Spectral element analysis of sound propagation in a muffler

Abstract

This paper presents a novel numerical method based on the least-squares spectral element formulation to analyze sound propagation in an expansion-chamber muffler with and without a mean flow. The method solves the linearized acoustic field equations derived from the full Navier–Stokes equations. Effects of the mean flow on the acoustic wave propagation in the muffler were taken into consideration. The method solves the first-order acoustic field equations in a finite number of elements which represent the chamber muffler. Within each element the method first approximates the solutions to these equations by a series of unknown coefficients with known basis functions, forms the residual of the approximation, and then minimizes the integral of the squares of the residual with respect to the unknown coefficients. The resultant system equations were discretized by the spectral element method for spatial derivatives and by the dual time stepping for the temporal derivative. Finally, the algebraic equations were solved by a Jacobin preconditioned conjugate gradient method. Numerical results were presented for pressure contours and transmission loss of sound waves propagating at various frequencies in the muffler. These results were compared with the analytical values available, and the comparison showed very good agreement.