A computational error-assessment of central finite-volume discretizations in large-eddy simulation using a Smagorinsky model

Abstract

We present a framework for the computational assessment and comparison of large-eddy simulation methods. We apply this to large-eddy simulation of homogeneous isotropic decaying turbulence using a Smagorinsky subgrid model and investigate the combined effect of discretization and model errors at coarse subgrid resolutions. We compare four different central finite-volume methods. These discretization methods arise from the four possible combinations that can be made with a second-order and a fourth-order central scheme for either the convective and the viscous fluxes. By systematically varying the simulation resolution and the Smagorinsky coefficient, we determine parameter regions for which a desired number of flow properties is simultaneously predicted with approximately minimal error. We include both physics-based and mathematics-based error definitions, leading to different error-measures designed to emphasize either errors in large- or in small-scale flow properties. It is shown that the evaluation of simulations based on a single physics-based error may lead to inaccurate perceptions on quality. We demonstrate however that evaluations based on a range of errors yields robust conclusions on accuracy, both for physics-based and mathematics-based errors. Parameter regions where all considered errors are simultaneously near-optimal are referred to as ‘multi-objective optimal’ parameter regions. The effects of discretization errors are particularly important at marginal spatial resolution. Such resolutions reflect local simulation conditions that may also be found in parts of more complex flow simulations. Under these circumstances, the asymptotic error-behavior as expressed by the order of the spatial discretization is no longer characteristic for the total dynamic consequences of discretization errors. We find that the level of overall simulation errors for a second-order central discretization of both the convective and viscous fluxes (the ‘2–2’ method), and the fully fourth-order (‘4–4’) method, is equivalent in their respective ‘multi-objective optimal’ regions. Mixed order methods, i.e. the ‘2–4’ and ‘4–2’ combinations, yield errors which are considerably higher.