WIAS Preprint No. 1830, (2013)

Low Mach asymptotic preserving scheme for the Euler--Korteweg model


  • Giesselmann, Jan

2010 Mathematics Subject Classification

  • 65M06 65M12 76T10


  • Multi-phase flows, phase transition, all-speed scheme, asymptotic preserving, low Mach number flows, finite difference scheme


We present an all speed scheme for the Euler-Korteweg model. We study a semi-implicit time-discretisation which treats the terms, which are stiff for low Mach numbers, implicitly and thereby avoids a dependence of the timestep restriction on the Mach number. Based on this we present a fully discrete finite difference scheme. In particular, the scheme is asymptotic preserving, i.e., it converges to a stable discretisation of the incompressible limit of the Euler-Korteweg model when the Mach number tends to zero.

Appeared in

  • IMA J. Numer. Anal. 35 (2) (2015) , pp. 802--833.

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