Effects of Numerical Diffusion on the Computation of Viscous Supersonic Flow Over a Flat Plate

Abstract

The effects of numerical diffusion on the computation of supersonic viscous flow over a flat plate at zero incidences are numerically investigated. The inviscid flux terms in the Navier-Stokes equations are computed using three schemes, namely, van Leer's Flux Vector Splitting, Liou and Steffen's Advection Upstream Splitting Method (AUSM) and Jaisankar and Raghurama Rao's Diffusion Regulated Local Lax Friedrichs (DRLLF) schemes. The results are correlated with the inherent numerical diffusion of these schemes. The study is also motivated by the necessity to examine whether reduced artificial viscosity can be used with the DRLLF scheme in computing viscous flows than was suggested in the original paper on inviscid computation. It is demonstrated that reduced artificial viscosity is not only possible, but it results in a scheme that is very efficient in the computation of the standard supersonic viscous flow over a flat plate, in that it is comparable in accuracy to the AUSM scheme in the boundary layer and better than it in shock resolution. Even with the reduced artificial viscosity suggested in this paper the DRLLF scheme shows good convergence behaviour comparable with the other two schemes.

A new approach for numerical-diffusion control of flux-vector-splitting schemes for viscous-compressible flows

“…Further it is observed that the AUSM, DRvLFV and DRAUSMV schemes compute the adiabatic wall temperature significantly closer to the DRLLFV and TV-AWS schemes. It may be recalled that the computed value of adiabatic wall temperature increases as the level of numerical diffusion increases (van Leer, 1991; Liou and Steffen, 1993; Kalita et al , 2016). Accordingly, Figure 3 indicates that the DRvLFV scheme offers significantly lower level of numerical diffusion compared with the vLFVS scheme and the DRAUSMV scheme exhibits marginal improvement over the AUSM scheme.…”

“…At the same time, it should be borne in the mind that excessive numerical diffusion spoils the accuracy by smearing the discontinuities and shear layers, especially in viscous flow computations. Consequently, such computations result in the underprediction of skin friction and wall heat fluxes (van Leer, 1991; Liou and Steffen, 1993; Kalita and Dass, 2016) and overprediction of the separation bubble sizes (Kalita and Dass, 2014) and adiabatic wall temperatures (Kalita et al , 2016). It may further be noted that stability demands relatively high numerical diffusion in zones of shocks or sharp gradients, whereas accuracy calls for minimal numerical diffusion in smooth flow regions including shear layers (Kalita and Dass, 2017).…”

Numerical Entropy Production as Smoothness Indicator for Shallow Water Equations

“…Numerical entropy production has further been used to develop numerical schemes for conservation laws and balance laws, such as those in the literature [1,15,30,[33][34][35]. Due to their wide range of applications, these laws have been of interest to a number of researchers [6,7,11,24,26,31,32].…”