Lattice Boltzmann Finite Volume Formulation with Improved Stability

Abstract

<jats:title>Abstract</jats:title><jats:p>The most severe limitation of the standard Lattice Boltzmann Method is the use of uniform Cartesian grids especially when there is a need for high resolutions near the body or the walls. Among the recent advances in lattice Boltzmann research to handle complex geometries, a particularly remarkable option is represented by changing the solution procedure from the original “stream and collide” to a finite volume technique. However, most of the presented schemes have stability problems. This paper presents a stable and accurate finite-volume lattice Boltzmann formulation based on a cell-centred scheme. To enhance stability, upwind second order pressure biasing factors are used as flux correctors on a D2Q9 lattice. The resulting model has been tested against a uniform flow past a cylinder and typical free shear flow problems at low and moderate Reynolds numbers: boundary layer, mixing layer and plane jet flows. The numerical results show a very good accuracy and agreement with the exact solution of the Navier-Stokes equation and previous numerical results and/or experimental data. Results in self-similar coordinates are also investigated and show that the time-averaged statistics for velocity and vorticity express self-similarity at low Reynolds numbers. Furthermore, the scheme is applied to simulate the flow around circular cylinder and the Reynolds number range is chosen in such a way that the flow is time dependent. The agreement of the numerical results with previous results is satisfactory.</jats:p>

Lattice Boltzmann-Based Approaches for Pore-Scale Reactive Transport

“…A coupled LB-FV method also has been adopted for different physical processes. For example, Zarghami et al (2012) developed a cell-centered FV method for discretizing the SRT to improve the stability of the fl ow fi elds over a range of Reynolds numbers (Re). More recently, coupled LB-FV methods have been developed for reactive transport processes for multiphysics problems.…”

Uma representação do fluxo sanguíneo pulsátil em artérias ou veias usando lattice Boltzmann

“…Outra vantagem com a utilização do LBMé a possibilidade de implementá-lo utilizando processos de paralelização [16,17], que agilizam a obtenção de resultados. Além disso,é um método que pode ser facilmente acoplado a outros métodos numéricos dependendo da necessidade apresentada no problema físico [15,18,19] e, dessa forma, possibilita-se a obtenção de resultados mais precisos do que se obteria com a utilização de apenas uma abordagem numérica. Tais acoplamentos também são vantajosos quando a referênciaé a hemodinâmica, justamente por se saber que o sangueé compostos por diversas partículas estruturalmente diferentes [6], além da necessidade de se modelar as paredes dos vasos por onde o fluxo sanguíneo percorre e a musculatura ao redor desses vasos.…”

Solving incompressible fluid flows on unstructured meshes with the lattice Boltzmann flux solver

“…This partially explains the lower drag coefficients that were obtained, since our 200D × 200D domain is much larger than that for all the other results presented. In fact, Zarghami et al (2012) use the smallest domain height, 16D, and obtain a much larger drag coefficient for Re = 20.…”

“…They concluded that their method showed better numerical stability than the central scheme. Zarghami, Maghrebi, Ghasemi, and Ubertini (2012) also use a cellcentered formulation, and address the stability issue by introducing upwind second order pressure-based biasing factors and artificial damping in the flux calculations.…”

“…We compare them to the results of other works based on a combination of the Boltzmann equation and the finite-volume approach. Zarghami et al (2012) use a finite-volume LBM formulation on a structured non-uniform mesh. Shu et al (2014) and use the LBFS, although the former use a structured curvilinear O-type mesh, and the latter use a structured non-uniform mesh.…”