This study presents an improved ghost-cell immersed boundary approach to represent a solid body in compressible flow simulations. In contrast to the commonly used approaches, in the present work ghost cells are mirrored through the boundary described using a level-set method to farther image points, incorporating a higher-order extra/interpolation scheme for the ghost cell values. In addition, a shock sensor is in- troduced to deal with image points near the discontinuities in the flow field. Adaptive mesh refinement (AMR) is used to improve the representation of the geometry efficiently. The improved ghost-cell method is validated against five test cases: (a) double Mach reflections on a ramp, (b) supersonic flows in a wind tunnel with a forward- facing step, (c) supersonic flows over a circular cylinder, (d) smooth Prandtl-Meyer expansion flows, and (e) steady shock-induced combustion over a wedge. It is demonstrated that the improved ghost-cell method can reach the accuracy of second order in L1 norm and higher than first order in L∞ norm. Direct comparisons against the cut-cell method demonstrate that the improved ghost-cell method is almost equally accurate with better efficiency for boundary representation in high-fidelity compressible flow simulations. Implementation of the improved ghost-cell method in reacting Euler flows further validates its general applicability for compressible flow simulations.

The presented dissertation thesis deals with a simulation of the human phonation in terms of latest theories. Phonation is considered here as a bi-directional fluid-structure-acoustic interaction, where the interaction between all three physical domains occurs due to the unsteady viscous compressible Navier-Stokes equations. There is a solid knowledge background in the first part of the thesis. It concerns the latest concepts in computational modeling of the human phonation, the most important and recent theories about the human voice production and some key aspects of the human anatomy, physiology and pathology. Also voice assessment is discussed. The second part of the thesis describes an in-depth analysis of a phonation simulation in a planar computational model. The basic concepts proceed from algorithms developed in the Institute of Solid Mechanics, Mechatronics and Biomechanics. Created models are able to reproduce sounds of all Czech vowels and the most common evaluated parameters very close to physiological ranges. The simulated pathology, Reinke's edema, is demonstrated in order to explore its influence on the vowel sound. The third part focuses on modeling of phonation in a spatial computational model. All Czech vowels are simulated also here and compared to the planar model and to actual measurement. The spatial model serves as the starting point to modeling of a longitudinal pretension incorporated in the vocal folds. In the last part of the thesis, a modeling of the phonation with vocal folds pretension is investigated. Although the models are tuned to a rather soft phonation, the results are in agreement with the relevant physiologic phenomena. While the spatial model is highly computationally expensive, a hybrid planar model with pretension is proposed. A special attention is paid to the analysis of self-sustained oscillation of the vocal folds. It is shown, the planar model cannot reproduce such kind of oscillation in the actual version, albeit time of oscillation was considerably extended. On the other hand, oscillation of the spatial vocal folds are stabilized without effects accompanying subduing of oscillation. It can be supposed that the spatial model is able to reproduce self-sustained oscillation as a basic principle present during the human phonation.