A robust, colocated, implicit algorithm for direct numerical simulation of compressible, turbulent flows

Yucheng Hou, Krishnan Mahesh

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A non-dissipative, robust, implicit algorithm is proposed for direct numerical and large-eddy simulation of compressible turbulent flows. The algorithm addresses the problems caused by low Mach numbers and under-resolved high Reynolds numbers. It colocates variables in space to allow easy extension to unstructured grids, and discretely conserves mass, momentum and total energy. The Navier-Stokes equations are non-dimensionalized using an incompressible scaling for pressure, and the energy equation is used to obtain an expression for the velocity divergence. A pressure-correction approach is used to solve the resulting equations, such that the discrete divergence is constrained by the energy equation. As a result, the discrete equations analytically reduce to the incompressible equations at very low Mach number, i.e., the algorithm overcomes the acoustic time-scale limit without preconditioning or solution of an implicit system of equations. The algorithm discretely conserves kinetic energy in the incompressible inviscid limit, and is robust for inviscid compressible turbulence on the convective time-scale. These properties make it well-suited for DNS/LES of compressible turbulent flows. Results are shown for acoustic propagation, the incompressible Taylor problem, periodic shock tube problem, and isotropic turbulence.

Original languageEnglish (US)
Pages (from-to)205-221
Number of pages17
JournalJournal of Computational Physics
Issue number1
StatePublished - May 1 2005

Bibliographical note

Funding Information:
This work was supported by the McKnight Land-Grant Professorship award, and the United States Department of Energy through the Stanford ASCI Alliance. Computing resources were provided by the Minnesota Supercomputing Institute and the San Diego Supercomputing Center.


  • All-Mach number
  • Compressible turbulence
  • Direct numerical simulation
  • Discrete energy conservation
  • Large-eddy simulation
  • Non-dissipative


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