Development and analysis of entropy stable no-slip wall boundary conditions for the Eulerian model for viscous and heat conducting compressible flows

Abstract

Nonlinear entropy stability analysis is used to derive entropy stable no-slip wall boundary conditions for the Eulerian model proposed by Svärd (Phys A Stat Mech Appl 506:350–375, 2018). The spatial discretization is based on entropy stable collocated discontinuous Galerkin operators with the summation-by-parts property for unstructured grids. A set of viscous test cases of increasing complexity are simulated using both the Eulerian and the classic compressible Navier–Stokes models. The numerical results obtained with the two models are compared, and similarities and differences are then highlighted. However, the differences are very small and probably smaller than what the current experimental technology allows to measure.

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

“…A naive rescaling of by some constant factor , such that = 0 + 1 , is not a viable option since it would make the model inconsistent with the incompressible Navier-Stokes and the Blasius solution. Furthermore, it was shown in [6,16] (with 1 = 0 ) that = 4∕3 is not as accurate as = 1 that we have considered here.…”

“…We conclude that, even without the modification suggested herein, the two models are, for all practical purposes [6,16], about as accurate models of compressible flows. However, ( 2) is easier to code, computationally less expensive and relaxes significantly faster to steady state solutions.…”

“…In summary, for noble gases the evidence provide some support, although far from conclusive, for the addition of an extra heat diffusion term. However, its impact for real flow applications is probably minuscule as previous validation of (2) suggest, [6,16]. For diatomic gases, the experimental evidence in the attenuation case is inconclusive and it is unclear if (2) should be augmented with an extra Fourier diffusion, and if so, what size it should have.…”

“…Hence this choice suggests that, 1 is so small that solutions remain within the accuracy limits of the experiments that have validated the Blasius layer. Furthermore, the system (2) with = 1 = 0 and = 0 ∕ where 0 is the dynamic viscosity, has been validated in the compressible regime for a wide range of Mach and Reynolds numbers, in [6] for NACA0012 and in [16,17] for cylinders. A remarkable agreement with the standard system (1) was demonstrated in all cases.…”

Analysis of an alternative Navier-Stokes system: Weak entropy solutions and a convergent numerical scheme

“…This value results in viscous terms that resemble those of the Navier-Stokes equations, and Fourier's law appears as a diffusive term in the energy equation of (1). In [DS21] and [SDP21], it was shown, in a suite of problems, that the new system (1)-(2) produces solutions that are next to indistinguishable from those of the NSF system. (The differences are much less than what can be measured in experiments.…”