Fully dissipative relativistic lattice Boltzmann method in two dimensions

In this paper, we develop and characterize the fully dissipative Lattice Boltzmann method for ultra-relativistic fluids in two dimensions using three equilibrium distribution functions: Maxwell-J\"uttner, Fermi-Dirac and Bose-Einstein. Our results stem from the expansion of these distribution functions up to fifth order in relativistic polynomials. We also obtain new Gaussian quadratures for square lattices that preserve the spatial resolution. Our models are validated with the Riemann problem and the limitations of lower order expansions to calculate higher order moments are shown. The kinematic viscosity and the thermal conductivity are numerically obtained using the Taylor-Green vortex and the Fourier flow respectively and these transport coefficients are compared with the theoretical prediction from Grad's theory. In order to compare different expansion orders, we analyze the temperature and heat flux fields on the time evolution of a hot spot

A Coupled Lattice Boltzmann-Volume Penalization for Flows Past Fixed Solid Obstacles with Local Mesh Refinement

A coupled Lattice Boltzmann-Volume Penalization (LBM-VP) with local mesh refinement is presented to simulate flows past obstacles in this article. Based on the finite-difference LBM, the local mesh refinement is incorporated into the LBM to improve computing efficiency. The volume penalization method is introduced into the LBM by an external forcing term. In the LBM-VP method, the processes of interpolating velocities on the boundaries points and distributing the force density to the Eulerian points near the boundaries are unnecessary. Performing the LBM-VP on a certain point, only the variables of this point are needed, which means the whole procedure can be conducted parallelly. As a consequence, the whole computing efficiency can be improved. To verify the presented method, flows past a single circular cylinder, a pair of cylinders in tandem arrangement, and a NACA-0012 are investigated. A good agreement between the present results and the data in the previous literatures is achieved, which demonstrates the accuracy and effectiveness of the present method to solve the flows past obstacle problems

A solution-adaptive lattice Boltzmann method for two-dimensional incompressible viscous flows

10.1016/j.jcp.2010.12.013Journal of Computational Physics23062246-2269JCTP

Laminer/türbülanslı akışlar için örtük kafes boltzmann yöntemi.

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 coding. In this thesis, an Implicit Finite Volume Lattice Boltzmann Method (IFVLBM) is developed. The method is limited for the incompressible fluid simulation, however loosely coupled Spalart-Allmaras turbulence model is incorporated for the simulations for high Reynolds numbers. Moreover, local time stepping techniques and dual time stepping techniques are also implemented for convergence acceleration to use in steady state and unsteady problems respectively. The IFVLBM demonstrates improvements in stability characteristics and convergence is accelerated as the limitation of CFL number is eased compared to the classical Lattice Boltzmann Methods. The test case results for laminar, turbulent, steady and unsteady flows are compared with either experimental or numerical data in the literature. Also, numerical data available in the literature from the CFL3D software, which is a Reynolds averaged Navier Stokes solver developed by NASA, is used for flow field comparisons. The results of the developed method are in good agreement with the data given in the literature.Ph.D. - Doctoral Progra

Development of Immersed Boundary-Phase Field-Lattice Boltzmann Method for Solid Multiphase Flow Interactions

Ph.DDOCTOR OF PHILOSOPH