An OpenFOAM solver for the extended Navier-Stokes equations

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.(c) 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

Classical continuum methods are inadequate for gas flows with higher Knudsen numbers. Various models have been developed in the past to extend the classical Navier-Stokes equations (CNSE) and incorporate the particle nature of the medium. One such approach considers the kinetic theory of gases, leading to the derivation of the extended Navier-Stokes equations (ENSE). Numerical methods, such as the Finite-Volume-Method, are commonly used to solve the CNSE, and this study utilizes the open-source tool OpenFOAM to develop an ENSE solver, which offers significant performance advantages by implicitly discretizing certain terms and defining additional diffusion face-flux fields. The results are validated against analytical formulas using a simple microchannel test case.