Numerical analysis of the semidiscrete Finite Element Method for computing the noise generated by turbulent flows

This paper studies the convergence of the Finite Element Method for predicting the noise generated by turbulent flows through the Lighthill model. The model’s derivation is given in an intuitive and physical manner. The model gives a non-homogeneous wave equation for the acoustic pressure where the right-hand side depends on the divergence of the nonlinear term of the NSE and external force. The stability, accuracy, convergence and implementation of the semidiscrete FEM scheme for a problem based on this model is studied. The rate of convergence depends on the FEM discretization for the wave equation and the L2(0,T;L2(Ω))L2(0,T;L2(Ω))-error of the flow variables acting as the acoustic source. We also present numerical results that confirm our theoretical predictions.