Hierarchical Micro-Macro Acceleration for Moment Models of Kinetic Equations

TL;DR

This paper introduces a hierarchical micro-macro acceleration method for moment models of kinetic equations, combining the efficiency of macroscopic models with the accuracy of microscopic models, suitable for simulating rarefied gases.

Contribution

It presents a novel hierarchical micro-macro acceleration framework with a four-step procedure, improving accuracy and speed over existing methods for kinetic equations.

Findings

Achieves high accuracy in 1D and 2D test cases.

Provides significant computational speedup.

Outperforms existing micro-macro methods.

Abstract

Fluid dynamical simulations are often performed using cheap macroscopic models like the Euler equations. For rarefied gases under near-equilibrium conditions, however, macroscopic models are not sufficiently accurate and a simulation using more accurate microscopic models is often expensive. In this paper, we introduce a hierarchical micro-macro acceleration based on moment models that combines the speed of macroscopic models and the accuracy of microscopic models. The hierarchical micro-macro acceleration is based on a flexible four step procedure including a micro step, restriction step, macro step, and matching step. We derive several new micro-macro methods from that and compare to existing methods. In 1D and 2D test cases, the new methods achieve high accuracy and a large speedup.