Turbulent combustion sits at the interface of two important nonlinear, multiscale phenomena:
chemistry and turbulence. Its study is extremely timely in view of the need to develop new …

This review summarizes the rigorous mathematical theory behind the lattice Boltzmann
equation (LBE). Relevant properties of the Boltzmann equation and a derivation of the LBE …

Predictive simulations of complex systems are essential for applications ranging from
weather forecasting to drug design. The veracity of these predictions hinges on their …

Cascaded lattice Boltzmann method (cascaded-LBM) employs a class of collision operators
aiming to stabilize computations and remove certain modeling artifacts for simulation of fluid …

We revisit the classical stability versus accuracy dilemma for the lattice Boltzmann methods
(LBM). Our goal is a stable method of second-order accuracy for fluid dynamics based on …

The modelling and simulation of high-dimensional multiscale systems is a critical challenge
across all areas of science and engineering. It is broadly believed that even with today's …

The lattice Boltzmann method (LBM) facilitates efficient simulations of fluid turbulence based
on advection and collision of local particle distribution functions. To ensure stable …

Stability is one of the main concerns in the lattice Boltzmann method (LBM). The objectives
of this study are to investigate the linear stability of the lattice Boltzmann equation with the …

To solve the 1D (linear) convection-diffusion equation, we construct and we analyze two
LBM schemes built on the D1Q2 lattice. We obtain these LBM schemes by showing that the …

Ab initio derivation of the cascaded lattice Boltzmann automaton Page 1 AB INITIO DERIVATION
OF THE CASCADED LATTICE BOLTZMANN AUTOMATON Martin Christian Geier Page 2 ii …