Abstract
Traditional Lattice-Boltzmann modelling of advection–diffusion flow is affected by numerical instability if the advective term becomes dominant over the diffusive (i.e., high-Péclet flow). To overcome the problem, two 3D one-way coupled models are proposed. In a traditional model, a Lattice-Boltzmann Navier–Stokes solver is coupled to a Lattice-Boltzmann advection–diffusion model. In a novel model, the Lattice-Boltzmann Navier–Stokes solver is coupled to an explicit finite-difference algorithm for advection–diffusion. The finite-difference algorithm also includes a novel approach to mitigate the numerical diffusivity connected with the upwind differentiation scheme.The models are validated using two non-trivial benchmarks, which includes discontinuous initial conditions and the case Peg→∞ for the first time, where Peg is the grid Péclet number. The evaluation of Peg alongside Pe is discussed. Accuracy, stability and the order of convergence are assessed for a wide range of Péclet numbers. Recommendations are then given as to which model to select depending on the value Peg—in particular, it is shown that the coupled finite-difference/Lattice-Boltzmann provide stable solutions in the case Pe→∞, Peg→∞.
Highlights
Advection–diffusion occurs in a wide range of fluid-flow problems, including transport of chemicals, natural convection heat transfer when thermal expansion can be ignored, assessment of mixing through a passive scalar tracer, and many more.Over the last decades, numerical modelling – in particular, computational fluid dynamics (CFD) – has been extensively used as a cheap but robust alternative to often lengthy and expensive experiments [1]
The lattice-Boltzmann is a particular type of explicit finite-difference method, with a tuneable diffusivity parameter [2]; this characteristics provides an advantage over traditional explicit finite-difference methods, as it allows the use of much larger timesteps than what would otherwise required to maintain stability
Sharp start on the non-periodical lattice: Lattice-Boltzmann
Summary
Advection–diffusion occurs in a wide range of fluid-flow problems, including transport of chemicals, natural convection heat transfer when thermal expansion can be ignored, assessment of mixing through a passive scalar tracer, and many more.Over the last decades, numerical modelling – in particular, computational fluid dynamics (CFD) – has been extensively used as a cheap but robust alternative to often lengthy and expensive experiments [1]. It represents a valid alternative to implicit/segregated finite-volume CFD methods traditionally used to solve the Navier–Stokes equations because of a number of advantages in terms of numerical efficiency and parallelizability, viz.: (i) full explicitness, with no internal loop being required—every timestep is updated through a limited and well-defined number of floating-point operations; (ii) separation between non-linear and non-local part of the algorithm with the latter being usually limited to first neighbour-access, thereby allowing large parallel runs with no significant efficiency loss due to non-scalable inter-processor communication; and (iii) structure simplicity, allowing relatively simple extensions towards a wide variety of phenomena [2,3,4]. There is clear a need for an advection–diffusion Lattice-Boltzmann method with the Nomenclature
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