Direct simulation of turbulence using massively parallel computers

Taking into account the direct numerical simulation of turbulent channel flow on a massively parallel supercomputer—a Cray T3D, this chapter discusses numerical method and parallel implementation and describes the format of turbulence databases. The chapter focuses on parallel implementation of a typical spectral DNS technique to allow efficient generation of turbulence statistics. Validation is discussed along with applications to more complex turbulence phenomena. Turbulence in fluids is a nonlinear phenomenon with a wide range of spatial and temporal scales. The largest space scales are usually fixed by the geometry of the flow, while the smallest scales are determined by viscosity. Estimates for the smallest scales are available from the Kolmogorov microscales, obtained from dimensional analysis, assuming dependence only upon viscosity v and dissipation rate ɛ. For computers with limited memory or disk space the resolution requirement has led to a preference for spectral methods. By comparison, second-order finite difference methods require approximately a factor of two more points in each spatial direction for accurate turbulence simulation, leading to a factor of eight more memory and disk space. Direct numerical simulation will not be a practical engineering tool for the near future, except in a few special low Reynolds number applications. The utility of direct numerical simulations is to have complete solutions of the governing equations of fluid flow for a variety of “building-block” flows, steady and unsteady. These full solutions can then be used to validate simpler theoretical or computational models that can be used in practical applications. The usefulness of direct numerical simulations has increased with the rise in power of supercomputers and desktop workstations.