Mathematics

Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of model order reduction techniques in various engineering and scientific applications including but not limited to mechanical, naval and aeronautical engineering. The focus here is kept limited to computational fluid mechanics and related applications. The advances in the reduced order modeling with proper orthogonal decomposition and reduced basis method are presented as well as a brief discussion of dynamic mode decomposition and also some present advances in the parameter space reduction. Here, an overview of the challenges faced and possible solutions are presented with examples from various problems.