Large eddy simulation of shock turbulence interaction

A nonconservative formulation of the energy equation (solving for internal energy) was used to perform large eddy simulations of compressible turbulence in Moin et al. due to its simplicity in implementing SGS models compared to the conservative formulation (solving for total energy). In problems with shocks in the domain, however, the total energy formulation is preferred due to its conservative nature. A conservative set of equations for the LES were derived from the nonconservative equations derived by Moin et al. Performance of the conservative formulation was compared with the experiment on decaying grid-generated turbulence as well as with the filtered DNS field. Various shock-capturing schemes were tested, and an ENO shock-capturing scheme of Shu and Osher was chosen for the simulation of shock/turbulence interaction. The scheme was tested and validated against the data base generated by DNS of weak shock waves. The results obtained with the essentially nonoscillatory (ENO) scheme were within 5 percent from the DNS results, and used less than 25 percent of the CPU time used in the DNS.