Pseudo-transient Continuation, Solution Update Methods, and CFL Strategies for DG Discretizations of the RANS-SA Equations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106459/1/AIAA2013-2686.pd

An a Posteriori Study of a DNS Database Describing Supercritical Binary-Species Mixing

Large Eddy Simulation (LES) a posteriori study is conducted for a mixing layer which initially contains different species in the lower and upper streams, and where the initial pressure is larger than the critical pressure of either species. An initially imposed-vorticity perturbation promotes roll-up and a double pairing of four initial spanwise vortices to reach a transitional state. The LES equations consist of the differential conservation equations coupled with a real-gas equation of state, and the equation set utilizes transport properties depending on the thermodynamic variables. Unlike all LES models to date, the differential equations contain, additional to the Subgrid Scale (SGS) fluxes, a new SGS term which is a pressure correction in the momentum equation. This additional term results from altering of the Direct Numerical Simulation (DNS) equations and represents the gradient of the difference between the filtered pressure and the pressure computed from the filtered flow field. A previous a priori analysis, using a DNS database for the same configuration, found this term to be of leading order in the momentum equation, a fact traced to the existence of high density-gradient magnitude regions that populated the entire flow; in that study, models were proposed for the SGS fluxes as well as this new term. In the present study, the previously-proposed constant-coefficient SGS-flux models of the a priori investigation are tested a posteriori in LES devoid or including the SGS pressure correction term. The present pressure-correction model is different from, and more accurate and less computationally intensive than that of the a priori study. The constant-coefficient SGS-flux models encompass the Smagorinsky (SMC), in conjunction with the Yoshizawa (YO) model for the trace, the Gradient (GRC) and the Scale Similarity (SSC) models, all exercised with the a priori study constant coefficients calibrated at the transitional state. The LES comparison is performed with the fitered-and-coarsened (FC) DNS which represents an ideal LES solution. Expectably, when the LES model is devoid of SGS terms, it is shown to be considerably inferior to models containing SGS effects. Among models containing SGS effects, those including the pressure-correction term are substantially superior to those devoid of it. The sensitivity of the predictions to the initial conditions and grid size are also investigated