A finite-volume gas-kinetic method for the solution of the Navier-Stokes equations

Abstract

Gas-kinetic theory is also valid in the continuum regime: the Euler and Navier-Stokes equations can be obtained as projection of the Boltzmann equation on to the physical space ( x,t ). The numerical schemes derived from gas-kinetic theory are computationally more expensive than Navier-Stokes based ones, but offer advantages which have been attracting a growing level of attention: they can ( i ) accommodate discontinuities at cells interface, ( ii ) provide high-resolution fluxes, ( iii ) provide advantages in the simulation of turbulence, ( iv ) handle hypersonic and/or rarefied flows. This study extends the validation of gas-kinetic schemes investigating a few turbulent flow cases. At a slightly higher computational cost, gas-kinetic schemes provide results comparable to those obtained with well-validated Navier-Stokes schemes using the same turbulence model, grid and reconstruction order. In the case of shock-separated flows, the results obtained with the gas-kinetic scheme are even closer to experimental data. These findings are consistent with the idea that gas-kinetic theory is a physically more consistent framework for investigating the mechanics of fluids.