A Parallel, Finite-Volume Algorithm for Large-Eddy Simulation of Turbulent Flows

A parallel, finite-volume algorithm has been developed for large-eddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear least-square reconstruction, trilinear finite-element interpolation, Roe flux-difference splitting, and second-order MacCormack time marching. Parallel implementation is done using the message-passing programming model. In this paper, the numerical algorithm is described. To validate the numerical method 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. Direct numerical simulation (DNS) results are available for this test case, and the accuracy of this algorithm for turbulence simulations can be ascertained by comparing the LES solutions with the DNS results. 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 affects the accuracy of the turbulence simulation. For accurate turbulence simulations, only 3–5 percent of the standard Roe fluxdifference splitting dissipation is needed. Nomenclature A area Roe flux-difference splitting matrix area of duct side walls c local speed of sound C SGS model constant  As 1 American Institute of Aero *Trong T. Bui, Aerospace Engineer, AIAA member, (805) 2582645, e-mail: [email protected]. Copyright  1999 by the American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Governmental purposes. All other rights are reserved by the copyright owner. CFD computational fluid dynamics CFL Courant number Smagorinsky constant specific heat at constant volume d normal distance from a solid wall d+ normal distance from a solid wall in wall units, D entire flow domain hydraulic diameter DNS direct numerical simulation elemental surface area on the boundary of a control volume elemental volume of a control volume total energy/unit volume normal component of the inviscid flux vector flux vector of the Navier-Stokes equations FDS flux-difference splitting inviscid flux vector viscous flux vector G spatial filter used in the LES equations I total number of grid points in the streamwise direction j Jacobian determinant J total number of grid points in the wallnormal direction k conduction heat-transfer coefficient K total number of grid points in the spanwise direction LES large-eddy simulation MPI Message-Passing Interface Cs cv d + ρuτd μ ----------=