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A lattice Boltzmann model for diffusion of binary gas mixtures that includes diffusion slip, Int
 J. Numer. Meth. Fluids
"... This thesis describes the development of a Lattice Boltzmann (LB) model for a binary gas mixture. Specifically, channel flow driven by a density gradient with diffusion slip occurring at the wall is studied in depth. The first part of this thesis sets the foundation for the multicomponent model use ..."
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This thesis describes the development of a Lattice Boltzmann (LB) model for a binary gas mixture. Specifically, channel flow driven by a density gradient with diffusion slip occurring at the wall is studied in depth. The first part of this thesis sets the foundation for the multicomponent model used in the subsequent chapters. Commonly used single component LB methods use a nonphysical equation of state, in which the relationship between pressure and density varies according to the scaling used. This is fundamentally unsuitable for extension to multicomponent systems containing gases of differing molecular masses that are modelled with the ideal gas equation of state. Also, existing methods for implementing boundary conditions are unsuitable for extending to novel boundary conditions, such as diffusion slip. Therefore, a new single component LB derivation and a new method for implementing boundary conditions are developed, and validated against Poiseuille flow. However, including a physical equation of state reduces stability and time accuracy, leading to longer computational times, compared with ‘incompressible ’ LB methods. The new method of analysing LB boundary conditions successfully explains observations from other commonly used schemes, such as the slip velocity associated with ‘bounceback’. The new model developed for multicomponent gases avoids the pitfalls of some other LB models, a single computational grid is shared by all the species and the diffusivity is independent of the viscosity. The NavierStokes equation for the mixture and the StefanMaxwell diffusion equation are both recovered by the model. However, the species momentum equations are not recovered correctly and this can lead to instability. Diffusion slip, the nonzero velocity of a gas mixture at a wall parallel to a concentration gradient, is successfully modelled and validated against a simple onedimensional model for channel flow. To increase the accuracy of the scheme a second order numerical implementation is needed. This can be achieved using a variable transformation method which does not result in an increase in computational time.
flow simulations Endothelial shear stress from largescale blood Subject collections
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Lattice Boltzmann method as a computational framework for multiscale haemodynamics Lattice Boltzmann method as a computational framework for multiscale haemodynamics
, 2013
"... Recent developments of the lattice Boltzmann method for largescale haemodynamic applications are presented, with special focus on multiscale aspects, including the selfconsistent dynamics of suspended biological bodies and their coupling to surface structures, such as the glycocalyx, in the proxi ..."
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Recent developments of the lattice Boltzmann method for largescale haemodynamic applications are presented, with special focus on multiscale aspects, including the selfconsistent dynamics of suspended biological bodies and their coupling to surface structures, such as the glycocalyx, in the proximity of endothelium using unstructured grids. The description of such multiscale phenomena, each one treated with a suitable variation of the lattice Boltzmann method, opens up new perspectives for a fundamental understanding of the physical mechanisms underlying cardiovascular pathologies, such as plaque growth and the subsequent development of atherosclerotic diseases.
Lattice Boltzmann simulations of a timedependent natural convection problem
, 2013
"... A twodimensional double MultipleRelaxationTime thermal lattice Boltzmann method is used to simulate natural convection flows in differentially heated cavities. The buoyancy effects are considered under the Boussinesq assumption. Flow and temperature fields are respectively solved with nine and fi ..."
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A twodimensional double MultipleRelaxationTime thermal lattice Boltzmann method is used to simulate natural convection flows in differentially heated cavities. The buoyancy effects are considered under the Boussinesq assumption. Flow and temperature fields are respectively solved with nine and five discrete velocities models. Boundary conditions are implemented with the classical bounceback or a “onnode ” approach. The latter uses popular Zou and He and CounterSlip formulations. This paper evaluates the differences between the two implementations for steady and timedependent flows as well as the space and time convergence orders.
Maximum Entropy Boundaries in Lattice Boltzmann Method
"... Abstract: We propose a universal approach in the framework of the lattice Boltzmann method (LBM) to modeling constant velocity constraints and constant temperature constraints on curved walls, which doesn’t depend on dimensionality, LBM scheme, boundary geometry; which is numerically stable, accurat ..."
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Abstract: We propose a universal approach in the framework of the lattice Boltzmann method (LBM) to modeling constant velocity constraints and constant temperature constraints on curved walls, which doesn’t depend on dimensionality, LBM scheme, boundary geometry; which is numerically stable, accurate and local and has a good physical background. This technique, called a maximum entropy method, utilizes the idea of recovering unknown populations on boundary nodes through minimizing node state deviation from equilibrium while assuring velocity or temperature restrictions. Also, theoretical justifications of a popular ZouHe boundaries technique and isothermal boundaries algorithm are provided on the basis of the method derived. Finally, while conducting numerical benchmarks, typical straight boundaries algorithm (ZouHe) was
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