Abstract : Over the last near three decades, the Lattice Boltzmann (LB) method has gained a prominent role as an efficient computational scheme for the numerical sim- ulation of complex flows across a broad range of scales, from fully-developed turbulence in real-life geometries, to multiphase microflows, all the way down to biopolymer translocation in nanopores. Lately, the method has also shown promising potential for the simulation of quantum-relativistic fluids, such as quark-gluon plasmas, electron transport in graphene and relativistic magneto- hydrodynamics. After a brief introduction to the main ideas behind the LB method, we shall illustrate a few selected applications, along with prospects for future multiscale applications.
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