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Abstract Vibrational spectroscopy enables critical insight into the structural and dynamic properties of molecules. Presently, the majority of theoretical approaches to spectroscopy employ wavefunction‐basedab initioor density functional methods that rely on the harmonic approximation. This approximation breaks down for large molecules with strongly anharmonic bonds or for molecules with large internuclear separations. An alternative to these methods involves generating molecular anharmonic potential energy surfaces (potentials) and using them to extrapolate the vibrational frequencies. This study examines the efficacy of density functional theory (DFT) and the correlation consistent Composite Approach (ccCA) in generating anharmonic frequencies from potentials of small main group molecules. Vibrational self‐consistent field Theory (VSCF) and post‐VSCF methods were used to calculate the fundamental frequencies of these molecules from their potentials. Functional choice, basis set selection, and mode‐coupling are also examined as factors in influencing accuracy. The absolute deviations for the calculated frequencies using potentials at the ccCA level of theory were lower than the potentials at the DFT level. With DFT resulting in bending modes that are better described than those of ccCA, a multilevel DFT:ccCA approach where DFT potentials are used for single vibrational mode potentials and ccCA is used for vibrational mode‐mode couplings can be utilized for larger polyatomic systems. The frequencies obtained with this multilevel approach using VCIPSI‐PT2 were closer to experimental frequencies than the scaled harmonic frequencies, indicating the success of utilizing post‐VSCF methods to generate more accurate representations of computed infrared spectra. 

Vortex breakdown is an instability which occurs in swirling flows and is seen in both incompressible and compressible flow regimes. The choice of numerical algorithm to com- pute this flow is critical to resolving the relevant physical phenomena. In previous work, we described the procedure of combining a Barely Implicit Correction (BIC) algorithm with a fourth-order Flux-Corrected Transport (FCT) algorithm to eliminate the sound speed limit for explicit calculations of low-speed flows, and showed that BIC-FCT could predict the three major vortex breakdown modes (spiral, bubble and double-helix). Here, we show a direct comparison of the implicit BIC and explicit FCT algorithms by using the same time step within the explicit stability limit. The comparison is conducted on simulations of a three-dimensional, swirling jet flow with vortex breakdown, by examining the flow structures and examining the property fields. Differences are observed in the phase of the downstream spiral and double-helix modes. Based on a pressure wave analysis, we attribute this phase shift to the difference of how the explicit FCT and implicit BIC treat an open outflow boundary. 

This work describes and tests the calibration process of the chemical-diffusive model (CDM) for the simulation of non-premixed diffusion flames. The CDM is an alternative, simplified approach for incorporating the effects of combustion in a fluid simulation, based on the ideas of regulating the rate of energy release such that the properties of combustion waves (e.g. flames and detonations) are reproduced. Past implementations of the CDM have considered single-stoichiometry fuel-air mixtures or mixtures with variable stoichiom- etry but with premixed modes of combustion. In this work, the CDM is tested and shown to work for non-premixed, low-Mach-number flames (i.e., diffusion flames) by incorporat- ing it into a numerical model which solves the reactive and compressible Navier-Stokes equations with the barely implicit correction (BIC) algorithm, which removes the acoustic limit on the integration time-step size. Simulations of one-dimensional premixed laminar flames reproduce the required premixed laminar flame speed, thickness, and temperature. A two-dimensional, steady-state, laminar coflow diffusion flame is computed, and the result demonstrates the ability of the algorithm to compute a non-premixed flame. Lastly, a two- dimensional simulation of two opposing jets of fuel and air show that the CDM approach can compute the structure of a counter-flow diffusion flame.