A high-order stabilized finite-element model for the Linearized Navier-Stokes equations

A numerical approach based on high-order stabilized finite elements is proposed to solve thermo-acoustic and visco-acoustic problems accounting for non-uniform mean flow effects. The the Linearized Navier-Stokes equations written in conservative form frequency domain. An adaptive polynomial Finite-Element Method (FEM) using hierarchic shape functions applied accuracy ease-of-use. new enrichment strategy, inspired by extended Finite Element (X-FEM), developed resolve finer scales near walls at a reasonable computational cost. It relies re-orthogonalization procedure preserve both continuity of solution conditioning properties discrete model. performance method first evaluated performing two-dimensional simulations acoustic waves affected visco-thermal wall losses effects while propagating duct. Numerical results are good agreement with analytical solution. applicability this methodology then demonstrated computing sound absorption an liner installed impedance tube presence grazing 2D. predictions pressure levels compared experimental data from literature.