Fast and Stable Transient Methods for Unbounded Vibro-Acoustic Problems of Industrial Complexity

The main goal of the project is to derive a stable, transient vibro-acoustic finite element/infinite element reduced order model that can handle models of industrial complexity and can be integrated into a vendor-independent functional mockup interface (FMI) for multiphysical system level modelling. Concrete objectives and criteria To achieve the main goal, the following concrete objectives are defined: 1. Investigation and improvement of time stable model order reduction techniques for vibro-acoustic models with finite and infinite elements In recent work stable Krylov based model order reduction schemes for vibro-acoustic systems built from a combination of finite and infinite elements have been derived and shown on small to medium scale examples [7]. The first objective is to find out how well these techniques scale to problems of industrial complexity that have millions of degrees of freedom. The numerical complexity of the involved algorithms will be assessed, efficiency and stability of the time integrators and reduction methods will be improved. 2. The development and assessment of high order and adaptive finite element + infinite elements for stable time domain model order reduction In previous research it has been shown that the calculation effort of acoustic finite elements can be reduced significantly in the frequency domain by using larger elements with high order shape functions [8]. These elements also lead to lower dispersion errors at higher frequencies. One of the objectives will be to use such high order elements and adaptivity in the context of time domain Reduced Order Models (ROMs) and assess its efficiency and accuracy as compared to conventional low order FEM for broadband transient excitations and several time marching schemes. 3. Incorporating advanced damping models to ROMs The proper inclusion of damping in time domain ROMs is needed in order to tackle an extended range of realistic industrial problems. Such damping can be present in both the structural and the acoustic part of the model. The focus will be on finding a generic method that starts from a damped frequency domain model and investigates multiple ways to convert such a model to the time domain and to reduce it in size with the model reduction techniques used in the first objective. Foreseen approaches are state augmentation, e.g. through the auxiliary differential equation method [9] or the approximate modeling of parallel frequency independent models by using filter banks [10]. 4. The demonstration of the newly developed methods for system level modelling and multi-physical co-simulation The final objective is to combine all the newly developed methodologies and demonstrate the added value in the context of multiphysical co-simulation and system level modelling, in particular, how they will enable a wide range of new applications. Virtual Sensing of damped unbounded vibro-acoustic systems, co-simulation for gear noise are among the examples. To achieve this, the reduced order model of the (coupled) vibro-acoustic system will be transformed to a state space format and abstracted into a functional mockup unit (FMU), thus allowing for coupling with other FMUs for the coupled multi-physics simulations.