A glimpse of hydrodynamics beyond the NavierStokes equations
Abstract
A solution of Maxwell's moment equations is obtained for the steady, onedimensional flow through a normal shock wave in a Maxwellian gas. The solution method makes use of a new representation for the conservation equations, a closure relation for a single thirdorder moment, and a spatially integrated form of Maxwell's equations of transfer. The integrated equations of transfer act as constraints in evaluating two sets of coefficients introduced in the conservation equations and the single closure relation. A total of only four coefficients are found to be fully sufficient when comparisons are made with results from the direct simulation Monte Carlo method, which show excellent agreement across all hydrodynamic variables including two fourthorder moments which the theory predicts.
 Publication:

Physics of Fluids
 Pub Date:
 October 2002
 DOI:
 10.1063/1.1502659
 Bibcode:
 2002PhFl...14.3403B
 Keywords:

 hydrodynamics;
 NavierStokes equations;
 Monte Carlo methods;
 flow simulation;
 Flow Visualization;
 Fluid Dynamics;
 Hydrodynamics;
 Maxwell Equation;
 Maxwell Fluids;
 Monte Carlo Method;
 NavierStokes Equation;
 Normal Shock Waves;
 Steady Flow;
 47.10.+g;
 Fluid Mechanics and Thermodynamics