The present study focuses on the unphysical effects induced by the use of non-uniform grids in the lattice Boltzmann method. In particular, the convection of vortical structures across a grid refinement interface is likely to generate spurious noise that may impact the whole computation domain. This issue becomes critical in the case of aeroacoustic simulations, where accurate pressure estimations are of paramount importance. The purpose of this article is to identify the issues occurring at the interface and to propose possible solutions yielding significant improvements for aeroacoustic simulations. More specifically, this study highlights the critical involvement of non-physical modes in the generation of spurious vorticity and acoustics. The identification of these modes is made possible thanks to linear stability analyses performed in the fluid core, and non-hydrodynamic sensors specifically developed to systematically emphasize them during a simulation. Investigations seeking pure acoustic waves and sheared flows allow for isolating the contribution of each mode. An important result is that spurious wave generation is intrinsically due to the change in the grid resolution (i.e. aliasing) independently of the details of the grid transition algorithm. Finally, the solution proposed to minimize spurious wave amplitude consists of choosing an appropriate collision model in the fluid core so as to cancel the non-hydrodynamic mode contribution regardless the grid coupling algorithm. Results are validated on a convected vortex and on a turbulent flow around a cylinder where a huge reduction of both spurious noise and vorticity are obtained.
The spurious currents observed in multiphase flow simulations with pseudo-potential lattice Boltzmann (LB) models are usually understood to be the result of the lack of isotropy of the model-generated interaction force between phases. Remedies have been proposed to utilize larger stencils to compute the interaction force with higher orders of isotropy. In this short communication, we point out the incompleteness in the current understanding and propose a new consistent implementation to more effectively suppress the spurious currents. We also demonstrate theoretically that certain low-level sp…
We show that, when a single relaxation time lattice Boltzmann algorithm is used to solve the hydrodynamic equations of a binary fluid for which the two components have different viscosities, strong spurious velocities in the steady state lead to incorrect results for the equilibrium contact angle. We identify the origins of these spurious currents, and demonstrate how the results can be greatly improved by using a lattice Boltzmann method based on a multiple-relaxation-time algorithm. By considering capillary filling we describe the dependence of the advancing contact angle on the interface ve…
The origin of the spurious interface velocity in finite difference lattice Boltzmann models for liquid - vapor systems is related to the first order upwind scheme used to compute the space derivatives in the evolution equations. A correction force term is introduced to eliminate the spurious velocity. The correction term helps to recover sharp interfaces and sets the phase diagram close to the one derived using the Maxwell construction.
Spurious currents, which are often observed near a curved interface in the multiphase simulations by diffuse interface methods, are unphysical phenomena and usually damage the computational accuracy and stability. In this paper, the origination and suppression of spurious currents are investigated by using the multiphase lattice Boltzmann method driven by chemical potential. Both the difference error and insufficient isotropy of discrete gradient operator give rise to the directional deviations of nonideal force and then originate the spurious currents. Nevertheless, the high-order finite diff…
The pseudopotential multiphase lattice Boltzmann (LB) model is a very popular model in the LB community for simulating multiphase flows. When the multiphase modeling involves a solid boundary, a numerical scheme is required to simulate the contact angle at the solid boundary. In this work, we aim at investigating the implementation of contact angles in the pseudopotential LB simulations with curved boundaries. In the pseudopotential LB model, the contact angle is usually realized by employing a solid-fluid interaction or specifying a constant virtual wall density. However, it is shown that the…
The lattice Boltzmann method (LBM) is routinely employed in the simulation of complex multiphase flows comprising bulk phases separated by non-ideal interfaces. LBM is intrinsically mesoscale with an hydro-dynamic equivalence popularly set by the Chapman-Enskog analysis, requiring that fields slowly vary in space and time. The latter assumptions become questionable close to interfaces, where the method is also known to be affected by spurious non hydrodynamical contributions. This calls for quantitative hydrodynamical checks. In this paper we analyze the hydrodynamic behaviour of LBM pseudo-po…
The goal of this work is to determine classes of traveling solitary wave solutions for Lattice Boltzmann schemes by means of an hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of nonlinear wave equation. The occurence of such a spurious solitary wave, which exhibits a very long life time, results in a non-vanishing numerical error for arbitrary time in unbounded numerical domain. Such a behavior is referred here to have a structural instability of the scheme, since the space of solutions spanned by the numerical scheme encompasses types of s…
Boiling is a complex phenomenon where different non-linear physical interactions take place and for which the quantitative modeling of the mechanism involved is not fully developed yet. In the last years, many works have been published focusing on the numerical analysis of this problem. However, a lack of numerical works assessing quantitatively the sensitivity of these numerical simulations to grid parameters can be identified, especially for the Lattice Boltzmann method (LBM). The main goal of this work is to propose a mesh refinement methodology for simulating phase-change heat transfer pro…
The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate representations of the solute, which is usually a complicated geometry. Here, we utilize adjoint-based analyses to form two goal-oriented error estimates that allows us to determine the contribution of each discretization element (panel) to the numerical error in the solvation free energy. This information is useful to identify high-error panels to then refine them …
Adaptive near-contact repulsion in conservative Allen-Cahn phase-field lattice Boltzmann multiphase model
Roma Tre University（罗马第三大学）；Pontifícia Universidade Católica do Paraná（巴拉那天主教大学）；Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche（意大利国家研究委员会计算应用研究所）；Center for Life Nano- & Neuro-Science, Fondazione Istituto Italiano di Tecnologia（意大利理工大学基金会生命纳米与神经科学中心）；PoreLab, Department of Physics, Norwegian University of Science and Technology（挪威科技大学物理系孔隙实验室）
A novel hybrid computational method based on the discrete-velocity (DV) approximation, including the lattice-Boltzmann (LB) technique, is proposed. Numerical schemes for the kinetic equations are used in regions of rarefied flows, and LB schemes are employed in continuum flow zones. The schemes are written under the finite-volume (FV) formulation to achieve the flexibility of local mesh refinement. The truncated Hermite polynomial expansion is used for matching of DV and LB solutions. Special attention is paid to preserving conservation properties in the coupling algorithm. The test results ob…
We analyse a linear lattice Boltzmann (LB) formulation for simulation of linear acoustic wave propagation in heterogeneous media. We employ the single-relaxation-time Bhatnagar-Gross-Krook (BGK) as well as the general multi-relaxation-time (MRT) collision operators. By calculating the dispersion relation for various 2D lattices, we show that the D2Q5 lattice is the most suitable model for the linear acoustic problem. We also implement a grid-refinement algorithm for the LB scheme to simulate waves propagating in a heterogeneous medium with velocity contrasts. Our results show that the LB schem…
A new finite volume (FV) discretisation method for the Lattice Boltzmann (LB) equation which combines high accuracy with limited computational cost is presented. In order to assess the performance of the FV method we carry out a systematic comparison, focused on accuracy and computational performances, with the standard $streaming$ (ST) Lattice Boltzmann equation algorithm. To our knowledge such a systematic comparison has never been previously reported. In particular we aim at clarifying whether and in which conditions the proposed algorithm, and more generally any FV algorithm, can be taken …
The present study proposes a highly accurate lattice Boltzmann direct coupling cell-vertex algorithm, well suited for industrial purposes, making it highly valuable for aeroacoustic applications. It is indeed known that the convection of vortical structures across a grid refinement interface, where cell size is abruptly doubled, is likely to generate spurious noise that may corrupt the solution over the whole computational domain. This issue becomes critical in the case of aeroacoustic simulations, where accurate pressure estimations are of paramount importance. Consequently, any interfering n…
The standard lattice Boltzmann equation (LBE) method usually fails to capture the physical equilibrium state of a two-phase fluid system, i.e., zero velocity and constant chemical potential. Consequently, spurious velocities and inconsistent thermodynamic density properties are frequently encountered in LBE simulations. In this work, based on a rigorous analysis of the discrete balance equation of LBE, we identify the structure of the force imbalance due to discretization errors from different parts. Then a well-balanced LBE is proposed which can achieve the discrete equilibrium state. The wel…
The simulation of geometrically resolved rigid particles in a fluid relies on coupling algorithms to transfer momentum both ways between the particles and the fluid. In this article, the fluid flow is modeled with a parallel Lattice Boltzmann method using adaptive grid refinement to improve numerical efficiency. The coupling with the particles is realized with the momentum exchange method. When implemented in plain form, instabilities may arise in the coupling when the particles are lighter than the fluid. The algorithm can be stabilized with a virtual mass correction specifically developed fo…
We simulate the two-dimensional fluid flow around National Advisory Committee for Aeronautics (NACA) 0012 airfoil using a hybrid lattice Boltzmann method (HLBM), which combines the standard lattice Boltzmann method with an unstructured finite-volume formulation. The aim of the study is to assess the numerical performances and the robustness of the computational method. To this purpose, after providing a convergence study to estimate the overall accuracy of the method, we analyze the numerical solution for different values of the angle of attack at a Reynolds number equal to $10^3$. Subsequentl…
We study the propagation of waves across fixed mesh refinement boundaries in linear and nonlinear model equations in 1--D and 2--D, and in the 3--D Einstein equations of general relativity. We demonstrate that using linear interpolation to set the data in guard cells leads to the production of reflected waves at the refinement boundaries. Implementing quadratic interpolation to fill the guard cells suppresses these spurious signals.
In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A novel forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with…
A hybrid thermal lattice Boltzmann (LB) model is presented to simulate thermal multiphase flows with phase change based on an improved pseudopotential LB approach [Q. Li, K. H. Luo, and X. J. Li, Phys. Rev. E 87, 053301 (2013)]. The present model does not suffer from the spurious term caused by the forcing-term effect, which was encountered in some previous thermal LB models for liquid-vapor phase change. Using the model, the liquid-vapor boiling process is simulated. The boiling curve together with the three boiling stages (nucleate boiling, transition boiling, and film boiling) is numericall…
The von Neumann stability analysis along with a Chapman-Enskog analysis is proposed for a single-relaxation-time lattice Boltzmann Method (LBM) for wave propagation in isotropic linear elastic solids, using a regular D2Q9 lattice. Different boundary conditions are considered: periodic, free surface, rigid interface. An original absorbing layer model is proposed to prevent spurious wave reflection at domain boundaries. The present method is assessed considering several test cases. First, a spatial Gaussian force modulated in time by a Ricker wavelet is used as a source. Comparisons are made wit…
Single component pseudo-potential lattice Boltzmann models have been widely studied due to their simplicity and stability in multiphase simulations. While numerous model have been proposed, comparative analysis and advantages and disadvantages of different force schemes is often lacking. A pseudo-potential model to simulate large density ratios proposed by Kupershtokh et al. is analyzed in detail in this work. Several common used force schemes are utilized and results compared. Based on the numerical results, the relatively most accurate force scheme proposed by Guo et al. is selected and appl…
The physical behaviour of a class of mesoscopic models for multiphase flows is analyzed in details near interfaces. In particular, an extended pseudo-potential method is developed, which permits to tune the equation of state and surface tension independently of each other. The spurious velocity contributions of this extended model are shown to vanish in the limit of high grid refinement and/or high order isotropy. Higher order schemes to implement self-consistent forcings are rigorously computed for 2d and 3d models. The extended scenario developed in this work clarifies the theoretical founda…
Owing to its conceptual simplicity and computational efficiency, the pseudopotential multiphase lattice Boltzmann (LB) model has attracted significant attention since its emergence. In this work, we aim to extend the pseudopotential LB model to simulate multiphase flows at large density ratio and relatively high Reynolds number. First, based on our recent work [Li et al., Phys. Rev. E. 86, 016709 (2012)], an improved forcing scheme is proposed for the multiple-relaxation-time pseudopotential LB model in order to achieve thermodynamic consistency and large density ratio in the model. Next, thro…
Lattice Boltzmann (LB) models used for the computation of fluid flows represented by the Navier-Stokes (NS) equations on standard lattices can lead to non-Galilean invariant (GI) viscous stress involving cubic velocity errors. This arises from the dependence of their third order diagonal moments on the first order moments for standard lattices, and strategies have recently been introduced to restore GI without such errors using a modified collision operator involving either corrections to the relaxation times or to the moment equilibria. Convergence acceleration in the simulation of steady flo…
The liquid-gas density ratio is a key property of multiphase flow methods to model real fluid systems. Here, a chemical-potential multiphase lattice Boltzmann method is constructed to realize extremely large density ratios. The simulations show that the method reaches very low temperatures, at which the liquid-gas density ratio is more than 10^14, while the thermodynamic consistency is still preserved. Decoupling the mesh space from the momentum space through a proportional coefficient, a smaller mesh step provides denser lattice nodes to exactly describe the transition region and the resultin…
A lattice-Boltzmann (LB) scheme, based on the Bhatnagar-Gross-Krook (BGK) collision rules is developed for a phase-field model of alloy solidification in order to simulate the growth of dendrites. The solidification of a binary alloy is considered, taking into account diffusive transport of heat and solute, as well as the anisotropy of the solid-liquid interfacial free energy. The anisotropic terms in the phase-field evolution equation, the phenomenological anti-trapping current (introduced in the solute evolution equation to avoid spurious solute trapping), and the variation of the solute dif…
The free-energy lattice Boltzmann (LB) model is one of the major multiphase models in the LB community. The present study is focused on a class of free-energy LB models in which the divergence of thermodynamic pressure tensor or its equivalent form expressed by the chemical potential is incorporated into the LB equation via a forcing term. Although this class of free-energy LB models may be thermodynamically consistent at the continuum level, it suffers from thermodynamic inconsistency at the discrete lattice level owing to numerical errors [Guo et al., Physical Review E 83, 036707 (2011)]. Th…
GPU-based compressible lattice Boltzmann simulations on non-uniform grids using standard C++ parallelism: From best practices to aerodynamics, aeroacoustics and supersonic flow simulations
Institute for Advanced Study, Beijing Normal - Hong Kong Baptist University（北京师范大学-香港浸会大学联合国际学院先进研究院）；Computer Science Department, University of Geneva（日内瓦大学计算机系）
We propose a lattice Boltzmann color-gradient model for immiscible ternary fluid flows, which is applicable to the fluids with a full range of interfacial tensions, especially in near-critical and critical states. An interfacial force for N-phase systems is derived based on the previously developed perturbation operator and is then introduced into the model using a body force scheme, which helps reduce spurious velocities. A generalized recoloring algorithm is applied to produce phase segregation and ensure immiscibility of three different fluids, where a novel form of segregation parameters i…
Over the past few decades, tremendous progress has been made in the development of particle-based discrete simulation methods versus the conventional continuum-based methods. In particular, the lattice Boltzmann (LB) method has evolved from a theoretical novelty to a ubiquitous, versatile and powerful computational methodology for both fundamental research and engineering applications. It is a kinetic-based mesoscopic approach that bridges the microscales and macroscales, which offers distinctive advantages in simulation fidelity and computational efficiency. Applications of the LB method have…
We present a simple and effective multigrid-based Poisson solver of second-order accuracy in both gravitational potential and forces in terms of the one, two and infinity norms. The method is especially suitable for numerical simulations using nested mesh refinement. The Poisson equation is solved from coarse to fine levels using a one-way interface scheme. We introduce anti-symmetrically linear interpolation for evaluating the boundary conditions across the multigrid hierarchy. The spurious forces commonly observed at the interfaces between refinement levels are effectively suppressed. We val…
In this paper, a novel lattice Boltzmann (LB) model based on the Allen-Cahn phase-field theory is proposed for simulating axisymmetric multiphase flows. The most striking feature of the model is that it enables to handle multiphase flows with large density ratio, which are unavailable in all previous axisymmetric LB models. The present model utilizes two LB evolution equations, one of which is used to solve fluid interface, and another is adopted to solve hydrodynamic properties. To simulate axisymmetric multiphase flows effectively, the appropriate source term and equilibrium distribution fun…
Towards nonlinear thermohydrodynamic simulations via the Onsager-Regularized Lattice Boltzmann Method
Istituto Italiano di Tecnologia（意大利理工学院）；Fondazione Istituto Italiano di Tecnologia（意大利理工学院基金会）；Indian Institute of Technology Bombay（印度孟买理工学院）；Consiglio Nazionale delle Ricerche（意大利国家研究委员会）；Harvard University（哈佛大学）
For theoretical gas dynamics, the flow regimes are classified according to the Knudsen number. For computational fluid dynamics (CFD), the numerical flow field is the projection of the physical flow field onto the discrete space and time, which is related to the cell Knudsen number. The real representable flow regimes are controlled by these two parameters. According to the values of Knudsen number and cell Knudsen number, we study the classification of the numerical flow regimes. In the process of mesh refinement, the numerical experiments show the change of numerical flow regime from continu…
A macroscopic-shadow-corrected lattice Boltzmann method for fast, time-accurate simulation of low-Reynolds-number transient flows
School of Mathematics and Computational Science, Xiangtan University（湘潭大学数学与计算科学学院）；National Center for Applied Mathematics in Hunan（湖南省应用数学中心）；Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University（湘潭大学计算与工程科学湖南省重点实验室）
