This paper is devoted to a centered IMEX scheme in a multidimensional framework for a wide class of multicomponent and isentropic flows. The proposed strategy is based on a regularized model where the advection velocity is modified by the gradient of the potential of the conservative forces in both mass and momentum equations. The stability of the scheme is ensured by the dissipation of mechanic energy, which stands for a mathematical entropy, under an advective CFL condition. The main physical properties, such as positivity, conservation of the total momentum, and conservation of the steady state at rest, are satisfied. In addition, asymptotic preserving properties in the regimes (``incompressible" and “acoustic") are analyzed. Finally, several simulations are presented to illustrate our results in a simplified context of oceanic flows in one dimension.


  1. conservation laws
  2. low-Mach number
  3. low-Froude number
  4. well-balanced scheme
  5. entropy dissipation
  6. asymptotic preserving

MSC codes

  1. 35L60
  2. 76M12
  3. 86A05
  4. 76E20
  5. 35B40

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Information & Authors


Published In

cover image SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Pages: 3083 - 3104
ISSN (online): 1095-7170


Submitted: 19 May 2015
Accepted: 21 July 2016
Published online: 11 October 2016


  1. conservation laws
  2. low-Mach number
  3. low-Froude number
  4. well-balanced scheme
  5. entropy dissipation
  6. asymptotic preserving

MSC codes

  1. 35L60
  2. 76M12
  3. 86A05
  4. 76E20
  5. 35B40



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