Benchmark computations based on lattice-Boltzmann, finite element and finite volume methods for laminar flows

Abstract

The goal of this article is to contribute to the discussion of the efficiency of lattice-Boltzmann (LB) methods as CFD solvers. After a short review of the basic model and extensions, we compare the accuracy and computational efficiency of two research simulation codes based on the LB and the finite-element method (FEM) for two-dimensional incompressible laminar flow problems with complex geometries. We also study the influence of the Mach number on the solution, since LB methods are weakly compressible by nature, by comparing compressible and incompressible results obtained from the LB code and the commercial code CFX. Our results indicate, that for the quantities studied (lift, drag, pressure drop) our LB prototype is competitive for incompressible transient problems, but asymptotically slower for steady-state Stokes flow because the asymptotic algorithmic complexity of the classical LB-method is not optimal compared to the multigrid solvers incorporated in the FEM and CFX code. For the weakly compressible case, the LB approach has a significant wall clock time advantage as compared to CFX. In addition, we demonstrate that the influence of the finite Mach number in LB simulations of incompressible flow is easily underestimated.

A Non-Isothermal Chemical Lattice Boltzmann Model Incorporating Thermal Reaction Kinetics and Enthalpy Changes

“…Many years of analysis have revealed that the above-described model can reproduce incompressible flow dynamics to second order accuracy [6][7][8][9][10]35]. Furthermore, the LBM can be applied to turbulent flows [6,10,36], and recent novel lattice schemes [37], entropic multi-speed approaches [38] and cumulant methods [39] have further broadened the range of applications amenable to simulation by the LBM.…”

Efficient Simulation of Transient Heat Transfer Problems in Civil Engineering

“…The issue of efficiency of the LB method in direct comparison with state-of-the-art FE and FV-discretizations of the Navier-Stokes equations is discussed e.g. in (Geller et al, 2006). Unlike the traditional computational fluid dynamics (CFD), which numerically solves the conservation equations of macroscopic properties (i. e., mass, momentum, and energy), LBM models the fluid consisting of fictitious particles, which perform consecutive propagation and collision processes over a discrete lattice.…”

Combinational Optimization of Strut Placement for Intracranial Stent Using a Realistic Aneurysm

“…Several studies have used the LB method to analyze aneurysmal flow, showing the adequacy of LB simulations and the application to a complex problem in a living system [12]- [16]. In addition, several studies have compared the LB method with the conventional finite-volume method (FVM) [12] [17] [18].…”