Date of Award

2015

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mechanical and Aerospace Engineering

Committee Chair

Kader Frendi

Committee Member

Robert A. Frederick

Committee Member

Sivaguru S. Ravindran

Committee Member

Babak Shotorban

Committee Member

Sarma L. Rani

Subject(s)

Computational fluid dynamics., Plasma electrodynamics., Finite differences., Time-domain analysis.

Abstract

The Flowfield Dependent Variation (FDV) method is fundamentally derived from the Lax-Wendroff scheme (LWS) by replacing the explicit time derivatives in LWS with a weighted combination of explicit and implicit time derivatives. The increased implicitness and the intrinsic numerical dissipation of FDV contribute to the scheme’s numerical stability, as well as monotonicity. The von Neumann stability analysis showed that FDV is more stable and less dispersive compared to LWS. At first, a detailed investigation of spatial accuracy of the FDV scheme was conducted for grid and polynomial order convergence using the Method of Manufactured Solutions. The order-of-accuracy test, spanning both Euler and Navier-Stokes equations, showed that the observed order-of-accuracy of the scheme is nearly equal to the order of the shape function polynomial plus one, in good agreement with theory. A new formulation was developed for quantifying the FDV numerical viscosity. Using this formulation, the intrinsic numerical viscosity and dissipation rate of the FDV scheme were quantified both in physical and spectral spaces, and compared with those of the explicit subgrid-scale (SGS) models namely, the standard Smagorinsky and dynamic Smagorinsky models. Large-eddy simulations (LES) of incompressible freely decaying inviscid isotropic turbulence were performed involving the implicit LES approach using the FDV numerical dissipation and the two explicit SGS models. In the initial stages of turbulence development, all the three LES cases have similar viscosities. But, once the turbulence is fully developed, implicit LES is less dissipative compared to the two SGS LES runs. Furthermore, at a finite number of flow realizations, the numerical viscosities of FDV and of Streamline Upwind/Petrov-Galerkin (SUPG) finite element method were compared. It was observed that the SUPG method is significantly more dissipative than the three FDV-based LES approaches. Simulations involving freely decaying viscous isotropic turbulence with and without an explicit SGS model were also performed, spanning both incompressible and compressible flow regimes. Results from the dynamic Smagorinsky model-based LES runs showed good agreement with the data from the experiments and those available in the published literature. These results suggest that the FDV scheme has potential for large-eddy simulations of free-shear turbulent flows.

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