Academic literature on the topic 'Boltzmann Scheme'
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Journal articles on the topic "Boltzmann Scheme"
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Venturi, Sara, Silvia Di Francesco, Martin Geier, and Piergiorgio Manciola. "Forcing for a Cascaded Lattice Boltzmann Shallow Water Model." Water 12, no. 2 (February 6, 2020): 439. http://dx.doi.org/10.3390/w12020439.
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This work compares three forcing schemes for a recently introduced cascaded lattice Boltzmann shallow water model: a basic scheme, a second-order scheme, and a centred scheme. Although the force is applied in the streaming step of the lattice Boltzmann model, the acceleration is also considered in the transformation to central moments. The model performance is tested for one and two dimensional benchmarks.
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Gao, Shangwen, Chengbin Zhang, Yingjuan Zhang, Qiang Chen, Bo Li, and Suchen Wu. "Revisiting a class of modified pseudopotential lattice Boltzmann models for single-component multiphase flows." Physics of Fluids 34, no. 5 (May 2022): 057103. http://dx.doi.org/10.1063/5.0088246.
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Since its emergence, the pseudopotential lattice Boltzmann (LB) method has been regarded as a straightforward and practical approach for simulating single-component multiphase flows. However, its original form always results in a thermodynamic inconsistency, which, thus, impedes its further application. Several strategies for modifying the force term have been proposed to eliminate this limitation. In this study, four typical and widely used improved schemes—Li's single-relaxation-time (SRT) scheme [Li et al., “Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows,” Phys. Rev. E 86, 016709 (2012)] and multiple-relaxation-times (MRT) scheme [Li et al., “Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model,” Phys. Rev. E 87, 053301 (2013)], Kupershtokh's SRT scheme [Kupershtokh et al., “On equations of state in a lattice Boltzmann method,” Comput. Math. Appl. 58, 965 (2009)], and Huang's MRT scheme [Huang and Wu, “Third-order analysis of pseudopotential lattice Boltzmann model for multiphase flow,” J. Comput. Phys. 327, 121 (2016)]—are systematically analyzed and intuitively compared after an extension of the MRT framework. The theoretical and numerical results both indicate that the former three schemes are specific forms of the last one, which thus help further understand the improvements of these pseudopotential LB models for achieving thermodynamic consistency. In addition, we modified the calculation of the additional source term in the LB evolution equation. Numerical results for stationary and moving droplets confirm the higher accuracy.
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Wang, Liang, Zhaoli Guo, Baochang Shi, and Chuguang Zheng. "Evaluation of Three Lattice Boltzmann Models for Particulate Flows." Communications in Computational Physics 13, no. 4 (April 2013): 1151–72. http://dx.doi.org/10.4208/cicp.160911.200412a.
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AbstractA comparative study is conducted to evaluate three types of lattice Boltzmann equation (LBE) models for fluid flows with finite-sized particles, including the lattice Bhatnagar-Gross-Krook (BGK) model, the model proposed by Ladd [Ladd AJC, J. Fluid Mech., 271, 285-310 (1994); Ladd AJC, J. Fluid Mech., 271, 311-339 (1994)], and the multiple-relaxation-time (MRT) model. The sedimentation of a circular particle in a two-dimensional infinite channel under gravity is used as the first test problem. The numerical results of the three LBE schemes are compared with the theoretical results and existing data. It is found that all of the three LBE schemes yield reasonable results in general, although the BGK scheme and Ladd’s scheme give some deviations in some cases. Our results also show that the MRT scheme can achieve a better numerical stability than the other two schemes. Regarding the computational efficiency, it is found that the BGK scheme is the most superior one, while the other two schemes are nearly identical. We also observe that the MRT scheme can unequivocally reduce the viscosity dependence of the wall correction factor in the simulations, which reveals the superior robustness of the MRT scheme. The superiority of the MRT scheme over the other two schemes is also confirmed by the simulation of the sedimentation of an elliptical particle.
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Xu, Kun, and Li-Shi Luo. "Connection Between Lattice-Boltzmann Equation and Beam Scheme." International Journal of Modern Physics C 09, no. 08 (December 1998): 1177–87. http://dx.doi.org/10.1142/s0129183198001072.
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In this paper we analyze and compare the lattice-Boltzmann equation with the beam scheme in detail. We notice the similarity and differences between the lattice Boltzmann equation and the beam scheme. We show that the accuracy of the lattice-Boltzmann equation is indeed second order in space. We discuss the advantages and limitations of the lattice-Boltzmann equation and the beam scheme. Based on our analysis, we propose an improved multi-dimensional beam scheme.
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Qiu, Ruofan, Rongqian Chen, and Yancheng You. "An implicit-explicit finite-difference lattice Boltzmann subgrid method on nonuniform meshes." International Journal of Modern Physics C 28, no. 04 (April 2017): 1750045. http://dx.doi.org/10.1142/s0129183117500450.
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In this paper, an implicit-explicit finite-difference lattice Boltzmann method with subgrid model on nonuniform meshes is proposed. The implicit-explicit Runge–Kutta scheme, which has good convergence rate, is used for the time discretization and a mixed difference scheme, which combines the upwind scheme with the central scheme, is adopted for the space discretization. Meanwhile, the standard Smagorinsky subgrid model is incorporated into the finite-difference lattice Boltzmann scheme. The effects of implicit-explicit Runge–Kutta scheme and nonuniform meshes of present lattice Boltzmann method are discussed through simulations of a two-dimensional lid-driven cavity flow on nonuniform meshes. Moreover, the comparison simulations of the present method and multiple relaxation time lattice Boltzmann subgrid method are conducted qualitatively and quantitatively.
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Wen, Mengke, Weidong Li, and Zhangyan Zhao. "A hybrid scheme coupling lattice Boltzmann method and finite-volume lattice Boltzmann method for steady incompressible flows." Physics of Fluids 34, no. 3 (March 2022): 037114. http://dx.doi.org/10.1063/5.0085370.
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We present a new hybrid method coupling the adaptive mesh refinement lattice Boltzmann method (AMRLBM) and the finite-volume lattice Boltzmann method (FVLBM) to improve both the simulation efficiency and adaptivity for steady incompressible flows with complex geometries. The present method makes use of the domain decomposition, in which the FVLBM sub-domain is applied to the region adjacent to the walls, and is coupled to the lattice Boltzmann method (LBM) sub-domain in the rest of the flow field to enhance the ability of the LBM to deal with irregular geometries without sacrificing the high efficiency and accuracy property of the LBM. In the LBM sub-domain, a cell-centered lattice structure-based AMRLBM is used and, in the FVLBM sub-domain, the gas-kinetic Bhatnagar–Gross–Krook (BGK) scheme-based FVLBM is adopted to reduce the numerical dissipation and enhance the efficiency of FVLBM. Moreover, not like the conventional LBM and Navier–Stokes equation solver-based hybrid schemes, the present hybrid scheme combines two kinds of lattice Boltzmann equation solvers, that is, AMRLBM and FVLBM, which makes the present scheme much simpler and better consistency than the conventional hybrid schemes. To assess the accuracy and efficacy of the proposed method, various benchmark studies, including the Kovasznay flow, the lid-driven cavity flow with Reynolds number [Formula: see text], 400, and 1000, and the steady flow past a cylinder with [Formula: see text] and 40, are also conducted. The numerical results show that the present scheme can be an efficient and reliable method for steady incompressible flows.
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SUGA, SHINSUKE. "STABILITY AND ACCURACY OF LATTICE BOLTZMANN SCHEMES FOR ANISOTROPIC ADVECTION-DIFFUSION EQUATIONS." International Journal of Modern Physics C 20, no. 04 (April 2009): 633–50. http://dx.doi.org/10.1142/s0129183109013856.
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The stability of the numerical schemes for anisotropic advection-diffusion equations derived from the lattice Boltzmann equation with the D2Q4 particle velocity model is analyzed through eigenvalue analysis of the amplification matrices of the scheme. Accuracy of the schemes is investigated by solving benchmark problems, and the LBM scheme is compared with traditional implicit schemes. Numerical experiments demonstrate that the LBM scheme produces stable numerical solutions close to the analytical solutions when the values of the relaxation parameters in x and y directions are greater than 1.9 and the Courant numbers satisfy the stability condition. Furthermore, the numerical solutions produced by the LBM scheme are more accurate than those of the Crank–Nicolson finite difference scheme for the case where the Courant numbers are set to be values close to the upper bound of the stability region of the scheme.
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Van Der Sman, R. G. M. "Lattice-Boltzmann Scheme for Natural Convection in Porous Media." International Journal of Modern Physics C 08, no. 04 (August 1997): 879–88. http://dx.doi.org/10.1142/s0129183197000758.
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A lattice-Boltzmann scheme for natural convection in porous media is developed and applied to the heat transfer problem of a 1000 kg potato packaging. The scheme has features new to the field of LB schemes. It is mapped on a orthorhombic lattice instead of the traditional cubic lattice. Furthermore the boundary conditions are formulated with a single paradigm based upon the particle fluxes. Our scheme is well able to reproduce (1) the analytical solutions of simple model problems and (2) the results from cooling down experiments with potato packagings.
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ZHENG, H. W., and C. SHU. "EVALUATION OF THE PERFORMANCE OF THE HYBRID LATTICE BOLTZMANN BASED NUMERICAL FLUX." International Journal of Modern Physics: Conference Series 42 (January 2016): 1660152. http://dx.doi.org/10.1142/s2010194516601526.
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It is well known that the numerical scheme is a key factor to the stability and accuracy of a Navier-Stokes solver. Recently, a new hybrid lattice Boltzmann numerical flux (HLBFS) is developed by Shu's group. It combines two different LBFS schemes by a switch function. It solves the Boltzmann equation instead of the Euler equation. In this article, the main object is to evaluate the ability of this HLBFS scheme by our in-house cell centered hybrid mesh based Navier-Stokes code. Its performance is examined by several widely-used bench-mark test cases. The comparisons on results between calculation and experiment are conducted. They show that the scheme can capture the shock wave as well as the resolving of boundary layer.
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LALLEMAND, PIERRE, and LI-SHI LUO. "HYBRID FINITE-DIFFERENCE THERMAL LATTICE BOLTZMANN EQUATION." International Journal of Modern Physics B 17, no. 01n02 (January 20, 2003): 41–47. http://dx.doi.org/10.1142/s0217979203017060.
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We analyze the acoustic and thermal properties of athermal and thermal lattice Boltzmann equation (LBE) in 2D and show that the numerical instability in the thermal lattice Boltzmann equation (TLBE) is related to the algebraic coupling among different modes of the linearized evolution operator. We propose a hybrid finite-difference (FD) thermal lattice Boltzmann equation (TLBE). The hybrid FD-TLBE scheme is far superior over the existing thermal LBE schemes in terms of numerical stability. We point out that the lattice BGK equation is incompatible with the multiple relaxation time model.
Dissertations / Theses on the topic "Boltzmann Scheme"
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Karra, Satish. "Modeling electrospinning process and a numerical scheme using Lattice Boltzmann method to simulate viscoelastic fluid flows." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1347.
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Guclu, Yaman. "Modular numerical environment for the characterization of a Helicon plasma thruster." Doctoral thesis, Università degli studi di Padova, 2011. http://hdl.handle.net/11577/3421711.
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The Helicon Plasma Thruster is a space propulsion system composed of a Helicon plasma source, with a properly designed magnetic nozzle. It is a very attractive concept due to the expected range of specific impulse and thrust-to-weight ratio, the scalability of the design, and the simplicity of construction; moreover, it is electrode-less and has no moving parts, and hence it can be expected to have an extended lifetime.
Although Helicon plasma sources have been used for decades in laboratories for producing high density plasmas, they are not fully understood yet. In fact, despite the simple geometry, a whole range of physical phenomena take place in the source: atomic physics, fluid kinetics, electrostatics and electromagnetism must be taken into account, and they are strongly interconnected to each other.
As a result, a Helicon plasma source is a very complex system to model, and to the author's knowledge, there is no reliable set of predictive tools for the design and optimization of such a source.
This thesis work focusses on Helicon plasma sources for space propulsion applications, and more precisely, it studies the configuration proposed in the HPH.com project (Helicon Plasma Hydrazine. COmbined Micro), in the Seventh Framework Programme of the European Union. The plasma source under study is small (approximately 15 cm in length), and the thruster is expected to provide just about 2 mN of thrust with 50 W of electric power consumption; as such, it is intended for use in the attitude control system of micro-satellites.
In order to optimize the computational resources available, a hybrid model is preferred to a monolithic model. In the former approach, the physical system is decomposed into subsystems, and each of these is simulated by a dedicated submodel, which (ideally) would use the most appropriate level of detail.
As no extensive theory on hybrid modeling exists, part of this thesis is dedicated to the investigation of the 'best way' to construct a hybrid model. An original approach is proposed, which is based on constructing submodels which rely on many different levels of detail, instead of just 'the best one'. This approach is natural, and it is believed to provide flexibility, robustness and physical insight.
According to the ideas above, a series of increasingly complicated models have been developed. Since the detailed and self-consistent simulation of the whole plasma source falls way beyond the scope of a single PhD thesis, most of the effort has been put into understanding the coupled dynamics of electrons and neutrals, which has not been throughly investigated yet.
In order to assess the ionization efficiency of the source, 0D and 1D analytic models of the neutral depletion process are presented. The comparison of the two models show the regimes where a higher level of detail is necessary, and the conditions under which the 1D model asymptotically recovers the 0D solution.
Subsequently, the neutral dynamics is coupled to the electron dynamics, by means of a semi-analytic 0D model which assumes Maxwellian electrons. The solution obtained gives a first estimate of the plasma parameters in the source, so that proper ranges for the characteristic lengths and time-scales of the various physical processes are calculated. Those results are essential to the preliminary design of a bounce averaged electron kinetic model, which is still 0D in space, but which calculates the electron energy distribution function self-consistently with the various processes.
After that, the 0D-1V electron kinetic model is designed in detail, including the effect of electromagnetic heating and various collisional processes. Accelerated convergence to the self-consistent steady-state is obtained by means of time-scale separation, fixed-point iteration, implicit time integration with Newton's solver and variable time-step, and a reduced auxiliary model. The neutral density in the source is obtained from the aforementioned 1D analytic model.
When the necessity for a detailed kinetic model for neutrals was realized, a 3D-3V semi-Lagrangian Convected Scheme was developed, which solves the Boltzmann equation in six-dimensional phase-space, plus time. Being the first implementation of the Convected Scheme to be 3D in space, several computational problems arose, and new solutions had to be found. For this reason, a considerable part of this thesis work had to deal with a new method for implementing diffuse boundary conditions, a new injector model, a new mass-, momentum- and energy-conserving collision operator for the Bhatnagar-Gross-Krook model, and a new angular mesh. Moreover, a novel third-order positivity-preserving remapping method with low numerical diffusion was developed.Un propulsore al plasma di tipo Helicon è un sistema di propulsione spaziale composto da una sorgente Helicon e da un ugello magnetico appositamente progettato. Tale tipo di propulsore attrae molto interesse per via dell'intervallo atteso per l'impulso specifico ed il rapporto spinta-su-peso, nonché per la scalabilità del concetto e la semplicità costruttiva. Inoltre, un propulsore Helicon è privo di elettrodi e di parti in movimento, dunque ci si aspetta una lunga durata di funzionamento. Malgrado le sorgenti Helicon siamo stata impiegate per decenni per produrre plasmi ad elevata densità, il loro funzionamento non è ancora del tutto compreso. Infatti, sebbene la geometria sia semplice, una vasta gamma di fenomeni fisici convivono all'interno della sorgente: vanno presi in considerazione la fisica atomica, la cinetica dei fluidi, l'elettrostatica e l'elettromagnetismo, e tutti questi sono strettamente interdipendenti. La sorgente Helicon è dunque un sistema molto complesso da modellare e, a conoscenza dell'autore, non è ancora stato sviluppato un sistema di strumenti per la progettazione e l'ottimizzazione di tale tipo di sorgente. Il lavoro svolto all'interno di questa tesi si concentra sullo studio di una sorgente Helicon da applicarsi nella propulsione spaziale e, più precisamente, sullo studio della configurazione proposta del progetto HPH.com (Helicon Plasma Hydrazine. COmbined Micro), nel settimo Framework Programme dell'Unione Europea. La sorgente di plasma considerata è di piccole dimensioni (circa 15 cm in lunghezza), e ci si aspetta che il propulsore fornisca circa 2 mN di spinta a fronte di 50 W di potenza elettrica fornita. Con queste caratteristiche, il propulsore è pensato per l'utilizzo nel controllo d'assetto di micro-satelliti. Con il fine di ottimizzare le risorse computazionali a disposizione, un modello ibrido risulta preferibile rispetto ad un modello monolitico. Secondo il primo approccio, il sistema fisico è decomposto in sotto-sistemi, ed ognuno di essi è simulato da un sotto-modello dedicato, che (idealmente) dovrebbe utilizzare un livello di dettaglio appropriato. Non esiste alcuna teoria esaustiva su come sviluppare modelli ibridi, e parte di questa tesi è dedicata ad investigare la 'via migliore' di costruire un modello ibrido. Viene qui proposto un approccio originale, basato sulla costruzione di sotto-modelli che si affidano a diversi livelli di dettaglio, invece che semplicemente sul miglior modello possibile. Tale approccio è naturale, e ci si aspetta che sia flessibile, robusto e che fornisca una migliore comprensione del fenomeno fisico. Seguendo tale metodologia, è stata sviluppata una serie di modelli via via più complessi. Poiché una simulazione dettagliata ed autoconsistente dell'intera sorgente non può essere completata in una singola tesi di Dottorato, la maggior parte di questo lavoro si concentra sulla comprensione della dinamica accoppiata di elettroni e neutri, che in questo sistema non è mai stata approfonditamente investigata. Per valutare l'efficienza di ionizzazione all'interno della sorgente, modelli analitici 0D e 1D del processo di deplezione dei neutri sono presentati. Il confronto dei due modelli suggerisce i regimi in cui è necessario un livello di dettaglio più elevato, e mostra le condizioni in cui il modello 1D converge asintoticamente alla soluzione 0D. Successivamente, la dinamica dei neutri è accoppiata alla dinamica degli elettroni, per mezzo di un modello semi-analitico 0D che assume che gli elettroni abbiano una distribuzione Maxwelliana. La soluzione ottenuta fornisce valori preliminari per i parametri di plasma all’interno della sorgente, dai quali è possibile valutare un intervallo di lunghezze caratteristiche e di scale temporali che caratterizzano i diversi processi fisici. Questi risultati sono essenziali per la progettazione preliminare di un modello cinetico per gli elettroni mediato su un elevato numero di oscillazioni all'interno della sorgente ('bounce averaged'); tale modello rimane 0D nello spazio, ma esso calcola la distribuzione energetica degli elettroni in modo autoconsistente con i vari processi. Successivamente, un modello 0D-1V cinetico per gli elettroni è stato progettato nel dettaglio, includendo l’effetto del riscaldamento elettromagnetico e dei diversi processi collisionali. La convergenza a regime stazionario è stata accelerata attraverso la separazione delle diverse scale temporali, iterazioni di punto fisso, integrazione implicita con un solutore di Newton a passo temporale variabile, ed un modello ausiliario ridotto. La densità dei neutri nella sorgente è ottenuta dal modello analitico 1D sopra citato. Quando si è ritenuto necessario un modello dettagliato dei neutri, è stato sviluppato un modello cinetico 3D-3V, che impiega un solutore semi-Lagrangiano chiamato Convected Scheme. Questo modello risolve l'equazione di Boltzmann nello spazio nelle fasi a sei dimensioni, più il tempo. Trattandosi della prima implementazione del Convective Scheme in tre dimensioni spaziali, si sono incontrati diversi problemi di natura computazionale, per i quali è stato necessario trovare soluzioni innovative. Per questa ragione, una parte consistente di questo lavoro di tesi è stata dedicata ad implementare nuove condizioni al contorno diffusive, un nuovo modello di iniettore, una nuova mesh angolare ed un innovativo operatore collisionale per il modello di Bhatnagar-Gross-Krook che conservi esattamente massa, quantità di moto ed energia. Inoltre, è stato sviluppato un metodo innovativo di rimappatura, accurato al terzo ordine, che preserva la positività della soluzione e possiede bassa diffusione numerica.
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Späth, Peter. "Renewed Theory, Interfacing, and Visualization of Thermal Lattice Boltzmann Schemes." Doctoral thesis, Universitätsbibliothek Chemnitz, 2000. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200000648.
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In this Doktorarbeit the Lattice Boltzmann scheme, a heuristic method for the simulation of flows in complicated boundaries, is investigated. Its theory is renewed by emphasizing the entropy maximization principle, and new means for the modelling of geometries (including moving boundaries) and the visual representation of evoluting flows are presented. An object oriented implemen- tation is given with communication between objects realized by an interpreter object and communication from outside realized via interprocess communica- tion. Within the new theoretical apprach the applicability of existing Lattice Boltzmann schemes to model thermal flows for arbitrary temperatures is reex- aminedIn dieser Doktorarbeit wird das Gitter-Boltzmann-Schema, eine heuristische Methode fuer die Simulation von Stroemungen innerhalb komplexer Raender, untersucht. Die zugrundeliegende Theorie wird unter neuen Gesichtspunkten, insbesondere dem Prinzip der Entropiemaximierung, betrachtet. Des weiteren werden neuartige Methoden fuer die Modellierung der Geometrie (einschl. beweglicher Raender) und der visuellen Darstellung aufgezeigt. Eine objektorientierte Implementierung wird vorgestellt, wobei die Kommunikation zwischen den Objekten über Interpreter-Objekte und die Kommunikation mit der Aussenwelt ueber Interprozess-Kommunikation gehandhabt wird. Mit dem neuen theoretischen Ansatz wird die Gueltigkeit bestehender Gitter-Boltzmann-Schemata fuer die Anwendung auf Stroemungen mit nicht konstanter Temperatur untersucht
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Uphoff, Sonja [Verfasser], and Manfred [Akademischer Betreuer] Krafczyk. "Development and Validation of turbulence models for Lattice Boltzmann schemes / Sonja Uphoff ; Betreuer: Manfred Krafczyk." Braunschweig : Technische Universität Braunschweig, 2013. http://d-nb.info/1175821896/34.
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Bernard, Florian. "Efficient Asymptotic Preserving Schemes for BGK and ES-BGK models on Cartesian grids." Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0040/document.
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Dans cette thèse, nous nous sommes intéressés à des écoulements complexes où les régimes hydrodynamique et raréfiés coexistent. On retrouve ce type d'écoulements dans des applications industrielles comme les pompes à vide ou encore les rentrées de capsules spatiales dans l'atmosphère, lorsque la distance entre les molécules de gaz devient si grande que le comportement microscopique des molécules doit être pris en compte. Pour ce faire, nous étudions 2 modèles de l'équation de Boltzmann, le modèle BGK et le modèle ES-BGK. Dans un premier temps, nous développons une nouvelle condition au bord permettant une transition continue de la solution du régime raréfié vers le régime hydrodynamique. Cette nouvelle condition permettant de préserver l'asymptotique vers les équations d'Euler compressible est ensuite incluse dans une méthode de frontière immergée pour traiter, à une précision raisonnable (ordre 2), le cas de solides immergés dans un écoulement, sur grilles cartésiennes. L'utilisation de grillescartésiennes permet une parallélisation aisée du code de simulation numérique afin d'obtenir une réduction considérable du temps de calcul, un des principaux inconvénients des modèles cinétiques. Par la suite, une approche dites aux grilles locales en vitesses est présentée réduisant également le temps de calcul de manière importante (jusqu'à 80%). Des simulations 3D sont également présentées montrant l'efficacité des méthodes. Enfin, le transport passive de particules solides dans un écoulement raréfié est étudié avec l'introduction d'un modèle de type Vlasov couplé au modèle cinétique. Grâce à une résolution basée sur des méthodes de remaillage, la pollution de dispositif optiques embarqués sur des satellites dues à des particules issues de la combustion incomplète dans les moteurs contrôlant d'altitude est étudiéeThis work is devoted to the study of complex flows where hydrodynamic and rarefled regimes coexist. This kind of flows are found in vacuum pumps or hypersonic re-entries of space vehicles where the distance between gas molecules is so large that their microscopicbehaviour differ from the average behaviour of the flow and has be taken into account. We then consider two modelsof the Boltzmann equation viable for such flows: the BGK model dans the ES-BGK model.We first devise a new wall boundary condition ensuring a smooth transition of the solution from the rarefled regime to the hydrodynamic regime. We then describe how this boundary condition (and boundary conditions in general) can be enforced with second order accuracy on an immersed body on Cartesian grids preserving the asymptotic limit towards compressible Euler equations. We exploit the ability of Cartesian grids to massive parallel computations (HPC) to drastically reduce the computational time which is an issue for kinetic models. A new approach considering local velocity grids is then presented showing important gain on the computational time (up to 80%). 3D simulations are also presented showing the efficiency of the methods. Finally, solid particle transport in a rarefied flow is studied. The kinetic model is coupled with a Vlasov-type equation modeling the passive particle transport solved with a method based on remeshing processes. As application, we investigate the realistic test case of the pollution of optical devices carried by satellites due to incompletely burned particles coming from the altitude control thrusters
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Février, Tony. "Extension et analyse des schémas de Boltzmann sur réseau : les schémas à vitesse relative." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112316/document.
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Cette thèse introduit et étudie une nouvelle classe de schémas de Boltzmann sur réseau appelés schémas à vitesse relative. Les schémas de Boltzmann sur réseau visent à approcher des problèmes de nature macroscopique en mimant la dynamique microscopique d’équations cinétiques du type Boltzmann. L’algorithme calcule des distributions de particules évoluant au travers de deux phases de transport et de relaxation, les particules se déplaçant en les noeuds d’un réseau cartésien en espace. Les schémas de Boltzmann à plusieurs temps de relaxation (ou schéma MRT de d’Humières), dont la relaxation im- plique un ensemble de moments combinaison linéaire polynomiale des distributions, constituent le cadre initial de la thèse. Les schémas à vitesse relative sont une extension de ces schémas de d’Humières. Ils sont inspirés du schéma cascade de Geier apportant davantage de stabilité que les schémas de d’Hu- mières pour des régimes peu visqueux des équations de Navier-Stokes. La différence avec ces schémas se situe au niveau de la relaxation : elle utilise un ensemble de moments relatifs à un paramètre champ de vitesse fonction du temps et de l’espace. Cette différence se matérialise par une matrice de tran- sition des moments fixes (les schémas de d’Humières correspondent à un paramètre champ de vitesse nul) aux moments mobiles. La structure algébrique de cette matrice est étudiée. Le schéma cascade est ensuite traduit comme un schéma à vitesse relative pour un nouvel ensemble de polynômes définissant les moments. L’étude de la consistance des schémas à vitesse relative par la méthode des équations équivalentes est un point central de la thèse. Les équations limites pour un nombre arbitraire de dimen- sions et de vitesses sont dérivées et illustrées sur des exemples tels que le D2Q9 pour les équations de Navier-Stokes. Ces équations équivalentes sont également un outil pour prédire la stabilité des schémas grâce à l’analyse des termes de diffusion et dispersion. La dernière partie traite de la stabilité suivant le choix du paramètre champ de vitesse. Nous sommes particulièrement intéressés en les deux choix de paramètre nul (d’Humières) et la vitesse du fluide (cascade). Le schéma D2Q9 pour les équations de Navier-Stokes est étudié numériquement par une méthode de Von Neumann puis appuyé sur des cas tests non linéaires. La stabilité des schémas relatifs à la vitesse du fluide est dépendante du choix des polynômes définissant les moments. L’amélioration la plus notable se produit si les polynômes du schéma cascade sont choisis. Nous étudions enfin les stabilités théorique et numérique d’un schéma bidimensionnel minimal. Le contexte physique est la simulation d’une équation d’advection diffusion linéaire. Le choix de la vitesse d’advection comme paramètre champ de vitesse annule certains termes de dispersion des équations équivalentes contrairement aux schémas de d’Humières. Ceci se traduit par un meilleur comportement en termes de stabilité pour de grandes vitesses, appuyé théoriquement à l’aide d’une notion de stabilité à poidsIn this PhD thesis, a new class of lattice Boltzmann schemes called relative velocity schemes is introduced and studied. The purpose of lattice Boltzmann schemes is to approximate problems of macroscopic nature using the microscopic dynamic of Boltzmann type kinetic equations. They compute particle distributions through two phases of transport and relaxation, the particles moving on the nodes of a cartesian lattice. The multiple relaxation times schemes---MRT of d'Humières---, whose relaxation uses a set of moments, linear combinations of the particle distributions, constitutes the initial framework of the thesis. The relative velocity schemes extend the MRT d'Humières schemes. They originate from the cascaded automaton of Geier which provides more stability for the low viscosity regime of the Navier-Stokes equations. Their difference with the d'Humières schemes is carried by the relaxation : a set of moments relative to a velocity field parameter function of space and time is used. This difference is represented by a shifting matrix sending the fixed moments---The d'Humières schemes are associated with a zero velocity field parameter---On the relative moments. The algebraic structure of this matrix is studied. The cascaded automaton is then interpreted as a relative velocity scheme for a new set of polynomials defining the moments. The consistency study of the relative velocity schemes with the equivalent equations method is a keypoint of the thesis. These equations are derived for an arbitrary number of dimensions and velocities. They are then illustrated on examples like the D2Q9 scheme for the Navier-Stokes equations. These equivalent equations are also a tool to predict the stability behaviour of the schemes by analysing their diffusion and dispersion terms. In a last part, the stability according to the velocity field parameter is studied. Two cases especially interest us : a parameter equal to zero---D'Humières schemes---And equal to the fluid velocity---Cascaded automaton. The D2Q9 scheme for the Navier-Stokes equations is numerically studied with a linear Von Neumann analysis and some non linear test cases. The stability of the relative velocity schemes depends on the choice of the polynomials defining the moments. The most important improvement occurs if the polynomials of the cascaded automaton are chosen. We finally study the theoretical and numerical stability of a minimal bidimensional scheme for a linear advection diffusion equation. If the velocity field parameter is chosen equal to the advection velocity, some dispersion terms of the equivalent equations vanish unlike the d'Humières scheme. This implies a better stability behaviour for high velocities, characterized thanks to theoretical weighted stability notion
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Herouard, Nicolas. "Optimisation, analyse et comparaison de méthodes numériques déterministes par la dynamique des gaz raréfiés." Thesis, Bordeaux, 2014. http://www.theses.fr/2014BORD0473/document.
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Lors de la rentrée atmosphérique, l’écoulement raréfié de l’air autour de l’objet rentrant est régi par un modèle cinétique dérivé de l’équation de Boltzmann ; celui-ci décrit l’évolution d’une fonction de distribution des particules de gaz dans l’espace des phases, de dimension 6 dans le cas général. La simulation numérique déterministe de cet écoulement requiert donc le traitement d’une quantité considérable de données, soit un espace mémoire et un temps de calcul importants. Nous étudions dans ce travail différents moyens de réduire le coût de ces calculs. La première approche est une méthode permettant d’optimiser la taille de la grille de vitesses discrètes employée dans le calcul par une prédiction de l’allure des fonctions de distribution dans l’espace des vitesses, en supposant un faible déséquilibre thermodynamique du gaz. La seconde approche consiste à essayer d’exploiter les propriétés de préservation asymptotique des schémas Galerkin Discontinu, déjà établies dans le cadre du transport linéaire des neutrons, qui permettent de tenir compte des effets de la couche limite cinétique sans que celle-ci soit résolue par le maillage, alors que les méthodes classiques (comme les Volumes Finis) imposent l’utilisation de maillages très raffinés en zone de proche paroi. Dans une dernière partie, nous comparons les performances respectives de ces schémas Galerkin Discontinu et de quelques schémas Volumes Finis, appliqués au modèle BGK sur un cas simple, en étudiant en particulier leur comportement près des parois et les conditions aux limites numériquesDuring the atmospheric re-entry of a space engine, the rarefied air flow around the body is determined by a kinetic model derived from the Boltzmann equation, which describes the evolution of a distribution function of gas molecules in the phase space, this means a 6-dimensional space in the general case. Consequently, a deterministic numerical simulation of this flow requires large computational ressources, both in memory storage and CPU time. The aim of this work is to reduce those ressources, using two different approaches. The first one is a method allowing to optimize the size of the discrete velocity grid used for the computation by a prediction of the shape of the distributions in the velocity space, assuming that the gas is close to thermodynamic equilibrium. The second approach is an attempt to use the asymptotic preservation properties of Discontinuous Galerkin schemes, already established for neutron transport, which allow to take into account the effects of kinetic boundary layers even if they are not resolved by the mesh, while classical methods (such as Finite Volumes) require very refined meshes along the direction normal to the walls. In a last part, we compare the performances of these Discontinuous Galerkin schemes with some classical Finite Volumes schemes, applied to the BGK equation in a simple case, and pay particular attention to their near-wall behavior and numerical boundary conditions
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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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Kotnala, Sourabh. "Lattice Boltzmann Relaxation Scheme for Compressible Flows." Thesis, 2012. http://hdl.handle.net/2005/3257.
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Lattice Boltzmann Method has been quite successful for incompressible
flows. Its extension for compressible (especially supersonic and hypersonic)
flows has attracted lot of attention in recent time. There have been some
successful attempts but nearly all of them have either resulted in complex
or expensive equilibrium function distributions or in extra energy levels.
Thus, an efficient Lattice Boltzmann Method for compressible fluid flows
is still a research idea worth pursuing for. In this thesis, a new Lattice
Boltzmann Method has been developed for compressible flows, by using the concept of a relaxation system, which is traditionally used as semilinear alternative for non-linear hypebolic systems in CFD. In the relaxation
system originally introduced by Jin and Xin (1995), the non-linear flux in a hyperbolic conservation law is replaced by a new variable, together with a relaxation equation for this new variable augmented by a
relaxation term in which it relaxes to the original nonlinear flux, in the limit of a vanishing relaxation parameter. The advantage is that instead of one non-linear hyperbolic equation, two linear hyperbolic equations need to be solved, together with a non-linear relaxation term. Based on the interpretation
of Natalini (1998) of a relaxation system as a discrete velocity Boltzmann equation, with a new isotropic relaxation system as the basic building block, a Lattice Boltzmann Method is introduced for solving the
equations of inviscid compressible flows. Since the associated equilibrium
distribution functions of the relaxation system are not based on a low Mach
number expansion, this method is not restricted to the incompressible limit.
Free slip boundary condition is introduced with this new relaxation system
based Lattice Boltzmann method framework. The same scheme is then extended
for curved boundaries using the ghost cell method. This new Lattice Boltzmann Relaxation Scheme is successfully tested on various bench-mark test cases for solving the equations of compressible flows such as shock tube problem in 1-D and in 2-D the test cases involving supersonic flow over a forward-facing step, supersonic oblique shock reflection from a flat plate, supersonic and hypersonic flows past half-cylinder.
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Kang, Wei-Yi, and 康偉逸. "Computation of Boltzmann Model Equation Using Asymptotic-Preserving and WENO Scheme." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/34783098081653499938.
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碩士國立臺灣大學
應用力學研究所
102
An accurate and direct algorithm for solving the classical Boltzmann equation and the semiclassical Boltzmann equation with relaxation time approximation in phase space is presented for parallel treatment of rarefied gas flows of particles of three statistics. In time domain, we use asymptotic-preserving method for solving two-dimensional Riemann problem by the classical Boltzmann equation and the semiclassical Boltzmann equation with very small relaxation time. After using asymptotic-preserving, we use fourth-order Runge-Kutta method to discrete time domain. In space domain, we use fifth-order weighted essentially non-oscillatory scheme to evolve the flux term. The discrete ordinate method is applied to remove the microscopic velocity dependency of the distribution function that renders the Boltzmann BGK equation in phase space to a set of hyperbolic conservation laws with source terms in physical space. Computational examples of two-dimensional Riemann problems for rarefied gas flows at very small relaxation time are presented. By using WENO scheme, the results show good resolution in capturing the main flow features while using grids with few good points.
Books on the topic "Boltzmann Scheme"
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Kun, Xu. Connection between the lattice Boltzmann equation and the beam scheme. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1999.
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Kun, Xu, and Institute for Computer Applications in Science and Engineering., eds. A gas-kinetic scheme for reactive flows. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.
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Kun, Xu, and Institute for Computer Applications in Science and Engineering., eds. A gas-kinetic scheme for reactive flows. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.
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Kun, Xu, and Institute for Computer Applications in Science and Engineering., eds. A gas-kinetic scheme for reactive flows. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.
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Kun, Xu, and Institute for Computer Applications in Science and Engineering., eds. A gas-kinetic scheme for reactive flows. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.
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Succi, Sauro. Lattice Boltzmann Models for Microflows. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0029.
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The Lattice Boltzmann method was originally devised as a computational alternative for the simulation of macroscopic flows, as described by the Navier–Stokes equations of continuum mechanics. In many respects, this still is the main place where it belongs today. Yet, in the past decade, LB has made proof of a largely unanticipated versatility across a broad spectrum of scales, from fully developed turbulence, to microfluidics, all the way down to nanoscale flows. Even though no systematic analogue of the Chapman–Enskog asymptotics is available in this beyond-hydro region (no guarantee), the fact remains that, with due extensions of the basic scheme, the LB has proven capable of providing several valuable insights into the physics of flows at micro- and nano-scales. This does not mean that LBE can solve the actual Boltzmann equation or replace Molecular Dynamics, but simply that it can provide useful insights into some flow problems which cannot be described within the realm of the Navier–Stokes equations of continuum mechanics. This Chapter provides a cursory view of this fast-growing front of modern LB research.
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Succi, Sauro. Entropic Lattice Boltzmann. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0021.
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The LB with enhanced collisions opened the way to the top-down design of LB schemes, with major gains in flexibility and computational efficiency. However, compliance with the second principle was swept under the carpet in the process, with detrimental effects on the numerical stability of the method. It is quite fortunate that, albeit forgotten, the above compliance did not get lost in the top-down procedure. Entropic LB schemes, the object of the present chapter, explain the whys and hows of this nice smile of Lady Luck.
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Succi, Sauro. Lattice Relaxation Schemes. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0014.
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In Chapter 13, it was shown that the complexity of the LBE collision operator can be cut down dramatically by formulating discrete versions with prescribed local equilibria. In this chapter, the process is taken one step further by presenting a minimal formulation whereby the collision matrix is reduced to the identity, upfronted by a single relaxation parameter, fixing the viscosity of the lattice fluid. The idea is patterned after the celebrated Bhatnagar–Gross–Krook (BGK) model Boltzmann introduced in continuum kinetic theory as early as 1954. The second part of the chapter describes the comeback of the early LBE in optimized multi-relaxation form, as well as few recent variants hereof.
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Cantor, Brian. The Equations of Materials. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198851875.001.0001.
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This book describes some of the important equations of materials and the scientists who derived them. It is aimed at anyone interested in the manufacture, structure, properties and engineering application of materials such as metals, polymers, ceramics, semiconductors and composites. It is meant to be readable and enjoyable, a primer rather than a textbook, covering only a limited number of topics and not trying to be comprehensive. It is pitched at the level of a final year school student or a first year undergraduate who has been studying the physical sciences and is thinking of specialising into materials science and/or materials engineering, but it should also appeal to many other scientists at other stages of their career. It requires a working knowledge of school maths, mainly algebra and simple calculus, but nothing more complex. It is dedicated to a number of propositions, as follows: 1. The most important equations are often simple and easily explained; 2. The most important equations are often experimental, confirmed time and again; 3. The most important equations have been derived by remarkable scientists who lived interesting lives. Each chapter covers a single equation and materials subject. Each chapter is structured in three sections: first, a description of the equation itself; second, a short biography of the scientist after whom it is named; and third, a discussion of some of the ramifications and applications of the equation. The biographical sections intertwine the personal and professional life of the scientist with contemporary political and scientific developments. The topics included are: Bravais lattices and crystals; Bragg’s law and diffraction; the Gibbs phase rule and phases; Boltzmann’s equation and thermodynamics; the Arrhenius equation and reactions; the Gibbs-Thomson equation and surfaces; Fick’s laws and diffusion; the Scheil equation and solidification; the Avrami equation and phase transformations; Hooke’s law and elasticity; the Burgers vector and plasticity; Griffith’s equation and fracture; and the Fermi level and electrical properties.
Book chapters on the topic "Boltzmann Scheme"
1
Vergassola, Massimo, R. Benzi, and S. Succi. "A Lattice Boltzmann Scheme for the Burger Equation." In Correlations and Connectivity, 320–21. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-2157-3_37.
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van der Sman, R. G. M. "Lattice Boltzmann Scheme for Diffusion on Triangular Grids." In Lecture Notes in Computer Science, 1072–81. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-44860-8_111.
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Albuquerque, Paul, Davide Alemani, Bastien Chopard, and Pierre Leone. "Coupling a Lattice Boltzmann and a Finite Difference Scheme." In Computational Science - ICCS 2004, 540–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-25944-2_70.
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Aristov, V. V. "Construction of Conservative Scheme for the Kinetic Equation." In Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows, 85–108. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0866-2_5.
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Derksen, J. J., J. L. Kooman, and H. E. A. van den Akker. "Parallel fluid flow simulations by means of a lattice-Boltzmann scheme." In High-Performance Computing and Networking, 524–30. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0031625.
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Zhang, Tao, and Shuyu Sun. "A Compact and Efficient Lattice Boltzmann Scheme to Simulate Complex Thermal Fluid Flows." In Lecture Notes in Computer Science, 149–62. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-93713-7_12.
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Majorana, A., and R. M. Pidatella. "A New Finite Difference Scheme for the Boltzmann — Poisson System on Semiconductor Devices." In Progress in Industrial Mathematics at ECMI 2000, 592–96. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04784-2_81.
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Kowalczyk, P., T. Platkowski, and W. Waluś. "Application of a Deterministic Scheme for the Boltzmann Equation in Modelling Shock Wave Focusing." In Traffic and Granular Flow ’99, 233–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-59751-0_22.
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Mohamad, A. A. "Multi-Relaxation Schemes." In Lattice Boltzmann Method, 101–5. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-455-5_7.
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Mohamad, A. A. "Multi-Relaxation Schemes." In Lattice Boltzmann Method, 145–49. London: Springer London, 2019. http://dx.doi.org/10.1007/978-1-4471-7423-3_10.
Full textConference papers on the topic "Boltzmann Scheme"
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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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Kravets, Bogdan, Muhammad S. Khan, and Harald Kruggel-Emden. "Development and application of a thermal lattice Boltzmann scheme." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912623.
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Ubertini, Stefano. "Computational Fluid Dynamics Through an Unstructured Lattice Boltzmann Scheme." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-41194.
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Computational fluid dynamics, in its conventional meaning, computes pertinent flow fields in terms of velocity, density, pressure and temperature by numerically solving the Navier-Stokes equations in time and space. At the turn of the 1980s, the Lattice Boltzmann Method (LBM) has been proposed as an alternative approach to solve fluid dynamics problems and due to the refinements and the extensions of the last years, it has been used to successfully compute a number of nontrivial fluid dynamics problems, from incompressible turbulence to multiphase flow and bubble flow simulations. The most severe limitation of the original method is the uniform Cartesian grid on which the LBM must be constructed, that requires the approximation of a curved solid boundary by a series of stair steps. This represents a particularly severe limitation for practical engineering purposes especially when there is a need for high resolutions near the body or the walls. Among the recent advances in lattice Boltzmann research that have lead to substantial enhancement of the capabilities of the method to handle complex geometries, a particularly remarkable option is represented by changing the solution procedure from the original “stream and collide” to a finite volume technique. This paper presents a compact and efficient finite-volume lattice Boltzmann formulation on unstructured grids based on a cell-vertex scheme recently proposed in literature to integrate the differential form of the lattice Boltzmann equation. It is shown that the method tolerates significant grid distortions without showing any appreciable numerical viscosity effects at second order in the mesh size, thus allowing a time-accurate description of transitional flows. Moreover, a new set of boundary conditions to handle flows with open boundaries is presented. The resulting model has been tested against typical flow problems at low and moderate Reynolds numbers.
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Hsu, C. T., S. W. Chiang, and K. F. Sin. "A Novel Dynamics Lattice Boltzmann Method for Gas Flows." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-31237.
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The lattice Boltzmann method (LBM), where discrete velocities are specifically assigned to ensure that a particle leaves one lattice node always resides on another lattice node, has been developed for decades as a powerful numerical tool to solve the Boltzmann equation for gas flows. The efficient implementation of LBM requires that the discrete velocities be isotropic and that the lattice nodes be homogeneous. These requirements restrict the applications of the currently-used LBM schemes to incompressible and isothermal flows. Such restrictions defy the original physics of Boltzmann equation. Much effort has been devoted in the past decades to remove these restrictions, but of less success. In this paper, a novel dynamic lattice Boltzmann method (DLBM) that is free of the incompressible and isothermal restrictions is proposed and developed to simulate gas flows. This is achieved through a coordinate transformation featured with Galilean translation and thermal normalization. The transformation renders the normalized Maxwell equilibrium distribution with directional isotropy and spatial homogeneity for the accurate and efficient implementation of the Gaussian-Hermite quadrature. The transformed Boltzmann equation contains additional terms due to local convection and acceleration. The velocity quadrature points in the new coordinate system are fixed while the correspondent points in the physical space change from time to time and from position to position. By this dynamic quadrature nature in the physical space, we term this new scheme as the dynamic quadrature scheme. The lattice Boltzmann method (LBM) with the dynamic quadrature scheme is named as the dynamic lattice Boltzmann method (DLBM). The transformed Boltzmann equation is then solved in the new coordinate system based on the fixed quadrature points. Validations of the DLBM have been carried with several benchmark problems. Cavity flows problem are used. Excellent agreements are obtained as compared with those obtained from the conventional schemes. Up to date, the DLBM algorithm can run up to Mach number at 0.3 without suffering from numerical instability. The application of the DLBM to the Rayleigh-Bernard thermal instability problem is illustrated, where the onset of 2D vortex rolls and 3D hexagonal cells are well-predicted and are in excellent agreement with the theory. In summary, a novel dynamic lattice Boltzmann method (DLBM) has been proposed with algorithm developed for numerical simulation of gas flows. This new DLBM has been demonstrated to have removed the incompressible and isothermal restrictions encountered by the traditional LBM.
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Seta, Takeshi, Kenichi Okui, and Eisyun Takegoshi. "Lattice Boltzmann Simulation of Nucleation." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45163.
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We propose a lattice Boltzmann model capable of simulating nucleation. This LBM modifies a pseudo-potential so that it recovers a full set of hydrodynamic equations for two-phase flows based on the van der Waals-Cahn-Hilliard free energy theory through the Chapman-Enskog expansion procedure. Numerical measurements of thermal conductivity and of surface tension agree well with theoretical predictions. Simulations of phase transition, nucleation, pool boiling are carried out. They demonstrate that the model is applicable to two-phase flows with thermal effects. Using finite difference Lattice Boltzmann method ensures numerical stability of the scheme.
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Fu, S. C., W. W. F. Leung, and R. M. C. So. "A Lattice Boltzmann Method Based Numerical Scheme for Microchannel Flows." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-67654.
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Lattice Boltzmann method (LBM) has been recently developed into an alternative and promising numerical scheme for modeling fluid physics and fluid flows. The equation is hyperbolic and can be solved locally, explicitly, and efficiently on parallel computers. LBM has been applied to different types of complex flows with varying degree of success, but rarely to micro-scale flow. Due to its small scale, micro-channel flow exhibits many interesting phenomena that are not observed in its macro-scale counterpart. It is known that the Navier-Stokes equations can still be used to treat micro-channel flows if a slip wall boundary condition is assumed. The setting of boundary conditions in LBM has been a difficult task, and reliable boundary setting methods are limited. This paper reports on the development of an algorithm to solve the Boltzmann equation with a splitting method that allows the application of a slip wall boundary condition. Moreover, the fluid viscosity is accounted for as an additional term in the equilibrium particle distribution function, which offers the ability to simulate both Newtonian and non-Newtonian fluids. An LBM based numerical scheme, which is suitable for micro-channel flows, is proposed. A two-dimensional nine-velocity lattice model is developed for the numerical simulation. Validation of the numerical scheme is carried out against micro-channel, micro-tube and driven cavity flows, and excellent agreement is obtained between numerical calculations and analytical solutions of these flows.
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Ma, Yu, Yahui Wang, Kuilong Song, and Qian Sun. "Adaptive Mesh Refinement for Neutron Transfer With Lattice Boltzmann Scheme." In 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-66093.
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This paper presents a novel lattice Boltzmann (LB) model for neutron transfer and a block-structured adaptive-mesh-refinement (SAMR) technique for proposed LB model. By discretizing the general Boltzmann equation, the LB model for neutron transfer is established and the corresponding parameters are obtained. The SAMR technique removes the requirement of tree-type data structure in traditional adaptive-mesh-refinement technique and adjusts the time step adaptively and identically in all blocks. By applying the node-type distribution function, the needs for rescaling the distribution functions is eliminated. To solve the discontinuities of scalar flux at fine-coarse blocks interface, a novel technique is presented which treats the inner boundary condition by streaming process of LB method. Simulation results show good accuracy and efficiency of the proposed neutron LB model with SAMR technique. This paper may provide a powerful technique for large engineering calculation.
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Ye Zhao. "GPU-accelerated surface denoising and morphing with lattice Boltzmann scheme." In 2008 IEEE International Conference on Shape Modeling and Applications (SMI). IEEE, 2008. http://dx.doi.org/10.1109/smi.2008.4547942.
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Sun, Xiuyu, Zhiqiang Wang, and George Chen. "Parallel active contour with Lattice Boltzmann scheme on modern GPU." In 2012 19th IEEE International Conference on Image Processing (ICIP 2012). IEEE, 2012. http://dx.doi.org/10.1109/icip.2012.6467208.
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Mikheev, Sergei A., and Gerasim V. Krivovichev. "Numerical analysis of two-step finite-difference-based lattice Boltzmann scheme." In 2014 International Conference on Computer Technologies in Physical and Engineering Applications (ICCTPEA). IEEE, 2014. http://dx.doi.org/10.1109/icctpea.2014.6893313.
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