10. A Higher-Order Cut-Cell Methodology for Large Eddy Simulation of Compressible Viscous Flow Problems with Embedded Boundaries

We have developed a finite volume-based conservative cut-cell method that is up to third-order accurate for simulation of compressible viscous flow problems. A sharp representation of the embedded boundaries, described using a signed distance function, is facilitated by use of block-structured adaptive mesh refinement. A high-order reconstruction is performed by using a cell-centered piecewise polynomial approximation of flow quantities. To ensure the stability of the scheme in the presence of very low volume cut-cells, a novel cell clustering approach that preserves the design order of accuracy even locally has been developed. It is shown through numerical examples that using the proposed approach, smooth representation of flow-field quantities and their derivatives can be achieved on embedded boundaries. Smooth reconstruction of wall shear stress and a high-order accuracy makes this approach a good candidate for large eddy simulation (LES). A multi-level extension of the one-equation kinetic subgrid energy-based closure to perform LES with local refinement and embedded boundaries is presented. Results are shown for various canonical cases to demonstrate the accuracy of the approach.