Grad's Distribution Function for 13 Moments based Moment Gas Kinetic Solver for Steady and Unsteady Rarefied flows: Discrete and Explicit Forms

TL;DR

This paper introduces a new 13-moments-based gas kinetic solver using Grad's distribution function, which simplifies flux computation and efficiently models both steady and unsteady rarefied flows.

Contribution

The paper develops an explicit, discrete form of the flux calculation in a 13-moments gas kinetic solver, avoiding complex PDE implementation and reducing computational cost.

Findings

Accurately simulates continuum and moderate rarefied flows.

Reduces computational and memory costs compared to traditional methods.

Provides a practical framework for steady and unsteady flow simulations.

Abstract

Efficient modeling of rarefied flow has drawn widespread interest for practical engineering applications. In the present work, we proposed the Grad's distribution function for 13 moments-based moment gas kinetic solver (G13-MGKS) and the macroscopic governing equations are derived based on the moment integral of discrete Boltzmann equation in the finite volume framework. Numerical fluxes at the cell interface related to the macroscopic variables, stress and heat flux can be reconstructed from the Boltzmann integration equation at surrounding points of the cell interface directly, so the complicated partial differential equations with tedious implementation of boundary conditions in the moment method can be avoided. Meanwhile, the explicit expression of numerical fluxes is proposed, which could release the present solver the from the discretization and numerical summation in molecular velocity space. To evaluate the Grad's distribution function for 13 moments in the present framework, the G13-MGKS with the discrete and explicit form of numerical fluxes are examined by several test cases covering the steady and unsteady rarefied flows. Numerical results indicate that the G13-MGKS could simulate continuum flows accurately and present reasonable prediction for rarefied flows at moderate Knudsen number. Moreover, the tests of computations and memory costs demonstrate that the present framework could preserve the highly efficient feature.