A parallel finite volume algorithm for large-eddy simulation of turbulent flows

A parallel unstructured finite volume algorithm is developed for large-eddy simulation of compressible turbulent flows. Major components of the algorithm include piecewise linear least-square reconstruction of the unknown variables, trilinear finite element interpolation for the spatial coordinates, Roe flux difference splitting, and second-order MacCormack explicit time marching. The computer code is designed from the start to take full advantage of the additional computational capability provided by the current parallel computer systems. Parallel implementation is done using the message passing programming model and message passing libraries such as the Parallel Virtual Machine (PVM) and Message Passing Interface (MPI).;The development of the numerical algorithm is presented in detail. The parallel strategy and issues regarding the implementation of a flow simulation code on the current generation of parallel machines are discussed. The results from parallel performance studies show that the algorithm is well suited for parallel computer systems that use the message passing programming model. Nearly perfect parallel speedup is obtained on MPP systems such as the Cray T3D and IBM SP2. Performance comparison with the older supercomputer systems such as the Cray YMP show that the simulations done on the parallel systems are approximately 10 to 30 times faster.;The results of the accuracy and performance studies for the current algorithm are reported. To validate the flow simulation code, a number of Euler and Navier-Stokes simulations are done for internal duct flows. Inviscid Euler simulation of a very small amplitude acoustic wave interacting with a shock wave in a quasi-1D convergent-divergent nozzle shows that the algorithm is capable of simultaneously tracking the very small disturbances of the acoustic wave and capturing the shock wave. Navier-Stokes simulations are made for fully developed laminar flow in a square duct, developing laminar flow in a rectangular duct, and developing laminar flow in a 90-degree square bend. The Navier-Stokes solutions show good agreements with available analytical solutions and experimental data.;To validate the flow simulation code for turbulence simulation, LES of fully-developed turbulent flow in a square duct is performed for a Reynolds number of 320 based on the average friction velocity and the hydraulic diameter of the duct. The accuracy of the above algorithm for turbulence simulations is evaluated by comparison with the DNS solution. The effects of grid resolution, upwind numerical dissipation, and subgrid scale dissipation on the accuracy of the LES are examined. Comparison with DNS results shows that the standard Roe flux difference splitting dissipation adversely affect the accuracy of the turbulence simulation. This problem is unique to the turbulence simulation, since it does not occur in the Euler and laminar Navier-Stokes simulations using the same code. For accurate turbulence simulation, it is found that only three to five percent of the standard Roe flux difference splitting dissipation is needed.