Abstract
We design and analyse a first-order accurate implicit–explicit (IMEX) scheme for the two-dimensional wave equation system in the low Mach number limit. It has been shown by Dellacherie [S. Dellacherie, Analysis of Godunov-type schemes applied to the compressible Euler system at low Mach number. J. Comput. Phys., 229(4): 978–1016, 2010, [1]] that the standard Godunov-type numerical schemes suffer from a severe loss of accuracy at low Mach numbers. This inaccuracy arises due to the inability of schemes to preserve the incompressible space of constant densities and divergence-free velocities. Guided by this principle, we design an IMEX scheme which possess the invariance property, and analyse its stability. The proposed scheme has been shown to be stable under a usual CFL-like condition, independent of the Mach number. The results of numerical experiments confirm the accuracy and stability of the new scheme when applied to low Mach number problems.
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References
S. Dellacherie, Analysis of Godunov type schemes applied to the compressible Euler system at low mach number. J. Comput. Phys. 229(4), 978–1016 (2010)
H. Guillard, C. Viozat, On the behaviour of upwind schemes in the low mach number limit. Comput. Fluids 28(1), 63–86 (1999)
S. Klainerman, A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Commun. Pure Appl. Math. 34(4), 481–524 (1981)
R. Klein, Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics I: one-dimensional flow. J. Comput. Phys. 121(2), 213–237 (1995)
S. Schochet, Fast singular limits of hyperbolic PDEs. J. Differ. Equ. 114(2), 476–512 (1994)
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Arun, K.R., Das Gupta, A.J., Samantaray, S. (2018). An Implicit–Explicit Scheme Accurate at Low Mach Numbers for the Wave Equation System. In: Klingenberg, C., Westdickenberg, M. (eds) Theory, Numerics and Applications of Hyperbolic Problems I. HYP 2016. Springer Proceedings in Mathematics & Statistics, vol 236. Springer, Cham. https://doi.org/10.1007/978-3-319-91545-6_8
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DOI: https://doi.org/10.1007/978-3-319-91545-6_8
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