Hydrodynamics from Grad's equations: What can we learn from exact solutions?

TL;DR

This paper investigates the derivation of hydrodynamics from Grad's moment equations, using exact solutions to compare approximation methods and understand extensions beyond Navier-Stokes.

Contribution

It provides an exact analysis of Chapman-Enskog derivation within Grad's systems, enabling comparison of approximation techniques in hydrodynamic modeling.

Findings

Grad's systems serve as minimal kinetic models for exact Chapman-Enskog analysis

Comparison of approximation methods like Pade approximants and invariance principle

Insights into extending hydrodynamics beyond Navier-Stokes

Abstract

A detailed treatment of the classical Chapman-Enskog derivation of hydrodynamics is given in the framework of Grad's moment equations. Grad's systems are considered as the minimal kinetic models where the Chapman-Enskog method can be studied exactly, thereby providing the basis to compare various approximations in extending the hydrodynamic description beyond the Navier-Stokes approximation. Various techniques, such as the method of partial summation, Pade approximants, and invariance principle are compared both in linear and nonlinear situations.