Analyzing stretched grids and introducing acoustic black hole layers as non-reflecting boundary conditions

Diploma Thesis from the year 2013 in the subject Engineering - Aerospace Technology, grade: 1,0, Technical University of Munich (Lehrstuhl für Aerodynamik und Strِmungsmechanik), course: Computational Aeroacoustics, language: English, abstract: Stretched grids as non-reflecting boundary conditions aim at gradual under-resolution and dissipation of sinusoidal waves and are computationally costly and ineffective if not implemented properly. This defines a need for insight to enable efficient implementation. Two methods of predicting the behavior of sinusoidal waves propagating through stretched grids are presented, an initial value and a boundary value approach. The initial value problem is an approximation and has the advantage that it can be applied with many higher order accurate finite difference schemes. The boundary value problem is more exact but is not applicable for higher order methods. Both methods are verified using a two-dimensional linearized Navier-Stokes solver, which is implemented in the framework of this study. Further, acoustic black hole layers are introduced as an alternative to stretched grids. Using both methods in combination reduces the number of grid points necessary in a boundary domain drastically. All methods are improved with respect to available parameters and their performance is compared using benchmark flows. Explicit recommendations for implementation are developed.