Lincheng Xu, Eric Serre, Pierre Sagaut. A theoretical analysis of mass leakage at boundaries within the lattice Boltzmann method. Physics of Fluids, 2022, Physics of fluids, 34 (065113). ⟨hal-03683744⟩ Plus de détails...
Mass leakage at boundaries can be a critical issue for reliability of the lattice Boltzmann (LB) method based on Cartesian grids. Despite numerous work based on the LB method, the intrinsic macroscopic mechanisms causing mass leakage are still not fully charac- terised, but are essential to improve the mass conservation of LB simulations. In this paper, an original theoretical investigation of mass leakage at boundaries is proposed within the general LB framework. It is demonstrated that the mass leakage originates from the in- trinsic deficiency of the wall-cut LB links at boundary nodes in recovering macroscopic momenta. From a mesoscopic-level definition, i.e. the net loss of distribution functions during the streaming process, the local mass leakage at individual boundary nodes and its averaged value along smooth boundaries are mathematically expressed using macroscopic variables. The local mass leakage is shown to be dominated by terms proportional to the tangential momentum component. In contrast, the averaged mass leakage is shown to be contributed from various terms including the boundary curvature, the tangential momen- tum, and the gradients of density, momentum and momentum flux. Meanwhile, amplitude of the averaged mass leakage is theoretically estimated to be proportional to the local grid spacing, based on which a first-order accurate correction scheme is proposed. In addition, both the local and averaged mass leakage are demonstrated to be significantly dependent on boundary orientation with respect to the grid. The proposed theoretical analysis is assessed by performing numerical experiments. Two-dimensional weakly compressible flows through straight and curved moving channels are considered to estimate each term appearing in the theoretical analysis. The numerical results are in very good agreement with the proposed analysis, and the proposed mass correction scheme based on the av- eraged mass leakage effectively cures the mass leakage problems in the considered test cases.
Lincheng Xu, Eric Serre, Pierre Sagaut. A theoretical analysis of mass leakage at boundaries within the lattice Boltzmann method. Physics of Fluids, 2022, Physics of fluids, 34 (065113). ⟨hal-03683744⟩
Guanxiong Wang, Lincheng Xu, Eric Serre, Pierre Sagaut. Large temperature difference heat dominated flow simulations using a pressure-based lattice Boltzmann method with mass correction. Physics of Fluids, 2021, 33 (11), pp.116107. ⟨10.1063/5.0073178⟩. ⟨hal-03438869⟩ Plus de détails...
This paper addresses simulation of heat dominated compressible flows in a closed cavity using a pressure-based lattice Boltzmann (LB) method, in which thermal effects are modeled by applying a pressure-featured zero-order moment of distribution functions. A focus is made on the conservation of mass at boundary nodes, which is a challenging issue that significantly complicated by the density-decoupled zero-order moment here. The mass leakage at boundary nodes is mathematically quantified, which enables an efficient local mass correction scheme. The performance of this solver is assessed by simulating buoyancy-driven flows in a closed deferentially heated cavity with large temperature differences (non-Boussinesq) at Rayleigh numbers ranging from 103 to 107. Simulations show that mass leakage at solid walls in such configurations is a critical issue to obtain reliable solutions, and it eventually leads to simulations overflow when the cavity is inclined. The proposed mass correction scheme is, however, shown to be effective to control the mass leakage and get accurate solutions. Thus, associated with the proposed mass conservation scheme, the pressure-based LB method becomes reliable to study natural convection dominated flows at large temperature differences in closed geometries with mesh aligned boundaries or not
Guanxiong Wang, Lincheng Xu, Eric Serre, Pierre Sagaut. Large temperature difference heat dominated flow simulations using a pressure-based lattice Boltzmann method with mass correction. Physics of Fluids, 2021, 33 (11), pp.116107. ⟨10.1063/5.0073178⟩. ⟨hal-03438869⟩
