Localized artificial diffusivity scheme for discontinuity capturing on curvilinear meshes

S. Kawai, S. K. Lele

Research output: Contribution to journalArticlepeer-review

178 Citations (Scopus)


A simple and efficient localized artificial diffusivity scheme is developed for the purpose of capturing discontinuities on curvilinear and anisotropic meshes using a high-order compact differencing scheme. The artificial diffusivity is dynamically localized in space to capture different types of discontinuities such as a shock wave, contact surface or material discontinuity. The method is intended for use with large-eddy simulation of compressible transitional and turbulent flows. The method captures the discontinuities on curvilinear and anisotropic meshes with minimum impact on the smooth flow regions. The amplitude of wiggles near a discontinuity and the number of grid points used to capture the discontinuity do not depend on the mesh size. The comparisons between the proposed method and high-order shock-capturing schemes illustrate the advantage of the method for the simulation of flows involving shocks, turbulence and their interactions. The multi-dimensional formulation is tested on a variety of 1D and 2D, steady and unsteady, different types of discontinuity-related problems on curvilinear and anisotropic meshes. A simplification of the method which reduces the computational cost does not show any major detrimental effect on the discontinuity capturing under the conditions examined.

Original languageEnglish
Pages (from-to)9498-9526
Number of pages29
JournalJournal of Computational Physics
Issue number22
Publication statusPublished - 2008 Nov 20


  • Compact differences
  • Compressible large-eddy simulation
  • Curvilinear coordinates
  • Discontinuity capturing
  • High-order methods


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