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Model reduction

Accurate simulations, especially in the case of models involving strong coupling between multiple physical fields, require complex numerical models that reveal to be costly in terms of computation time.

The principle of model reduction methods consists in processing these numerical models to extract educed models that involve very few variables but remain representative of the initial model behaviours of interest.

The reduced models can be simulated using dedicated softwares, such as OOFELIE in MS Excel, developed by Open Engineering, or they can also be included in more complex finites element model as sub-structures.

The first step consists in the creation of the model to reduce. It corresponds usually to a standard finite element model that includes a mesh, the definition of the type and properties of finite elements, boundary conditions and loads. Reduction does not involve any particular requirement. Nevertheless, the model must be consistent, that means well defined, and the physical behaviour it addresses must match the scope of the available reduction algorithms.

The addition, the user selects “retained” degrees of freedom (DOF), which means that the DOF of interest in terms of which the model will be reduced. These DOF are usually the DOF that characterize the behaviour of the system and the DOF that are used to connect it with its environment. According to the algorithms used to reduce the model, the user can also select additional variables to match his requirements in terms of reduced model accuracy. The application of the reduction algorithms implemented in OOFELIE generates a model of superelement. This is data structure that describes the reduced model topology and its internal definition in terms of DOF and equations governing its behaviour.

ReductionOrganigram-2

The models of superelement are used to generate one or multiple superelements in a generic finite element model. Indeed, a superelement can be simulated independently or multiple superelements can be combined together if each of them corresponds to a substructure. The generation of a superelement is called “instantiation”. The simulations of superelements can be performed in OOFELIE or in MS Excel thanks to the interface that has been developed. Finally, the results computed using reduced models can be expanded to the initial model used to generate the superelement model. This last step is called “backward restitution”. This operation allows the visualisation of the complete physical fields on the initial geometry. This can be particularly interesting as reduced model results involve only global variables.