11. Model Reduction for Large-Scale Applications in Computational Fluid Dynamics

Abstract

Recent years have seen considerable progress in solution and optimization methods for partial differential equations (PDEs), leading to advances across a broad range of engineering applications. Improvements in methodology, together with a substantial increase in computing power, are such that real-time simulation and optimization of systems governed by PDEs is now an attainable goal; however, a number of challenges remains for applications such as real-time control of dynamic processes. In many cases, computational models for such applications yield very large systems that are computationally intensive to solve. A critical element towards achieving a real-time simulation capability is the development of accurate, efficient models that can be solved sufficiently rapidly to permit control decisions in real time. Model reduction is a powerful tool that allows the systematic generation of cost-efficient representations of large-scale systems resulting from discretization of PDEs. Reduction methodology has been developed and applied for many different disciplines, including controls, fluid dynamics, structural dynamics, and circuit design. Considerable advances in the field of model reduction for large-scale systems have been made and many different applications have been demonstrated with success; however, a number of open issues remain, including the reliability of reduction techniques, guarantees associated with the quality of the reduced models, and validity of the model over a range of operating conditions. The cost of performing the reduction may also be an issue if there is a need to adapt the reduced-order model