A new second-order accurate implicit temporal numerical scheme for the direct numerical simulation of turbulent flows is presented. The formulation of the implicit method and the corresponding tunable parameters are introduced. The numerical simulation results are compared with the results given by explicit Runge-Kutta schemes, theoretical results, and published experimental and numerical data. An assessment of the accuracy and performance of the method to simulate turbulent flows is made for temporally decaying isotropic turbulence and subsonic and supersonic turbulent boundary layers. Whereas no significant advantage over typical explicit time integration methods are found for the incompressible flows; it is shown that the implicit scheme yields significant reduction in computer cost while assuring time-accurate solutions for compressible turbulence simulations.
Bibliographical noteFunding Information:
This work was sponsored by the National Science Foundation under Grant number CTS-0238390 and by the Army High Performance Computing Research Center under the auspices of the Department of the Army, Army Research Laboratory cooperative agreement DAAD191-01-2-0014, the content of which does not necessarily reflect the position or policy of the government, and no official should be inferred. The computing time was provided by the CROCCO Laboratory in Princeton University.
- Direct numerical simulation
- Implicit time integration
- Wall-bounded turbulent flow