M.Sc Thesis

M.Sc StudentRoman Reitbort
SubjectParabolic Approximations of Wave Propagation for Large-
Scale Aero- Acoustics
DepartmentDepartment of Aerospace Engineering
Supervisor Full Professors Givoli Dan
Full Thesis textFull thesis text - English Version


The goal of this work is to analyze the acoustic field propagating at long distances from an aircraft, flying above ground with given impedance and topography. In particular, due to the importance of the subject in environmental engineering, we seek the acoustic field near the ground, and its effect on human hearing. In this case, solving the acoustic problem using a standard Helmholtz solver is impractical, for various reasons that will be explained. One important issue is the irregular boundary caused by ground topography. A procedure often used in under-water acoustics, which is borrowed here for use for the large-scale aero-acoustic problem, is to approximate the Helmholtz equation by a parabolic equation justified asymptotically, and solve the latter numerically. This is known as the Parabolic Approximation (PA). The advantage of doing this is that owing to the parabolic character of the differential equation, the numerical solution can be advanced in the range direction by simple range-stepping, very similarly to the way in which time-stepping is preformed in time-dependant problems. The accuracy of the narrow-angle and wide-angle PA is investigated in the present context both theoretically and numerically. A solution scheme based on the PA is devised using the Finite Element method in the height direction and implicit range-stepping. The computational scheme is verified using some simple test problems. Numerical results for the
Sound Pressure Level (SPL) envelopes in some cases of interests (various impedance values, various topographies) are presented.