A parallel implicit method for the direct numerical simulation of wall-bounded compressible turbulence

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.