A fractional step lattice Boltzmann scheme is presented to greatly improve the stability of the lattice Boltzmann method (LBM) in modelling incompressible flows at high Reynolds number. This method combines the good features of the conventional LBM and the fractional step technique. Through the fractional step, the flow at an extreme case of infinite Reynolds number (inviscid flow) can be effec...

Efficient, nonlinearly stable entropic lattice Boltzmann models for computational fluid dynamics are presented. A new method of fast evaluation of equilibria to machine precision is proposed. Analytical solution is found for the collision step which guarantees stability and thermodynamic consistency of the scheme. As an example, a novel 15-velocity lattice Boltzmann model is derived and validat...

The relation between the Lattice Boltzmann Method, which has recently become popular, and the Kinetic Schemes, which are routinely used in Computational Fluid Dynamics, is explored. A new discrete velocity model for the numerical solution of Navier–Stokes equations for incompressible fluid flow is presented by combining both the approaches. The new scheme can be interpreted as a pseudo-compress...

Using the Taylor expansion method, we show that it is possible to improve the lattice Boltzmann method for acoustic applications. We derive a formal expansion of the eigenvalues of the discrete approximation and fit the parameters of the scheme to enforce fourth order accuracy. The corresponding discrete equations are solved with the help of symbolic manipulation. The solutions are obtained in ...

The OpenLB project aims at setting up an open source implementation of lattice Boltzmann methods in an object oriented framework. The code, which is written in C++, is intended to be used both by application programmers and by developers who may add their own particular dynamics. It supports advanced data structures that take into account complex geometries and parallel program executions. The ...

Thermal radiation plays a very important role in the heat transfer combination through the various components of the SOFC fuel cell operating at high temperatures. Lattice Boltzmann method is used for treating conduction-radiation heat transfer in the electrolyte. The thermal radiation heat transfer is coupled to the overall energy conservation equations through the divergence of the local radi...

The Lattice Boltzmann method, a molecule kinetic-based approach, is presented to solve fluid dynamics. Based on the theory of turbulence and molecule kinetics, an extended Lattice Boltzmann equation is put forward to solve turbulent flow with high Reynolds number, in which sub-grid turbulence model is used to simulate vortex viscosity as well as turbulence relaxation time is introduced to modif...

Lees-Edwards boundary conditions (LEbc) for Molecular Dynamics simulations [1] are an extension of the well known periodic boundary conditions and allow the simulation of bulk systems in a simple shear flow. We show how the idea of LEbc can be implemented in lattice Boltzmann simulations and how LEbc can be used to overcome the problem of a maximum shear rate that is limited to less then 1/Ly (...

For numerically solving fluid dynamics problems efficiently one is often facing the problem that one has to confine the computational domain to a small domain of interest introducing so-called non-reflecting boundary conditions (NRBCs). In this work we address the problem of supplying NRBCs in fluid simulations in two space dimensions using the lattice Boltzmann method (LBM): socalled character...

If we consider a finite difference method simply as a set of equations containing a small parameter (the grid spacing), it is evident that the tools of asymptotic analysis can give us useful information about the method. The applicability of this approach for studying consistency, long time behavior and stability is demonstrated. As example, we use a simple lattice Boltzmann scheme for the 1D a...