Assessing the numerical dissipation rate and viscosity in numerical simulations of fluid flows

We propose a method for quantifying the effective numerical dissipation rate and effective numerical viscosity in Computational Fluid Dynamics (CFD) simulations. Different from previous approaches that were formulated in spectral space, the proposed method is developed in a physical-space representation and allows for determining numerical dissipation rates and viscosities locally, that is, at the individual cell level, or for arbitrary subdomains of the computational domain. The method is self-contained and uses only the results produced by the Navier-Stokes solver being investigated. As no further information is required, it is suitable for a straightforward quantification of numerical dissipation as a post-processing step. We demonstrate the method's capabilities on the example of implicit large-eddy simulations of a three-dimensional Taylor-Green vortex flow, serving as a test flow going through laminar, transitional, and turbulent stages of time evolution. For validation, we compare results for the effective numerical dissipation rate with exact reference data we obtained with an accurate, spectral-space approach.