Chaos, transport and mesh convergence for fluid mixing


DOI: 10.1007/s10255-008-8019-8

Cite this article as:
Lim, H., Yu, Y., Glimm, J. et al. Acta Math. Appl. Sin. Engl. Ser. (2008) 24: 355. doi:10.1007/s10255-008-8019-8


Chaotic mixing of distinct fluids produces a convoluted structure to the interface separating these fluids. For miscible fluids (as considered here), this interface is defined as a 50% mass concentration isosurface. For shock wave induced (Richtmyer-Meshkov) instabilities, we find the interface to be increasingly complex as the computational mesh is refined. This interfacial chaos is cut off by viscosity, or by the computational mesh if the Kolmogorov scale is small relative to the mesh. In a regime of converged interface statistics, we then examine mixing, i.e. concentration statistics, regularized by mass diffusion. For Schmidt numbers significantly larger than unity, typical of a liquid or dense plasma, additional mesh refinement is normally needed to overcome numerical mass diffusion and to achieve a converged solution of the mixing problem. However, with the benefit of front tracking and with an algorithm that allows limited interface diffusion, we can assure convergence uniformly in the Schmidt number. We show that different solutions result from variation of the Schmidt number. We propose subgrid viscosity and mass diffusion parameterizations which might allow converged solutions at realistic grid levels.


Schmidt number mass diffusion turbulence multiphase flow 

2000 MR Subject Classification

76F65 76R50 76T30 

Copyright information

© Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH 2008

Authors and Affiliations

  • H. Lim
    • 1
  • Y. Yu
    • 1
  • J. Glimm
    • 1
    • 2
  • X. L. Li
    • 1
  • D. H. Sharp
    • 3
  1. 1.Department of Applied Mathematics and StatisticsStony Brook UniversityStony BrookUSA
  2. 2.Computational Science CenterBrookhaven National LaboratoryUptonUSA
  3. 3.Los Alamos National LaboratoryLos AlamosUSA