Memory-Efficient Interpolatory Projection Techniques for the Stabilization of Incompressible Navier-Stokes Flows

Authors

  • Mahtab Uddin Institute of Natural Sciences, United International University, Dhaka-1212, Bangladesh https://orcid.org/0000-0002-6526-9276
  • M. Monir Uddin Department of Mathematics and Physics, North South University, Dhaka-1229, Bangladesh
  • Md. Abdul Hakim Khan Department of Mathematics, Bangladesh University of Engineering & Technology, Dhaka-1000, Bangladesh

DOI:

https://doi.org/10.37256/cm.5120243646

Keywords:

incompressible Navier-Stokes flow, Riccati-based optimal feedback stabilization, Krylov subspace techniques, sparsity-preserving projections scheme, eigenvalue decomposition

Abstract

In this article, we are proposing an updated form of Krylov subspace-based interpolatory projection techniques for the stabilization of incompressible Navier-Stokes flows. In the proposed techniques, we utilize the reduced-order modelling approach implicitly, where reduced-order matrices need not be gathered explicitly. To estimate the aimed optimal feedback matrix, only the factored solution of the desired continuous-time algebraic Riccati equation (CARE) needs to be stored through the classical eigenvalue decomposition. The sparse structure of the target systems will remain invariant within the matrix-vector operations for generating the bases of the projector matrices through Krylov subspace techniques, where a cohesive projection scheme will be incorporated to ensure the potency of the projector matrices. So, the proposed techniques will be feasible for memory allocation and enhance the rapid convergence of the simulation. Analysis of the target systems’ transient characteristics, such as eigenvalues and step-responses, will be used to ascertain the competence and reliability of the proposed techniques. Necessary computation will be done numerically through MATLAB. Stabilization of the transient behaviors and minimization of the simulation time are the prime concerns in this work. Eventually, by comparing with the contemporary techniques the advancement of the proposed techniques will be confirmed.

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Published

2024-03-04

How to Cite

1.
Uddin M, Uddin MM, Khan MAH. Memory-Efficient Interpolatory Projection Techniques for the Stabilization of Incompressible Navier-Stokes Flows. Contemp. Math. [Internet]. 2024 Mar. 4 [cited 2024 Oct. 14];5(1):913-29. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3646