| This thesis presents the rigorous numerical analysis of the aerodynamic noise generation via Lighthill acoustic analogy, [36], which is a non-homogeneous wave equation describing the sound waves. Over more than five decades, the Lighthill analogy was extensively used as one of the major tools in engineering applications in acoustics. However, the first mathematical research of the Finite Element approximation for it is introduced here. Specifically, we focus on both Direct Numerical and Large Eddy Simulations. The more or less intuitive derivation of the Lighthill analogy is reviewed in section 1.3.;First, the semidiscrete and fully discrete Finite Element methods in DNS are presented and the effect of the computational error in the right-hand side of the wave equation is pointed out. The convergence of this error to zero is studied in the semidiscrete case. The computational results support obtained theoretical predictions.;Second, the numerical analysis, using the negative norms of the error, is presented in the semidiscrete case. The negative norms help obtain better convergence rate and require less regularity of the data than positive norms.;Third, the sound power is defined as a non-linear functional of acoustic variables and three independent ways of computing it in the semidiscrete case in DNS are presented. All of these methods are based on the Finite Element scheme presented earlier. The methods are compared from the point of view of computational cost, accuracy and simplicity. Again, the computational experiments are presented.;Finally, the concept of Large Eddy Simulation is introduced for aeroacoustic research via Lighthill analogy. Two subgrid scale models, these are van Cittert deconvolution and Bardina, are presented for the filtered acoustic analogy. The semidiscrete Finite Element Method is analyzed for both of them. We present the numerical experiments for this research as well. |
