Asymptotic analysis of the lattice Boltzmann equation

By Michael Junk, Axel Klar, Li-Shi Luo. 2005

391 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/b8d12a6fac3ba1a5faddf3eaabf46957c9aed9e5

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In Computational Mechanics

In Electrical and Electronic Engineering

Citations in the corpus

The cumulant lattice Boltzmann equation in three dimensions: Theory and validation (2015, methodology): “To obtain the equivalent partial differential equations for the lattice Boltzmann equation we apply a combination of Taylor expansion [48] and asymptotic expansion [49].”
Benchmark computations based on Lattice-Boltzmann, Finite Element and Finite Volume Methods for laminar Flows (2006, background): “convergence is first order in time and second order in space [16, 17 ].”
Lattice-Boltzmann simulations in reconstructed parametrized porous media (2006, methodology): “1987) or an asymptotic expansion using the diffusive scaling (Junk et al. 2005), it can be shown that the LB method is a scheme of first-order in time and second-order in space for the incompressible Navier–Stokes equations.”
An adaptive scheme using hierarchical grids for lattice Boltzmann multi-phase flow simulations (2006, methodology): “Using an asymptotic and Taylor expansion, it can be shown that the LB method is a scheme of second order both in space and time for the compressible Navier–Stokes equations in the low Mach number limit using the advective scaling and a scheme of first order in time and second order in space for the ”
Consistent initial conditions for lattice Boltzmann simulations (2006, background): “This error of cubic velocity is well known [20–23] and is intrinsic to most existing LBE models.”
TeraFLOP computing on a desktop PC with GPUs for 3D CFD (2008, positive): “Performing either a Chapman–Enskog (Frisch et al. 1987) or an asymptotic expansion (Inamuro et al. 1997, Junk et al. 2005) of Equation (2), it can be shown that the LBM is a scheme of ﬁrst order in time and second order in space for the incompressible Navier–Stokes equations in the low Mach number…”
In Silico Modeling of Magnetic Resonance Flow Imaging in Complex Vascular Networks (2014, background): “time, it is able to produce results that obey the Navier–Stokes equations to a high level of accuracy [29], [30].”
Multiple-relaxation-time lattice Boltzmann model for the convection and anisotropic diffusion equation (2010, methodology): “Therefore, we allow U to be slower than C by applying the diffusive scaling [9,49,50] as described below.”
An evaluation of lattice Boltzmann schemes for porous medium flow simulation (2006, methodology): “Thus, the LBE method can be viewed as a discrete approximation of the incompressible Navier–Stokes equations, based on kinetic theory rather than continuum theory [ 10 ].”