A Technique for Developing an Entropy Consistent System of Second-Order Hydrodynamic Equations
Abstract
This paper presents the development of a novel set of second-order hydrodynamic equations known as the BGK-Burnett equations for computing flows in the continuum-transition regime. The second-order distribution function that forms the basis of this formulation is approximated by the first three terms of the Chapman-Enskog expansion. Such and expression, however, does not readily satisfy the moment closure property. Hence an exact closed form expression for the same is obtained by enforcing moment closure and solving a system of algebraic equations to determine the closure coefficients. Through a series of conjectures the closure coefficients are designed to move the resulting system of hydrodynamic equations towards an entropy consistent set. An important step in the formulation of the higher-order distribution functions is the proper representation of the material derivatives in terms of the spatial derivatives. White the material derivatives in the first-order distribution function are approximated by the Euler equations, proper representations to these derivatives in the second-order distribution function are determined by an entropy consistent relaxation technique. The BGK-Burnett equations, obtained by taking moments of the Boltzmann equation in the second-order distribution function, are shown to be stable to small wavelength disturbances and entropy consistent for a wide range of grid points and Mach numbers.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 2000
- Accession Number
- ADA400919
Entities
People
- Ramesh Balakrishnan
- Ramesh K. Agarwal
Organizations
- University of Illinois Urbana–Champaign