High Resolution Methods for Computing Turbulent Flows

Numerical dissipation and the bottleneck effect in simulations of compressible isotropic turbulence

“…Then the common approach is to run a LES which resolves only the largest scales and invokes some model for turbulence on smaller scales. On the other hand, it has been suggested to let merely the dissipative effect of a finite-volume scheme smooth out the flow on length scales just above the numerical cutoff and dispose of accumulating kinetic energy [18]. In particular, this assumption was put forward and exhaustively tested for the piece-wise parabolic method (PPM) [5,7,8,9].…”

“…Of course, the question arises, whether the action of numerical dissipation mimics the effect of Navier-Stokes viscous dissipation properly [9,18]. We attempted to re-investigate this issue by means of turbulence energy spectra and parameters specifying the effect of numerical dissipation.…”

“…Apart from that, we use a high-order Godunov scheme, namely, the piece-wise parabolic method (PPM), which applies to fully compressible flows and, in fact, introduces numerical dissipation [5]. Of course, the question arises, whether the action of numerical dissipation properly mimics the effect of Navier-Stokes viscous dissipation in direct numerical simulations (DNS) or the action of subgrid scale turbulence stresses in large-eddy simulations (LES) [9,18]. One cannot reasonably expect that the local rate of dissipation in the former case or the energy transfer toward unresolved scale in the latter case is exactly matched by the dissipative effects of the PPM.…”

Embedded turbulence model in numerical methods for hyperbolic conservation laws

“…Previous studies [1][2][3][4][5][6][7][8][9] have shown that high-resolution (non-oscillatory) advection methods can represent the e ects of the unresolved scales of motion in computations of turbulent ows without using a SGS model. Following Harten's deÿnition [10], we classify as high resolution methods those with the following properties: (i) provide at least second-order of accuracy in smooth areas of the ow, (ii) produce numerical solutions (relatively) free from spurious oscillations, and (iii) in the case of discontinuities, the number of grid points in the transition zone containing the shock wave is smaller in comparison with that of ÿrst-order monotone methods.…”