High-Order Implicit Hybridizable Discontinuous Galerkin Method for the Boltzmann Equation

TL;DR

This paper introduces a high-order hybridizable discontinuous Galerkin method combined with an implicit iterative scheme and spectral techniques to efficiently solve the steady-state Boltzmann equation with full collision integral on 2D meshes.

Contribution

It develops a novel high-order HDG method with spectral collision evaluation and polynomial approximation to improve accuracy and computational efficiency for the Boltzmann equation.

Findings

The method achieves high accuracy in steady-state solutions.

It significantly reduces computational cost compared to traditional approaches.

The scheme is validated as both accurate and efficient.

Abstract

The high-order hybridizable discontinuous Galerkin (HDG) method combining with an implicit iterative scheme is used to find the steady-state solution of the Boltzmann equation with full collision integral on two-dimensional triangular meshes. The velocity distribution function and its trace are approximated in the piecewise polynomial space of degree up to 4. The fast spectral method (FSM) is incorporated into the DG discretization to evaluate the collision operator. Specific polynomial approximation is proposed for the collision term to reduce the computational cost. The proposed scheme is proved to be accurate and efficient.