Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical and Aerospace Engineering

Committee Chair

Sarma Rani

Committee Member

Kader Frendi

Committee Member

Sivaguru Ravindran

Committee Member

Shankar Mahalingam

Committee Member

Robert Frederick


Turbulence--Mathematical models., Eddies--Mathematical models.


In recent times, the limitations of popular subgrid-scale models for Large-Eddy Simulation have led to the development of a number of sophisticated modeling approaches. An approach that utilizes the numerical viscosity arising from the non-linear discretization of convective fluxes to model the smaller more isotropic eddies has received considerable attention. This method is referred to as Implicit Large-Eddy Simulation (ILES). The goal of this dissertation is to advance current understanding of a class of ILES techniques based on shock-capturing schemes. This is achieved through intricate quantitative insights into the stability and diffusive characteristics of Roe-MUSCL-based shock-capturing scheme. The first step towards achieving the goal involved developing a formulation to quantify the numerical viscosity of the Roe-MUSCL scheme for the case of non-linear advection equation. The expression derived is a function of the flux limiter employed, distance between cell centers on either side of a face, face-normal velocity and a scaling factor. The significance of the scaling factor is revealed when the Roe-MUSCL scheme, originally developed for 1-D scenarios, is applied to 2-D scalar advection problems. It is seen that without the scaling factor, the MUSCL scheme may not necessarily be monotonic in multi-dimensional scenarios. In the next step, Roe's original shock-capturing scheme developed for 1-D Euler equations is extended to three dimensions in a manner that is consistent with the finite volume framework. After extending the scheme to second-order using van Leer's MUSCL extrapolation technique, an expression for numerical viscosity is derived following the procedure outlined for the advection equation case. To minimize the excessive dissipation of Roe-MUSCL for turbulent flows, the high numerical viscosity is mitigated using a z-factor that depends on the local Mach number. In order to demonstrate the performance of Roe-MUSCL in capturing the physics of turbulent flows, a detailed investigation is conducted for decaying homogeneous isotropic turbulence with varying degrees of compressibility. The spectral profiles of numerical viscosity and dissipation rate demonstrate the effectiveness of the z-factor both in narrowing the wavenumber range in which dissipation occurs, and in shifting the location of the dissipation peak closer to the cut-off wavenumber. A number of statistical parameters for mesh resolution greater than 32^3 showed good agreement with prior direct numerical simulation and experimental studies. In the final step, Roe-MUSCL together with three Runge-Kutta temporal schemes is investigated for the Taylor-Green vortex transitional flow problem. The spectral profiles of numerical dissipation rate show that the Runge-Kutta scheme of Shu-Osher is the most stable and together with Roe-MUSCL accurately captures the physics of vortex stretching and subsequent production of dissipative eddies.



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