This thesis presents the rigorous numerical analysis of the aerodynamic noise generation viaLighthill acoustic analogy, which is a non-homogeneous wave equation describing thesound waves. Over more than five decades, the Lighthill analogy was extensively used as oneof the major tools in engineering applications in acoustics. However, the first mathematicalresearch of the Finite Element approximation for it is introduced here. Specifically, we focuson both Direct Numerical and Large Eddy Simulations. The more or less intuitive derivationof the Lighthill analogy is reviewed in section 1.3.First, the semidiscrete and fully discrete Finite Element methods in DNS are presentedand the effect of the computational error in the right-hand side of the wave equation ispointed out. The convergence of this error to zero is studied in the semidiscrete case. Thecomputational results support obtained theoretical predictions.Second, the numerical analysis, using the negative norms of the error, is presented in thesemidiscrete case. The negative norms help obtain better convergence rate and require lessregularity of the data than positive norms.Third, the sound power is defined as a non-linear functional of acoustic variables andthree independent ways of computing it in the semidiscrete case in DNS are presented. Allof these methods are based on the Finite Element scheme presented earlier. The methodsare 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 researchvia Lighthill analogy. Two subgrid scale models, these are van Cittert deconvolution andBardina, are presented for the filtered acoustic analogy. The semidiscrete Finite ElemetMethod is analyzed for both of them. We present the numerical experiments for this researchas well.
展开▼
