Entropy-stable schemes in the low-Mach-number regime: Flux-preconditioning, entropy breakdowns, and entropy transfers

Gouasmi, Ayoub; Duraisamy, Karthik; Murman, Scott M.

doi:10.1016/j.jcp.2022.111036

Cited by 3 publications

(2 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The pressure loss downstream of the cylinder is due to the fact a first order scheme has been used, but the smooth error profiles 3b and 4b indicate that the pressure is free of chequerboard modes. There is a very small amount of entropy generated at the wall visible in 3c and 4c -which is unavoidable with standard upwind schemes, although is reduced by the curvature corrected boundary conditions (see [16] for a recent example of low Mach number entropy conserving/stable schemes) -and the density profiles 3d and 4d resemble the pressure profiles as expected.…”

Section: Circular Cylindermentioning

confidence: 54%

“…The Liou-Steffen splitting generates slightly more entropy than the Roe scheme, which is the opposite of the trend seen in the circular cylinder test case. The profiles in 16a and 17a are similar to the entropy production modes of an entropy stable Roe scheme shown in figure 11 of [16] smeared by a quarter turn, and the entropy production after a single timestep closely resembles the production mode. The entropy profiles found with the first Zha-Bilgen and Toro-Vasquez forms and the convective scaling have much larger variations, and their shape is consistent with what would be expected from the limit equation ( 40) i.e.…”

Section: Isentropic Vortexmentioning

confidence: 56%

See 1 more Smart Citation

Artificial diffusion for convective and acoustic low Mach number flows II: Application to Liou-Steffen, Zha-Bilgen and Toro-Vasquez convection-pressure flux splittings

Hope-Collins¹,

Mare²

2023

Preprint

View full text Add to dashboard Cite

Liou-Steffen splitting (AUSM) schemes are popular for low Mach number simulations, however, like many numerical schemes for compressible flow they require careful modification to accurately resolve convective features in this regime. Previous analyses of these schemes usually focus only on a single discrete scheme at the convective limit, only considering flow with acoustic effects empirically, if at all. In our recent paper Hope-Collins & di Mare, 2023 we derived constraints on the artificial diffusion scaling of low Mach number schemes for flows both with and without acoustic effects, and applied this analysis to Roe-type finite-volume schemes. In this paper we form approximate diffusion matrices for the Liou-Steffen splitting, as well as the closely related Zha-Bilgen and Toro-Vasquez splittings. We use the constraints found in Hope-Collins & di Mare, 2023 to derive and analyse the required scaling of each splitting at low Mach number. By transforming the diffusion matrices to the entropy variables we can identify erroneous diffusion terms compared to the ideal form used in Hope-Collins & di Mare, 2023. These terms vanish asymptotically for the Liou-Steffen splitting, but result in spurious entropy generation for the Zha-Bilgen and Toro-Vasquez splittings unless a particular form of the interface pressure is used. Numerical examples for acoustic and convective flow verify the results of the analysis, and show the importance of considering the resolution of the entropy field when assessing schemes of this type.

show abstract

Section: Circular Cylindermentioning

confidence: 54%

Section: Isentropic Vortexmentioning

confidence: 56%