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Liou-Steffen splitting (AUSM) schemes are popular for low Mach numbersimulations, however, like many numerical schemes for compressible flow theyrequire careful modification to accurately resolve convective features in thisregime. Previous analyses of these schemes usually focus only on a singlediscrete scheme at the convective limit, only considering flow with acousticeffects empirically, if at all. In our recent paper Hope-Collins & di Mare,2023 we derived constraints on the artificial diffusion scaling of low Machnumber schemes for flows both with and without acoustic effects, and appliedthis analysis to Roe-type finite-volume schemes. In this paper we formapproximate diffusion matrices for the Liou-Steffen splitting, as well as theclosely related Zha-Bilgen and Toro-Vasquez splittings. We use the constraintsfound in Hope-Collins & di Mare, 2023 to derive and analyse the requiredscaling of each splitting at low Mach number. By transforming the diffusionmatrices to the entropy variables we can identify erroneous diffusion termscompared to the ideal form used in Hope-Collins & di Mare, 2023. These termsvanish asymptotically for the Liou-Steffen splitting, but result in spuriousentropy generation for the Zha-Bilgen and Toro-Vasquez splittings unless aparticular form of the interface pressure is used. Numerical examples foracoustic and convective flow verify the results of the analysis, and show theimportance of considering the resolution of the entropy field when assessingschemes of this type.

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