An Exploration of numerical approaches to Boltzmann equation regarding hydrodynamics

Şahin, Alper
The Lattice Boltzmann Method (LBM) has become an alternative tool in computational fluid dynamics (CFD) techniques. While traditional CFD methods are based on Navier-Stokes equations that describe the fluid in terms of macroscopic quantities, LBM takes a mesoscopic description of the fluid thus closing the gap between macroscale and microscale. Overall, LBM provides a simple and efficient framework for simulation of fluid flows. In this approach, Boltzmann kinetic equation with BGK collision operator is discretized over a square lattice and solved to compute the evolution of a particle distribution function whose velocity moments are connected to the macroscopic primitive variables such as velocity and density. In this study, we explore two main approaches in the velocity discretization of the Boltzmann equation, namely, Galerkin and Collocation approaches. The foundations leading to these approaches are systematically laid down and some numerical examples are presented. These examples include, plane channel (Poiseuille), flow over circular and square cylinders and flow over an array of cylinders. Comparisons with available analytic and other numerical techniques show a satisfactory agreement.


Implicit lattice boltzmann method for laminar/turbulent flows
Çevik, Fatih; Albayrak, Kahraman; Department of Mechanical Engineering (2016)
Lattice Boltzmann Method is an alternative computational method for fluid physics problems. The development of the method started in the late 1980s and early 1990s. Various numerical schemes like stream and collide, finite difference, finite element and finite volume schemes are used to solve the discrete Lattice Boltzmann Equation. Almost all of the numerical schemes in the literature are explicit schemes to exploit the natural features of the discrete Lattice Boltzmann Equation like parallelism and easy c...
A finite element variational multiscale method for the Navier-Stokes equations
Volker, John; Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01)
This paper presents a variational multiscale method (VMS) for the incompressible Navier-Stokes equations which is defined by a large scale space L-H for the velocity deformation tensor and a turbulent viscosity nu(T). The connection of this method to the standard formulation of a VMS is explained. The conditions on L-H under which the VMS can be implemented easily and efficiently into an existing finite element code for solving the Navier - Stokes equations are studied. Numerical tests with the Smagorinsky ...
A novel cfd code based on method of lines for reacting flows: Verification on methane/air diffusion flame
Tarhan, Tanil; Selçuk, Nevin (2007-01-01)
A novel parallel computational fluid dynamic (CFD) code based on method of lines (MOL) approach was developed for the numerical simulation of multi-component reacting flows using detailed transport and thermodynamic models. The code was applied to the prediction of a confined axi-symmetric laminar co-flowing methane-air diffusion flame for which experimental data were available in the literature. 1-, 5- and 10-step reduced finite-rate reaction mechanisms were employed for methane-air combustion sub-model. S...
A Fully Implicit Finite Volume Lattice Boltzmann Method for Turbulent Flow
Cevik, Fatih; Albayrak, Kahraman (2017-08-01)
Almost all schemes existed in the literature to solve the Lattice Boltzmann Equation like stream & collide, finite difference, finite element, finite volume schemes are explicit. However, it is known fact that implicit methods utilizes better stability and faster convergence compared to the explicit methods. In this paper, a method named herein as Implicit Finite Volume Lattice BoltzmannMethod (IFVLBM) for incompressible laminar and turbulent flows is proposed and it is applied to some 2D benchmark test cas...
A Spectral Solenoidal-Galerkin Method for Flow Past a Circular Cylinder
Tarman, Işık Hakan (null; 2017-09-25)
Flow past a circular cylinder embodies many interesting features of fluid dynamics as a challenging fluid phenomenon. In this preliminary study, flow past a cylinder is simulated numerically using a Galerkin procedure based on solenoidal bases. The advantages of using solenoidal bases are twofold: first, the incompressibility condition is exactly satisfied due to the expansion of the flow field in terms of the solenoidal bases and second, the pressure term is eliminated in the process of Galerkin projection...
Citation Formats
A. Şahin, “An Exploration of numerical approaches to Boltzmann equation regarding hydrodynamics,” Thesis (M.S.) -- Graduate School of Natural and Applied Sciences. Engineering Sciences., Middle East Technical University, 2019.