On asymptotic behavior of HLL-type schemes at low Mach numbers
type: Item
instance of: scholarly article
title: On asymptotic behavior of HLL-type schemes at low Mach numbers
zbMATH Open document ID: 1459.76131
DOI: 10.1155/2020/7451240
author: Yanyan Li
published in: Mathematical Problems in Engineering
publication date: 2020-10-12T00:00:00Z
review text: Summary: The HLLEM approximate Riemann solver can capture discontinuities sharply, maintain positive definiteness, and satisfy the entropy condition automatically. These attractive properties make the HLLEM scheme widely used in the simulations of many compressible fluid problems. However, in the simulations of low Mach incompressible flow, the accuracy of HLLEM solver cannot be guaranteed. In the current study, a detailed discrete asymptotic analysis is conducted on the HLLEM scheme and the responsible terms for the loss of accuracy are identified. This allows us to develop two modified methods to solve this low Mach number problem. The first method is to add a low Mach number correction term on the basis of the original HLLEM scheme. The second is to simply rescale the responsible terms with a Mach number-based function. The asymptotic analysis of these two low Mach correction methods shows that the difference between the continuous system and the discrete system disappears, which means the resulting LM-HLLEM and LM-HLLEM2 schemes are both capable of obtaining physically correct solutions in low Mach limit. The results obtained from various test cases demonstrate that both these two HLLEM-type schemes can simulate incompressible and compressible fluid problems accurately and robustly.
Mathematics Subject Classification ID: 76Nxx
Mathematics Subject Classification ID: 76M12
Mathematics Subject Classification ID: 76M20
zbMATH DE Number: 7259660
describes a project that uses: Spalart-Allmaras
describes a project that uses: AUSM
describes a project that uses: HLLE
describes a project that uses: HE-E1GODF
describes a project that uses: L2Roe
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/7451240
OpenAlex ID: W3049514440
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description: scientific article; zbMATH DE number 7259660