A study of the diffusive properties of a modified compressible Navier-Stokes model

Abstract

The aim of this study is to provide further validation for the weakly well-posed modified compressible Navier-Stokes system proposed in Svärd (Phys A 506:350–375, 2018) when applied to ideal gases. We do so by considering sound attenuation, both theoretically and numerically for argon and oxygen, and make comparisons with experimental values in the literature. Furthermore, we compute shock profiles for argon and nitrogen, and compare them with experiments in the literature. Our numerical simulations have revealed problems when using experimental attenuation data, as presented in the available literature, for validation and determination of diffusion coefficients. However, comparisons with the shock data, suggest that the modified system may benefit from an additional heat diffusive term. In view of these and previously published validation tests, the model proposed in Svärd (Phys A 506:350–375, 2018) is equally accurate as the standard compressible system. However, with more complete experimental information for the attenuation case at hand, it might be possible to further improve the accuracy by more precise determination of the diffusion coefficients. We propose a tentative adjustment of the model that may be tested/validated, if more detailed experimental information becomes available.