| The objective of this research is to derive a kinetic-theory based flux vector splitting scheme for the 3-D Navier-Stokes equations. From kinetic theory, the velocity distribution function corresponding to the Navier-Stokes equations is the Chapman-Enskog velocity distribution function. Because of the complexity of the Chapman-Enskog velocity distribution function representation, it is very difficult to manually derive the split kinetic fluxes, which involve more than 400 triple-integrals. With the help of modern day magic, MATHEMATICA, a set of three dimensional split kinetic fluxes for the Navier-Stokes equations is derived for the first time. It is amazing how compact these split kinetic fluxes are, considering the fact that they were arrived at through hundreds of triple-integrals.;The most important concept of kinetic flux vector splitting (KFVS) is that it takes advantage of the linear hyperbolic equation at the Boltzmann equation level and projects this property onto the non-linear Navier-Stokes equations level. The moment equations are the tools used to map the upwind conditions and stability conditions from the Boltzmann equation (microscopic) level to the conservation equations (macroscopic) level. Unlike the conventional upwind scheme, which is based on the Eigenvalues of the flux jacobian in continuum theory, the KFVS scheme, in contrast, relies on the signal propagation associated with the microscopic particle velocity.;A high-order flux vector splitting scheme, coupled with the Chapman-Enskog split kinetic fluxes, is developed for the numerical solution of the Navier-Stokes equations. Stability conditions for the corresponding KFVS scheme and a compatible kinetic flux boundary condition treatment will be discussed. Finally, some numerical results are presented. |
