InterPore2026

Realizable Entropic Lattice Boltzmann Method for High-P'eclet Scalar Transport in Complex Porous Media

22 May 2026, 10:20

1h 30m

Poster Presentation (MS08) Mixing, dispersion and reaction processes across scales in heterogeneous and fractured media Poster

Speaker

Dr Jingsen Feng (University of Exeter)

Description

Simulating high-P\'eclet advection--diffusion processes within complex porous media remains a formidable computational challenge. Standard lattice Boltzmann (LB) methods frequently destabilize when resolving transport through intricate pore networks, where sharp scalar fronts and strong gradients generated by pore-throat constrictions induce spurious oscillations. These numerical artifacts, typically manifesting as Gibbs phenomena, violate physical realizability by producing negative concentrations. These violations are far from trivial; they frequently precipitate severe numerical instabilities that cause simulation divergence, thereby precluding long-time predictions, or otherwise fundamentally bias global effective dispersion statistics. This work establishes a robust stabilization strategy designed to strictly preserve conservation laws and locality while retaining high-order accuracy in smooth flow regimes.

The proposed method rests on a strictly convex H-function which provides a convex Lyapunov functional to govern the relaxation process. The collision relaxation is computed locally and adaptively by enforcing a discrete H-theorem condition along the collision direction via a constrained one-dimensional line search. This mechanism functions as a non-linear, self-adaptive filter that selectively dissipates energy in unstable, high-wavenumber spectral modes while preserving the physical transport dynamics of well-resolved hydrodynamic scales. To ensure strictly non-negative solutions even under shock-like gradients, the scheme incorporates a hard realizability control. This step projects the post-collision population onto the admissible non-negative manifold through a minimal, mass-conserving redistribution, thereby eliminating negative concentrations without introducing excessive artificial diffusion.

Validation encompasses three distinct regimes relevant to porous media physics. First, in 2D deformational flow, the realizability correction completely eliminates non-physical undershoots with negligible impact on the computed effective diffusivity. Second, for Taylor--Aris dispersion in a capillary, the model captures the full temporal evolution of the dispersion coefficient. It accurately resolves the pre-asymptotic regime extending over several decades of P\'eclet number up to $\mathrm{Pe}\sim 2\times 10^{5}$. Third, we simulate transport through a homogeneous granular pack to investigate scalar dissipation rates. The method recovers the theoretical late-time scalar-dissipation scaling $\chi\sim t^{-1.5}$ across $\mathrm{Pe}=1$--$10000$. Crucially, the solver resolves the early-time transition, capturing the emergence of an intermediate convective scaling regime approaching $\chi\sim t^{-2.5}$ driven by shear-induced 2D mixing dynamics. The combined convex H-function stabilization and realizability control provide a mathematically rigorous path for simulating pore-scale transport, ensuring fidelity to analytic dispersion theory and physical dissipation scaling in heterogeneous and fractured media.