Galerkin and Control-Volume FEMs evaluation for AcousticProblems

摘要

Two Finite Element Methods for harmonic acoustic problems are presented, one based on the Control Volume (CVFEM) and the other on a classical Galerkin approach (FEM). The CVFEM is a hybrid of the cell-centred approach which has been focused onrnin a variety of studies in many areas such as ruid mechanics, structures, thermal analysis and electromagnetism problems. Few works have dealt specifically with acoustic problems,rnthey concern issues in bounded Domains only. The formalism is the same for both CVFEM and FEM, it is based on an unstructured mesh and a weak variational formulation. Theyrndiffer in return in the definition of integration subdomains around a node and in the choice of weighting functions. In order to compare the methods for problems in bounded domain,rnthe two formulations are evaluated for eigenvalues calculation in a unit square cavity with rigid walls. At last, Boundary Infinite Elements and Mapped Wave Envelope Elements are respectively associated with CVFEM and FEM to solve acoustical radiation in unbounded domain. They are both then applied to dipole and quadrupole radiation. Numerical results are compared with analytic solutions.