Anisotropic adaptivity of the p-FEM for time-harmonic acoustic wave propagation

Abstract

This paper deals with the a-priori assignment of polynomial order in the p-version of the FEM for the efficient simulation of time-harmonic acoustics problems. Anisotropic p-refinement, allowing direction-dependent polynomial approximations is examined, including for unstructured meshes with curved elements. A methodology to automatically choose the order repartition in the model is proposed and verified. These features are important for two main reasons. First, they allow to better control the accuracy on distorted elements with large aspect ratios. This in turn makes the numerical model less sensitive to the quality of the finite element mesh. Secondly, this allows to deal efficiently with problems where the wave properties are anisotropic. The restriction on the numerical resolution can be relaxed to obtain significant reductions in the computational cost compared to classical, isotropic order adaptivity. The paper presents several examples of the efficiency and robustness of the method for the propagation of acoustic waves on distorted meshes and/or in the presence of strong background mean flows.