Lattice Boltzmann method is implemented to study hydrodynamically and thermally developing steady laminar flows in a channel. Numerical simulation of two-dimensional convective heat transfer problem is conducted using two-dimensional, nine directional D2Q9 thermal lattice Boltzmann arrangements. The velocity and temperature profiles in the developing region predicted by Lattice Boltzmann method...

The thesis presents an analysis of the continuous forcing approach of the immersed boundary method for the simulation of the interaction between uid and rigid particles in combination with the single relaxation lattice Boltzmann method. The immersed boundary method as a numerical algorithm is implemented in the context of two massively parallel software frameworks (waLBerla and pe) developed at...

[1] This paper introduces new methods for simulating subsurface solute and heat transport in heterogeneous media using large‐scale lattice‐Boltzmann models capable of representing both macroscopically averaged porous media and open channel flows. Previous examples of macroscopically averaged lattice‐Boltzmann models for solute and heat transport are only applicable to homogeneous media. Here, w...

Compared to conventional techniques in computational fluid dynamics, the lattice Boltzmann method (LBM) seems to be a completely different approach to solve the incompressible Navier-Stokes equations. The aim of this article is to correct this impression by showing the close relation of LBM to two standard methods: relaxation schemes and explicit finite difference discretizations. As a side eff...

We consider the lattice Boltzmann method for immiscible multiphase flow simulations. Classical lattice Boltzmann methods for this problem, e.g. the colour gradient method or the free energy approach, can only be applied when density and viscosity ratios are small. Moreover, they use additional fields defined on the whole domain to describe the different phases and model phase separation by spec...

In this paper, we recall the linear version of the lattice Boltzmann schemes in the framework proposed by d’Humières. According to the equivalent equations we introduce a definition for a scheme to be isotropic at some order. This definition is chosen such that the equivalent equations are preserved by orthogonal transformations of the frame. The property of isotropy can be read through a group...

In this contribution we extend the Taylor expansion method proposed previously by one of us and establish equivalent partial differential equations of the lattice Boltzmann scheme proposed by d’Humières [11] at an arbitrary order of accuracy. We derive formally the associated dynamical equations for classical thermal and linear fluid models in one to three space dimensions. We use this approach...