An all-speed relaxation scheme for interface flows with surface tension

  • Authors:

  • Benjamin Braconnier;Boniface Nkonga

  • Affiliations:

  • Glaizer Group: Générateur de Technologies Innovantes, 32 rue Guy Moquet, 92240 Malakoff, France and MAB, Univ. Bordeaux 1/INRIA Futurs, ScAlApplix 351 cours de la libération, 33400 ...;Laboratoire J.A. Dieudonné, U.M.R. C.N.R.S. No. 6621, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 02, France and MAB, Univ. Bordeaux 1/INRIA Futurs, ScAlApplix 35 ...

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

We consider interface flows where compressibility and capillary forces (surface tension) are significant. These flows are described by a non-conservative, unconditionally hyperbolic multiphase model. The numerical approximation is based on finite-volume method for unstructured grids. At the discrete level, the surface tension is approximated by a volume force (CSF formulation). The interface physical properties are recovered by designing an appropriate linearized Riemann solver (Relaxation scheme) that prevents spurious oscillations near material interfaces. For low-speed flows, a preconditioning linearization is proposed and the low Mach asymptotic is formally recovered. Numerical computations, for a bubble equilibrium, converge to the required Laplace law and the dynamic of a drop, falling under gravity, is in agreement with experimental observations.