Viscothermal acoustics can be described by the linearized Navier Stokes equations. Besides inertia and compressibility, these equations take the heat conductivity and the viscosity of the medium (air) into account. These 'viscothermal' effects are significant in, for example, miniature acoustic transducers and MEMS devices. A finite element for viscothermal acoustics, which can be used to model such devices, is presented. The particular set of equations used in the model of viscothermal acoustics leads to a complex symmetric finite element system matrix. Several different FEM discretizations are studied on a 2D thin gap problem. These discretizations are known, in the context of the Stokes equation, as the Taylor Hood quadrilateral and triangle elements, the Crouzeix Raviart element and the MINI element. All elements are implemented in the FEM software COMSOL. The elements with quadratic velocity and temperature shape functions show the best orders of convergence.
Kampinga, W. R., Wijnant, Y. H., & de Boer, A. (2010). Performance of several viscothermal acoustic finite elements. Acustica united with Acta Acustica, 96(1), 115-124. https://doi.org/10.3813/AAA.918262