Numerical Simulation of Acoustics-Acoustics- and Structural Mechanics- Acoustics- Couplings on Nonmatching Grids

In the first period of the project, we have exploited the capability of the Mortar FEM for the acoustic wave equation and both linear and nonlinear coupled mechanical-acoustic systems. In this renewal project, we want to enhance the Mortar FEM towards complex multiphysics applications. We will focus on computational aeroacoustics and ultrasound heating. The first topic will be concentrated on more general wave equations to model ow induced sound taking into account refraction and convection effects. Furthermore, we intend to consider a multi-model approach, where we compute the generated and propagating acoustic waves by different PDEs and couple them along the interfaces within the framework of the Mortar FEM. The second topic will be dedicated to the open question, on how ambient tissue is effected by cancer treatment applying high intensity ultrasound. Therewith, we will focus on a coupled physical model for the numerical computation of the ultrasound heating process by considering the ultrasound generation mechanism of the transducer, the interaction between the acoustic and thermal fields in the tissue as well as the ow and thermal fields within blood vessels. Especially in this multiphysics setting, the Mortar FEM will be a powerful tool allowing different grids along coupling interfaces as well as different grids for PDEs being computed on the same subdomain. Both topics will have in common the necessity of using the Mortar FEM to achieve computable models, multi-time stepping techniques and efficient treatment of free radiation conditions for the acoustic waves.

In many technical applications a sensor or/and actuator is immersed in an acoustic fluid, e.g. HIFU (High Intensity Focused Ultrasound) applications as used in medical therapy, electro-dynamic loudspeakers, capacitive microphones, etc. Thereby, the numerical simulation of the sensor / actuator mechanism within the structure is quite complex, since in most cases we have to deal with a non-linear coupled problem (e.g. the electrostaticmechanical principle used in many micro-electromechanical systems), where in addition to the non-linear coupling terms each single field is non-linear (e.g. geometric nonlinearity in mechanics, moving body problem in the electrostatic field). Further on, in most cases the discretization within the structure has to be much finer than the one we need for the acoustic wave propagation in the fluid. A very similar problem arises in computational aeroacoustics, when solving the inhomogeneous wave equation according to Lighthills analogy. Therefore, the project has investigated non-matching grid techniques based on the Mortar method, which allows sub-regions to have a substantially finer computational grid than other sub-regions. First of all, we have successfully applied the Mortar Finite-Element-Method (FEM) to real engineering applications and thus could demonstrate the superiority of this method as compared to the standard FEM. To be concrete, the advantage of Mortar FEM in these applications was the distinct simplification of the meshing process, since this method can handle the coupling of subdomains, where at the interfaces the individual meshes do not match. Furthermore, the individual meshing of the involved subdomains resulted in a considerably reduction of the unknowns and thus in the computational time. Furthermore, with our applications we could demonstrate that the framework of Mortar FEM fits perfectly to the numerical handling of multi-physics computations. Within this project we have exploited the capability of Mortar FEM to high-intensity focused ultrasound (HIFU) and aeroacoustic applications. Therewith, further research to enhance this method would be towards other multi-physics phenomena (e.g., fluid-solid-interaction (FSI), mechanics-electromagnetics-coupling including moving / deforming parts, etc.), towards rotating systems (e.g., wind turbines, electrical motors, etc.).