Transmission in nonuniform ducts - A comparative evaluation of finite element and weighted residuals computational schemes

The Method of Weighted Residuals (MWR) and the Finite Element Method (FEM) are considered as computational schemes in the problem of acoustic transmission in nonuniform ducts. MWR is presented in an improved form which includes the interaction of acoustic modes (irrotational) and hydrodynamic modes (rotational). FEM is based on a weighted residuals formulation using eight noded isoparametric elements. Both are applicable to two-dimensional and axially symmetric problems. Calculations are made for several sample problems to demonstrate accuracy and relative efficiency. One test case has implications in the phenomenon of subsonic acoustic choking and it is found that a large transmission loss is not an automatic consequence of propagation against a high subsonic mean flow.