An OpenFOAM solver for the extended Navier–Stokes equations

Abstract

Classical continuum methods fail in predicting gas flows with higher Knudsen numbers. Several models have been derived in the past which extend the classical Navier–Stokes equations (CNSE) in order to capture the particle character of the medium. One approach takes into account the kinetic theory of gases. Accordingly, an additional self-diffusive mass flux can occur, which is a result of strong temperature and pressure gradients. These effects led to the derivation of the so called extended Navier–Stokes equations (ENSE). Under rare conditions they can be treated analytically. However, in most cases numerical methods are necessary. Usually the Finite-Volume-Method is utilized for numerically solving the CNSE, which is why the present work uses the well-known open-source-tool OpenFOAM as a foundation for developing an ENSE solver. It is pointed out that the advantage of being able to discretize certain terms implicitly and define additional diffusion face-flux fields leads to a huge performance gain in this case. Using a simple microchannel test case, the results are verified against analytical formulas.

Keywords

• Extended Navier–Stokes equations
• OpenFOAM solver
• Computational fluid dynamics
• Microchannel flow