Hybrid numerical and analytical solutions for acoustic boundary problems in thermo-viscous fluids

The present work aims at contributing to the investigation of methods to solve some classes of problems of acoustic propagation in thermo-viscous fluids, in unbounded or bounded media. The focus here is on thermal and vortical diffusion at the boundaries, which have to be considered for an accurate description of the acoustic field in small fluid-filled cavities and ducts. Existing boundary element or finite element acoustic software does not include these phenomena, as they are not compatible with the basic equations involved. A methodology is given to solve such problems when using this software, introducing a hybrid method which combines both numerical solutions and analytical solutions (for the fields inside the boundary layers). A detailed application is presented to validate the process using a boundary elements method.