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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Low Mach number limit of some staggered schemes for compressible barotropic flows
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by R. Herbin, J.-C. Latché and K. Saleh HTML | PDF
Math. Comp. 90 (2021), 1039-1087 Request permission


In this paper, we study the behaviour of some staggered discretization based numerical schemes for the barotropic Navier-Stokes equations at low Mach number. Three time discretizations are considered: the implicit-in-time scheme and two non-iterative pressure correction schemes. The two latter schemes differ by the discretization of the convection term: linearly implicit for the first one, so that the resulting scheme is unconditionally stable, and explicit for the second one, so that the scheme is stable under a CFL condition involving the material velocity only. We prove rigorously that these three variants are asymptotic preserving in the following sense: for a given mesh and a given time step, a sequence of solutions obtained with a sequence of vanishing Mach numbers tends to a solution of a standard scheme for incompressible flows. This convergence result is obtained by mimicking the proof of convergence of the solutions of the (continuous) barotropic Navier-Stokes equations to that of the incompressible Navier-Stokes equation as the Mach number vanishes. Numerical results performed with a hand-built analytical solution show the behaviour that is expected from the analysis. Additional numerical results are obtained for the shock solutions of problems which are not in the scope of the present non dimensionalization but are nevertheless interesting to understand the behaviour of the scheme.
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Additional Information
  • R. Herbin
  • Affiliation: Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France
  • MR Author ID: 244425
  • ORCID: 0000-0003-0937-1900
  • Email:
  • J.-C. Latché
  • Affiliation: Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PSN-RES/SA21, Cadarche, St. Paul-lez Durance, 13115 France
  • MR Author ID: 715367
  • Email:
  • K. Saleh
  • Affiliation: Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, F-69622 Villeurbanne, France
  • MR Author ID: 960776
  • Email:
  • Received by editor(s): January 31, 2019
  • Received by editor(s) in revised form: December 5, 2019, and July 22, 2020
  • Published electronically: February 4, 2021
  • © Copyright 2021 American Mathematical Society
  • Journal: Math. Comp. 90 (2021), 1039-1087
  • MSC (2020): Primary 35Q31, 65N12, 76M10, 76M12
  • DOI:
  • MathSciNet review: 4232217