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An unsteady Reynolds-averaged Navier-Stokes solver is applied for the simulation of a synthetic (zero net mass flow) jet created by a single diaphragm piezoelectric actuator in quiescent air. This configuration was designated as case I for the Computational Fluid Dynamics Validation 2004 (CFDVAL2004) workshop held at Williamsburg, Virginia, in March 2004. Time-averaged and instantaneous (phase-averaged) data for this case were obtained at NASA Langley Research Center, using multiple measurement techniques. Computational results from two-dimensional simulations with one-equation Spalart-Allmaras and two-equation Menter's turbulence models are presented along with the experimental data. The effect of grid refinement, preconditioning, and time-step variation are also examined. [ABSTRACT FROM AUTHOR]

The accuracy and efficiency of several lower and higher order time integration schemes are investigated for engineering solution of the discretized unsteady compressible Navier–Stokes equations. Fully implicit methods tested are either the backward differentiation formulas (BDF) or stage-order two, explicit, singly diagonally implicit Runge–Kutta (ESDIRK) methods. For this comparison an unsteady two-dimensional laminar flow problem is chosen: flow around a circular cylinder at Re=1200. At temporal error tolerances consistent with engineering simulation, ∊≈10−1–10−2, first-order implicit Euler (BDF1) is uncompetitive. While BDF3 is quite efficient, its lack of A-stability may be problematic in the presence of convection. At these same error tolerances, the fourth-order ESDIRK scheme is 2.5 times more efficient than BDF2. It is concluded that reliable integration is most efficiently provided by fourth-order Runge–Kutta methods for this problem where order reduction is not observed. Efficiency gains are more dramatic at smaller tolerances. [Copyright &y& Elsevier]