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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

Last updated: 31 July 2025

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Journal articles on the topic "Discrete Boltzmann equation"

1

Bobylev, Aleksandr Vasil'evich. "Boltzmann-type kinetic equations and discrete models." Russian Mathematical Surveys 79, no. 3 (2024): 459–513. http://dx.doi.org/10.4213/rm10161e.

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The known non-linear kinetic equations (in particular, the wave kinetic equation and the quantum Nordheim-Uehling-Uhlenbeck equations) are considered as a natural generalization of the classical spatially homogeneous Boltzmann equation. To this end we introduce the general Boltzmann-type kinetic equation that depends on a function of four real variables $F(x,y;v,w)$. The function $F$ is assumed to satisfy certain commutation relations. The general properties of this equation are studied. It is shown that the kinetic equations mentioned above correspond to different forms of the function (polyn

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Bobylev, Aleksandr Vasil'evich. "Boltzmann-type kinetic equations and discrete models." Uspekhi Matematicheskikh Nauk 79, no. 3(477) (2024): 93–148. http://dx.doi.org/10.4213/rm10161.

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The known non-linear kinetic equations (in particular, the wave kinetic equation and the quantum Nordheim-Uehling-Uhlenbeck equations) are considered as a natural generalization of the classical spatially homogeneous Boltzmann equation. To this goal we introduce the general Boltzmann-type kinetic equation that depends on a function of four real variables $F(x,y;v,w)$. The function $F$ is assumed to satisfy certain commutation relations. The general properties of this equation are studied. It is shown that the kinetic equations mentioned above correspond to different forms of the function (poly

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3

Bobylev, A. V. "On discrete models of Boltzmann-type kinetic equations." Contemporary Mathematics. Fundamental Directions 70, no. 1 (2024): 15–24. http://dx.doi.org/10.22363/2413-3639-2024-70-1-15-24.

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The known nonlinear kinetic equations, in particular, the wave kinetic equation and the quantum Nordheim–Uehling–Uhlenbeck equations are considered as a natural generalization of the classical spatially homogeneous Boltzmann equation. To this goal we introduce the general Boltzmann-type kinetic equation that depends on a function of four real variables \(F(x,y; v,w)\). The function \(F\) is assumed to satisfy certain simple relations. The main properties of this kinetic equation are studied. It is shown that the above mentioned specific kinetic equations correspond to different polynomia

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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 (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 equili

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Bobylev, Alexander Vasilievich, and Sergei Borisovitch Kuksin. "Boltzmann equation and wave kinetic equations." Keldysh Institute Preprints, no. 31 (2023): 1–20. http://dx.doi.org/10.20948/prepr-2023-31.

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The well-known nonlinear kinetic equations (in particular, the wave kinetic equation and the quantum Nordheim – Uehling – Uhlenbeck equations) are considered as a natural generalization of the classical spatially homogeneous Boltzmann equation. To this goal we introduce the generalized kinetic equation that depends on a function of four real variables F(x1; x2; x3; x4). The function F is assumed to satisfy certain commutation relations. The general properties of this equation are studied. It is shown that the above mentioned kinetic equations correspond to different forms of the function (poly

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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 simplici

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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 (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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BELLOUQUID, A. "A DIFFUSIVE LIMIT FOR NONLINEAR DISCRETE VELOCITY MODELS." Mathematical Models and Methods in Applied Sciences 13, no. 01 (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 applicatio

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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 whe

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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 Kram

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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 son

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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, u

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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 equil

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Raghavendra, Nandagiri Venkata. "Discrete Velocity Boltzmann Schemes for Inviscid Compressible Flows." Thesis, 2017. http://etd.iisc.ac.in/handle/2005/4314.

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It is known that high-speed flows are compressible. In large parts of the flow domains, the inviscid approximation is valid and this leads to Euler equations of gas dynamics. These inviscid compressible flows are modelled by coupled nonlinear hyperbolic systems of partial differential equations and generally require numerical solution techniques, as analytical solutions are usually not available. Out of all the numerical methods developed over the past five decades to solve the Euler equations, the schemes based on kinetic theory of gases are elegant ones with distinct advantages of simplicit

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Books on the topic "Discrete Boltzmann equation"

1

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

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

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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. 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. 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. 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. 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. 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. 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. 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. Elsevier, 2011. http://dx.doi.org/10.1016/b978-0-12-387779-6.00012-0.

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"5 Discrete models of the Boltzmann equation." In Landau Equation, Boltzmann-type Equations, Discrete Models, and Numerical Methods. De Gruyter, 2024. http://dx.doi.org/10.1515/9783110551006-006.

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"7 General Boltzmann-type equations." In Landau Equation, Boltzmann-type Equations, Discrete Models, and Numerical Methods. De Gruyter, 2024. http://dx.doi.org/10.1515/9783110551006-008.

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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 evaluatio

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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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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 fo

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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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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"

1

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), 1995. http://dx.doi.org/10.2172/106676.

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