On the simulation of stratified turbulent flows

In the first part of this report, the effects of numerical dissipation presented in a turbulence Direct Numerical Simulation (DNS) code called SMPM is investigated through the use of the effective numerical eddy viscosity, a concept pioneered by Domaradzki and Xiao in 2003. This SMPM algorithm, which is inherently free of any intrinsic truncation error, employs three numerical stabilizers, i.e., Fourier filtering, Legendre filtering and Penalty method to ensure the numerical stability in the calculations of turbulent flows with very high Reynolds number, for which the simulation is often under-resolved. Numerical data extracted from the simulation of a turbulent wake flow is employed to quantify the effective numerical eddy viscosity for all three explicit numerical stabilizers. The results shown that the effects of the stabilizers can be significant, if not dominated, compared to the physical molecular viscosity. Away from the vertical subdomain interfaces, all three stabilizers behave expectedly to remove the kinetic energy from the system, i.e., dissipative. At the subdomain interfaces, the Legendre filtering and the Penalty scheme exhibit the unexpected anti-dissipative character, i.e., to increase the energy of the system. Such counter-intuitive behavior is attributed to the discontinous formulism of the Penalty scheme, which is absolutely necessary if multi-domain method is employed. This anti-dissipative behavior diminishes quickly only a few grid points away from the subdomain interfaces.;The original formulism of effective numerical viscosity was dedicated to a turbulence DNS code with triply-periodic boundary conditions. It has been successfully extended to our SMPM code whose boundary condition is not periodic in the vertical direction, the direction aligns with the only non-zero external force field, i.e., gravity. The success of this extension gives us the confidence that the same concept can be applied to any numerical algorithm for under-resolved simulation, so long as the baseline case can be defined.