Realizable entropic lattice Boltzmann method for high-Péclet scalar transport.

We present a realizable entropic lattice Boltzmann method (RELBM) for scalar transport at high Péclet (Pe) number. The method combines an ADE-tailored entropic relaxation with a nonorthogonality correction to ghost-mode damping and a strictly conservative population-space realizability limiter activated only when required to enforce positivity. Comprehensive benchmarks including deformational mixing, Graetz transport, and Taylor dispersion up to Pe=2×10^{5}, demonstrating suppression of spurious oscillations and quantitative agreement with theory. Furthermore, pore-scale simulations in a homogeneous geometry up to Pe=10^{4} resolve scalar-dissipation dynamics consistent with intermediate lamellar and late-time Fickian scalings. These results establish the method's robustness and physical fidelity for multiscale advection-diffusion dynamics across diverse systems.