Influence of Numerical Parameters for Large Eddy Simulations of Complex Flow Fields

Large eddy simulation (LES) becomes more and more important for the simulation of practical turbulent flows. The application for technically relevant, complex configurations leads to systems from around 500,000 up to several million degrees of freedom. For a statistical analysis of the turbulent flow field a large number of time steps have to be computed. Efficient algorithms are required to ensure acceptable computing times. When using implicit schemes -- allowing for relatively large time step sizes -- the chosen convergence criteria for stopping the solution procedure within the individual time steps, turns out to be an important issue. For optimizing the computational effort it is beneficial to have a detailed knowledge about the influence of the convergence criteria to the characteristic values of the flow field. The investigation of the corresponding effects is the major subject of the present paper. The flow solver employed is the fully parallel multigrid finite-volume code FASTEST with second-order accurate discretizations in space and time. For the LES, the Smagorinsky model with the dynamic approach of Germano is implemented. The attainable convergence criteria for LES in complex geometries when using a standard geometric multi-grid scheme is limited by the visible frequencies on the coarse grid . To overcome this, and to reach smaller residuals within acceptable computing times, an improved multi-grid algorithm is introduced which exploits the good convergence rate of the multi-grid algorithm in the first V-cycles and then employ the fine grid for the last iterations. As a complex application of practical interest we consider the large eddy simulation of the flow in a mixing chamber corresponding to the swirling flow in an aircraft combustion chamber. Comparisons to experimental results are presented and the influence of the convergence criteria is studied in detail by analyzing statistical values, energy spectra, and computational effort