inverse optimization problem. The results show that the convergence rate of the optimization algorithm using both equations is identical and the evaluated gradients have a very good agreement with each other.

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Bernhoff, Niclas. "Boundary Layers and Shock Profiles for the Broadwell Model." International Journal of Differential Equations 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/5801728.

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We consider the existence of nonlinear boundary layers and the typically nonlinear problem of existence of shock profiles for the Broadwell model, which is a simplified discrete velocity model for the Boltzmann equation. We find explicit expressions for the nonlinear boundary layers and the shock profiles. In spite of the few velocities used for the Broadwell model, the solutions are (at least partly) in qualitatively good agreement with the results for the discrete Boltzmann equation, that is the general discrete velocity model, and the full Boltzmann equation.

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Banoo, K., F. Assad, and M. S. Lundstrom. "Formulation of the Boltzmann Equation as a Multi-Mode Drift-Diffusion Equation." VLSI Design 8, no. 1-4 (January 1, 1998): 539–44. http://dx.doi.org/10.1155/1998/59373.

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We present a multi-mode drift-diffusion equation as reformulation of the Boltzmann equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.

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MARTYS, NICOS S. "ENERGY CONSERVING DISCRETE BOLTZMANN EQUATION FOR NONIDEAL SYSTEMS." International Journal of Modern Physics C 10, no. 07 (October 1999): 1367–82. http://dx.doi.org/10.1142/s0129183199001121.

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The BBGKY formalism is utilized to obtain a set of moment equations to be satisfied by the collision operator in an energy conserving discrete Boltzmann equation for the case of a nonlocal interaction potential. A modified BGK form of the collision operator consistent with these moment equations is described. In the regime of isothermal flows, a previous proposed nonideal gas model is recovered. Other approaches to constructing the collision operator are discussed. Numerical implementation of the modified BGK form, using a thermal lattice Boltzmann model, is illustrated as an example. The time dependence of the density autocorrelation function was studied for this model and found, at early times, to be strongly affected by the constraint of total energy conservation. The long time behavior of the density autocorrelation function was consistent with the theory of hydrodynamic fluctuations.

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BELLOUQUID, A. "A DIFFUSIVE LIMIT FOR NONLINEAR DISCRETE VELOCITY MODELS." Mathematical Models and Methods in Applied Sciences 13, no. 01 (January 2003): 35–58. http://dx.doi.org/10.1142/s0218202503002374.

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This paper is devoted to the analysis of the diffusive limit for a general discrete velocity model of the Boltzmann equation in any dimension of the physical space, for densities which remain in a suitable small neighbourhood of global Maxwellians. The scaled solutions of discrete Boltzmann equation are shown to have fluctuations that converge locally in time weakly to a limit governed by a solution of incompressible Stokes equations provided that the initial fluctuations are smooth. The weak limit becomes strong when the initial fluctuations converge to appropriate initial data. As applications the Carleman model and the one-dimensional Broadwell model are analyzed in detail.

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He, Xiaoyi, Xiaowen Shan, and Gary D. Doolen. "Discrete Boltzmann equation model for nonideal gases." Physical Review E 57, no. 1 (January 1, 1998): R13—R16. http://dx.doi.org/10.1103/physreve.57.r13.

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ANDALLAH, LAEK S., and HANS BABOVSKY. "A DISCRETE BOLTZMANN EQUATION BASED ON HEXAGONS." Mathematical Models and Methods in Applied Sciences 13, no. 11 (November 2003): 1537–63. http://dx.doi.org/10.1142/s0218202503003021.

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We develop the theory of a Boltzmann equation which is based on a hexagonal discretization of the velocity space. We prove that such a model contains all the basic features of classical kinetic theory, like collision invariants, H-theorem, equilibrium solutions, features of the linearized problem etc. This theory includes the infinite as well as finite hexagonal grids which may be used for numerical purposes.

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Makai, Mihály. "Discrete Symmetries of the Linear Boltzmann equation." Transport Theory and Statistical Physics 15, no. 3 (May 1986): 249–73. http://dx.doi.org/10.1080/00411458608210452.

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Dissertations / Theses on the topic "Discrete Boltzmann equation"

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Morris, Aaron Benjamin. "Investigation of a discrete velocity Monte Carlo Boltzmann equation." Thesis, [Austin, Tex. : University of Texas, 2009. http://hdl.handle.net/2152/ETD-UT-2009-05-127.

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Håkman, Olof. "Boltzmann Equation and Discrete Velocity Models : A discrete velocity model for polyatomic molecules." Thesis, Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-76143.

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In the study of kinetic theory and especially in the study of rarefied gas dynamics one often turns to the Boltzmann equation. The mathematical theory developed by Ludwig Boltzmann was at first sight applicable in aerospace engineering and fluid mechanics. As of today, the methods in kinetic theory are extended to other fields, for instance, molecular biology and socioeconomics, which makes the need of finding efficient solution methods still important. In this thesis, we study the underlying theory of the continuous and discrete Boltzmann equation for monatomic gases. We extend the theory where needed, such that, we cover the case of colliding molecules that possess different levels of internal energy. Mainly, we discuss discrete velocity models and present explicit calculations for a model of a gas consisting of polyatomic molecules modelled with two levels of internal energy.
I studiet av kinetisk teori och speciellt i studiet av dynamik för tunna gaser vänder man sig ofta till Boltzmannekvationen. Den matematiska teorien utvecklad av Ludwig Boltzmann var vid första anblicken tillämpbar i flyg- och rymdteknik och strömningsmekanik. Idag generaliseras metoder i kinetisk teori till andra områden, till exempel inom molekylärbiologi och socioekonomi, vilket gör att vi har ett fortsatt behov av att finna effektiva lösningsmetoder. Vi studerar i denna uppsats den underliggande teorin av den kontinuerliga och diskreta Boltzmannekvationen för monatomiska gaser. Vi utvidgar teorin där det behövs för att täcka fallet då kolliderande molekyler innehar olika nivåer av intern energi. Vi diskuterar huvudsakligen diskreta hastighetsmodeller och presenterar explicita beräkningar för en modell av en gas bestående av polyatomiska molekyler modellerad med två lägen av intern energi.

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Fonte, Massimo. "Analysis of singular solutions for two nonlinear wave equations." Doctoral thesis, SISSA, 2005. http://hdl.handle.net/20.500.11767/4197.

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Bernhoff, Niclas. "On Half-Space and Shock-Wave Problems for Discrete Velocity Models of the Boltzmann Equation." Doctoral thesis, Karlstads universitet, Fakulteten för teknik- och naturvetenskap, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-2373.

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We study some questions related to general discrete velocity (with arbitrarily number of velocities) models (DVMs) of the Boltzmann equation. In the case of plane stationary problems the typical DVM reduces to a dynamical system (system of ODEs). Properties of such systems are studied in the most general case. In particular, a topological classification of their singular points is made and dimensions of the corresponding stable, unstable and center manifolds are computed. These results are applied to typical half-space problems of rarefied gas dynamics, including the problems of Milne and Kramer. A classification of well-posed half-space problems for linearized DVMs is made. Exact solutions of a (simplified) linearized kinetic model of BGK type are found as a limiting case of the corresponding discrete models. Existence of solutions of weakly non-linear half-space problems for general DVMs are studied. The solutions are assumed to tend to an assigned Maxwellian at infinity, and the data for the outgoing particles at the boundary are assigned, possibly depending on the data for the incoming particles. The conditions, on the data at the boundary, needed for the existence of a unique (in a neighborhood of the assigned Maxwellian) solution of the problem are investigated. Both implicit, in the non-degenerate cases, and sometimes, in both degenerate and non-degenerate cases, explicit conditions are found. Shock-waves can be seen as heteroclinic orbits connecting two singular points (Maxwellians) for DVMs. We give a constructive proof for the existence of solutions of the shock-wave problem for the general DVM. This is worked out for shock speeds close to a typical speed, corresponding to the sound speed in the continuous case. We clarify how close the shock speed must be for our theorem to hold, and present an iteration scheme for obtaining the solution. The main results of the paper can be used for DVMs for mixtures as well as for DVMs for one species.

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Hübner, Thomas [Verfasser]. "A monolithic, off-lattice approach to the discrete Boltzmann equation with fast and accurate numerical methods / Thomas Hübner." Dortmund : Universitätsbibliothek Technische Universität Dortmund, 2011. http://d-nb.info/1011570777/34.

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Mittal, Arpit. "Prediction of Non-Equilibrium Heat Conduction in Crystalline Materials Using the Boltzmann Transport Equation for Phonons." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1316471562.

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D'ALMEIDA, AMAH SENA. "Etude des solutions des equations de boltzmann discretes et applications." Paris 6, 1995. http://www.theses.fr/1995PA066007.

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L'etude de certains ecoulements de gaz rarefies necessite la resolution effective de l'equation de boltzmann. La theorie cinetique discrete permet de remplacer cette equation par un systeme d'equations aux derivees partielles plus simples. A l'oppose de la theorie cinetique continue, les modeles discrets peuvent ne pas avoir toutes les variables macroscopiques physiques independantes ou au contraire avoir en plus des variables macroscopiques non physiques. Ces problemes sont resolus par un choix convenable de modeles. De plus, les definitions usuelles de la temperature et de la pression ne sont pas valables en theorie discrete. On propose une definition de la temperature et de la pression en accord avec les principes de la thermodynamique. Un prealable a l'etude des ecoulements de gaz est la determination des conditions aux limites correctes a imposer sur leurs frontieres. Apres avoir ecrit les conditions aux limites generales et discute de quelques cas particuliers, on etudie l'existence des solutions stationnaires du probleme aux limites resultant de la modelisation des phenomenes physiques par des modeles discrets. Enfin, on traite les problemes de l'ecoulement entre deux plaques paralleles, de l'evaporation et de la condensation. Ceci a permis de mettre en evidence et d'expliquer certains phenomenes de rarefaction parfois difficiles a analyser avec l'equation classique de boltzmann

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Jobic, Yann. "Numerical approach by kinetic methods of transport phenomena in heterogeneous media." Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4723/document.

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Les phénomènes de transport en milieux poreux sont étudiés depuis près de deux siècles, cependant les travaux concernant les milieux fortement poreux sont encore relativement peu nombreux. Les modèles couramment utilisés pour les poreux classiques (lits de grains par exemple) sont peu applicables pour les milieux fortement poreux (les mousses par exemple), un certain nombre d’études ont été entreprises pour combler ce manque. Néanmoins, les résultats expérimentaux et numériques caractérisant les pertes de charge dans les mousses sont fortement dispersés. Du fait des progrès de l’imagerie 3D, une tendance émergente est la détermination des paramètres des lois d’écoulement à partir de simulations directes sur des géométries reconstruites. Nous présentons ici l’utilisation d’une nouvelle approche cinétique pour résoudre localement les équations de Navier-Stokes et déterminer les propriétés d’écoulement (perméabilité, dispersion, ...)
A novel kinetic scheme satisfying an entropy condition is developed, tested and implemented for the simulation of practical problems. The construction of this new entropic scheme is presented. A classical hyperbolic system is approximated by a discrete velocity vector kinetic scheme (with the simplified BGK collisional operator), but applied to an inviscid compressible gas dynamics system with a small Mach number parameter, according to the approach of Carfora and Natalini (2008). The numerical viscosity is controlled, and tends to the physical viscosity of the Navier-Stokes system. The proposed numerical scheme is analyzed and formulated as an explicit finite volume flux vector splitting (FVS) scheme that is very easy to implement. It is close in spirit to Lattice Boltzmann schemes, but it has the advantage to satisfy a discrete entropy inequality under a CFL condition and a subcharacteristic stability condition involving a cell Reynolds number. The new scheme is proved to be second-order accurate in space. We show the efficiency of the method in terms of accuracy and robustness on a variety of classical benchmark tests. Some physical problems have been studied in order to show the usefulness of both schemes. The LB code was successfully used to determine the longitudinal dispersion of metallic foams, with the use of a novel indicator. The entropic code was used to determine the permeability tensor of various porous media, from the Fontainebleau sandstone (low porosity) to a redwood tree sample (high porosity). These results are pretty accurate. Finally, the entropic framework is applied to the advection-diffusion equation as a passive scalar

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Hegermiller, David Benjamin. "A new method to incorporate internal energy into a discrete velocity Monte Carlo Boltzmann Equation solver." Thesis, 2011. http://hdl.handle.net/2152/ETD-UT-2011-08-4328.

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A new method has been developed to incorporate particles with internal structure into the framework of the Variance Reduction method [17] for solving the discrete velocity Boltzmann Equation. Internal structure in the present context refers to physical phenomena like rotation and vibration of molecules consisting of two or more atoms. A gas in equilibrium has all modes of internal energy at the same temperature as the translational temperature. If the gas is in a non-equilibrium state, translational temperature and internal temperatures tend to proceed towards an equilibrium state during equilibration, but they all do so at different relaxation rates. In this thesis, rotational energy of a distribution of molecules is modeled as a single value at a point in a discrete velocity space; this represents the average rotational energy of molecules at that specific velocity. Inelastic collisions are the sole mechanism of translational and rotational energy exchange, and are governed by a modified Landau-Teller equation. The method is tested for heat bath simulations, or homogeneous relaxations, and one dimensional shock problems. Homogeneous relaxations demonstrate that the rotational and translational temperatures equilibrate to the correct final temperature, which can be predicted by conservation of energy. Moreover, the rates of relaxation agree with the direct simulation Monte Carlo (DSMC) method with internal energy for the same input parameters. Using a fourth order method for convecting mass along with its corresponding internal energy, a one dimensional Mach 1.71 normal shock is simulated. Once the translational and rotational temperatures equilibrate downstream, the temperature, density and velocity, predicted by the Rankine-Hugoniot conditions, are obtained to within an error of 0.5%. The result is compared to a normal shock with the same upstream flow properties generated by the DSMC method. Internal vibrational energy and a method to use Larsen Borgnakke statistical sampling for inelastic collisions is formulated in this text and prepared in the code, but remains to be tested.
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Books on the topic "Discrete Boltzmann equation"

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Discrete nonlinear models of the Boltzmann equation. Moscow: General Editorial Board for Foreign Language Publications, Nauka Publishers, 1987.

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Luigi, Preziosi, ed. Fluid dynamic applications of the discrete Boltzmann equation. Singapore: World Scientific, 1991.

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Book chapters on the topic "Discrete Boltzmann equation"

1

Cabannes, Henri. "Discrete Boltzmann Equation with Multiple Collisions." In Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects, 109–18. Wiesbaden: Vieweg+Teubner Verlag, 1993. http://dx.doi.org/10.1007/978-3-322-87871-7_13.

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Bellomo, Nicola, and Luciano M. de Socio. "On the Discrete Boltzmann Equation for Binary Gas Mixtures." In Rarefied Gas Dynamics, 1269–76. Boston, MA: Springer US, 1985. http://dx.doi.org/10.1007/978-1-4613-2467-6_58.

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Cabannes, Henri. "Survey on Exact Solutions for Discrete Models of the Boltzmann Equation." In Computational Fluid Dynamics, 103–14. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-79440-7_7.

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Muljadi, Bagus Putra, and Jaw-Yen Yang. "A Direct Boltzmann-BGK Equation Solver for Arbitrary Statistics Using the Conservation Element/Solution Element and Discrete Ordinate Method." In Computational Fluid Dynamics 2010, 637–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-17884-9_81.

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Cornille, H. "Hierarchies of (1+1)-Dimensional Multispeed Discrete Boltzmann Model Equations." In Solitons and Chaos, 142–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-84570-3_17.

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Kawashima, Shuichi, and Shinya Nishibata. "Stationary Waves for the Discrete Boltzmann Equations in the Half Space." In Hyperbolic Problems: Theory, Numerics, Applications, 593–602. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8372-6_13.

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Vedenyapin, Victor, Alexander Sinitsyn, and Eugene Dulov. "Discrete Models of Boltzmann Equation." In Kinetic Boltzmann, Vlasov and Related Equations, 183–93. Elsevier, 2011. http://dx.doi.org/10.1016/b978-0-12-387779-6.00010-7.

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Vedenyapin, Victor, Alexander Sinitsyn, and Eugene Dulov. "Discrete Boltzmann Equation Models for Mixtures." In Kinetic Boltzmann, Vlasov and Related Equations, 211–26. Elsevier, 2011. http://dx.doi.org/10.1016/b978-0-12-387779-6.00012-0.

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"THE DISCRETE BOLTZMANN EQUATION MODELLING AND THERMODYNAMICS." In Series on Advances in Mathematics for Applied Sciences, 1–37. WORLD SCIENTIFIC, 1991. http://dx.doi.org/10.1142/9789814439350_0001.

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Kawashima, Shuichi, and Yasushi Shizuta. "The Navier-Stokes Equation Associated with the Discrete Boltzmann Equation." In North-Holland Mathematics Studies, 15–30. Elsevier, 1989. http://dx.doi.org/10.1016/s0304-0208(08)70504-8.

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Conference papers on the topic "Discrete Boltzmann equation"

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Bernhoff, Niclas. "Discrete quantum Boltzmann equation." In 31ST INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS: RGD31. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5119631.

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Majorana, Armando. "Deterministic numerical solutions to a semi-discrete Boltzmann equation." In 31ST INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS: RGD31. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5119550.

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KAWASHIMA, Shuichi. "Asymptotic Behavior of Solutions to the Discrete Boltzmann Equation." In The Colloquium Euromech No. 267. WORLD SCIENTIFIC, 1991. http://dx.doi.org/10.1142/9789814503525_0004.

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Li, Like, Renwei Mei, and James F. Klausner. "Heat Transfer in Thermal Lattice Boltzmann Equation Method." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-87990.

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The evaluation of the boundary heat flux and total heat transfer in the lattice Boltzmann equation (LBE) simulations is investigated. The boundary heat fluxes in the discrete velocity directions of the thermal LBE (TLBE) model are obtained directly from the temperature distribution functions at the lattice nodes. With the rectangular lattice uniformly spaced the effective surface area for the discrete heat flux is the unit spacing distance, thus the heat flux integration becomes simply a summation of all the discrete heat fluxes with constant surface areas. The present method for the evaluation of total heat transfer is very efficient and robust for curved boundaries because it does not require the determination of the normal heat flux on the boundary and the surface area. To validate its applicability and accuracy, several numerical tests with analytical solutions are conducted, including 2-dimensional (2D) steady thermal flow in a channel, 1-D transient heat conduction in an inclined semi-infinite solid, 2-D transient conduction inside a circle, and 3-D steady thermal flow in a circular pipe. For straight boundaries perpendicular to one of the discrete velocity vectors, the total heat transfer is second-order accurate. For curved boundaries only first-order accuracy is obtained for the total heat transfer due to the irregularly distributed lattice fractions cut by the curved boundary.

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Cabannes, Henri. "The Discrete Boltzmann Equation : The Regular Plane Model with Four Velocities." In RAREFIED GAS DYNAMICS: 24th International Symposium on Rarefied Gas Dynamics. AIP, 2005. http://dx.doi.org/10.1063/1.1941514.

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Malkov, E. A., S. O. Poleshkin, and M. S. Ivanov. "Discrete velocity scheme for solving the Boltzmann equation with the GPGPU." In 28TH INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS 2012. AIP, 2012. http://dx.doi.org/10.1063/1.4769532.

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Gabetta, E., and R. Monaco. "THE DISCRETE BOLTZMANN EQUATION FOR GASES WITH BI-MOLECULAR CHEMICAL REACTIONS." In The Colloquium Euromech No. 267. WORLD SCIENTIFIC, 1991. http://dx.doi.org/10.1142/9789814503525_0003.

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Adzhiev, S. Z. "On One-dimensional Discrete Velocity Models of The Boltzmann Equation For Mixtures." In RAREFIED GAS DYNAMICS: 24th International Symposium on Rarefied Gas Dynamics. AIP, 2005. http://dx.doi.org/10.1063/1.1941524.

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Chen, Leitao, Laura Schaefer, and Xiaofeng Cai. "An Accurate Unstructured Finite Volume Discrete Boltzmann Method." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-87136.

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Unlike the conventional lattice Boltzmann method (LBM), the discrete Boltzmann method (DBM) is Eulerian in nature and decouples the discretization of particle velocity space from configuration space and time space, which allows the use of an unstructured grid to exactly capture complex boundary geometries. A discrete Boltzmann model that solves the discrete Boltzmann equation (DBE) with the finite volume method (FVM) on a triangular unstructured grid is developed. The accuracy of the model is improved with the proposed high-order flux schemes and interpolation scheme. The boundary treatment for commonly used boundary conditions is also formulated. A series of problems with both periodic and non-periodic boundaries are simulated. The results show that the new model can significantly reduce numerical viscosity.

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Morris, A. B., P. L. Varghese, D. B. Goldstein, and Takashi Abe. "Improvement of a Discrete Velocity Boltzmann Equation Solver With Arbitrary Post-Collision Velocities." In RARIFIED GAS DYNAMICS: Proceedings of the 26th International Symposium on Rarified Gas Dynamics. AIP, 2008. http://dx.doi.org/10.1063/1.3076521.

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Reports on the topic "Discrete Boltzmann equation"

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Prinja, A. K. Multigroup discrete ordinates solution of Boltzmann-Fokker-Planck equations and cross section library development of ion transport. Office of Scientific and Technical Information (OSTI), August 1995. http://dx.doi.org/10.2172/106676.

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