Mixing, scalar boundedness, and numerical dissipation in large-eddy simulations

Abstract

Numerical schemes for scalar transport and mixing in turbulent flows must be high-order accurate, and observe conservation and boundedness constraints. Discretization accuracy can be evaluated from the truncation error, and assessed by its dispersion and dissipation properties. Dispersion errors can cause violation of physical scalar bounds, whereas numerical dissipation is key to mitigating those violations. Numerical dissipation primarily alters the energy at small scales that are critical to turbulent mixing. Influence of additional dissipation on scalar mixing in large-eddy simulations (LES) of incompressible temporally evolving shear flow is examined in terms of the resolved passive-scalar field, Z¯. Scalar fields in flows with different mixing behavior, exhibiting both uniform and non-uniform mixed-fluid composition across a shear layer, are compared for different grid resolutions, subgrid-scale models, and scalar-convection schemes. Scalar mixing is assessed based on resolved passive scalar probability density function (PDF), variance, and spectra. The numerical-dissipation influence on mixing is found to depend on the nature of the flow. Mixing metrics sensitive to numerical dissipation are applied to examine the performance of limiting methods employed to mitigate unphysical scalar excursions. Two approaches, using a linear-scaling limiter for finite-volume schemes and a monotonicity-preserving limiter for finite-difference schemes, are studied. Their performance with respect to accuracy, conservation, and boundedness is discussed.