Central-moment-based discrete Boltzmann modeling of compressible flows

TL;DR

This paper introduces a central-moment-based discrete Boltzmann method for simulating compressible flows with variable heat ratios, capturing thermodynamic nonequilibrium effects beyond traditional models.

Contribution

It develops a novel CDBM that directly models nonequilibrium thermal effects, improving upon existing raw-moment based DBMs for compressible flow simulations.

Findings

Accurately simulates shock tube and wave phenomena.

Shows excellent agreement with theoretical results.

Validates capability to handle thermodynamic nonequilibrium.

Abstract

In this work, a central-moment-based discrete Boltzmann method (CDBM) is constructed for fluid flows with variable specific heat ratios. The central kinetic moments are employed to calculate the equilibrium discrete velocity distribution function in the CDBM. In comparison to previous incompressible central-moment-based lattice Boltzmann method, the CDBM possesses the capability of investigating compressible flows with thermodynamic nonequilibrium effects beyond conventional hydrodynamic models. Unlike all existing DBMs which are constructed in raw-moment space, the CDBM stands out by directly providing the nonequilibrium effects related to the thermal fluctuation. The proposed method has been rigorously validated using benchmarks of the Sod shock tube, Lax shock tube, shock wave phenomena, two-dimensional sound wave, and the Taylor-Green vortex flow. The numerical results exhibit an exceptional agreement with theoretical predictions.