| In the first part of this dissertation, the scalar filtered mass density function (SFMDF) methodology is implemented into the computer code US3D. The SFMDF is a sub-grid scale closure and is simulated via a Lagrangian Monte Carlo solver. US3D is an Eulerian finite volume code and has proven very effective for compressible flow simulations. The resulting SFMDF-US3D code is employed for large eddy simulation (LES) of compressible turbulent flows on unstructured meshes. Simulations are conducted of subsonic and supersonic flows. The consistency and accuracy of the simulated results are assessed along with appraisal of the overall performance of the methodology.;In the second part of this dissertation, a new methodology is developed for accurate capturing of discontinuities in multi-block finite difference simulations of hyperbolic partial differential equations. The fourth-order energy-stable weighted essentially non-oscillatory (ESWENO) scheme on closed domains is combined with simultaneous approximation term (SAT) weak interface and boundary conditions. The capability of the methodology is demonstrated for accurate simulations in the presence of significant and abrupt changes in grid resolution between neighboring subdomains. Results are presented for the solutions of linear scalar hyperbolic wave equations and the Euler equations in one and two dimensions. Strong discontinuities are passed across subdomain interfaces without significant distortions. It is demonstrated that the methodology provides stable and accurate solutions even when large differences in the grid-spacing exist, whereas strong imposition of the interface conditions causes noticeable oscillations.;Keywords: Large eddy simulation, filtered density function, turbulent reacting flows, multi-block finite difference schemes, high-order numerical methods, WENO shock-capturing, computational fluid dynamics. |
