An efficient extended block Arnoldi algorithm for feedback stabilization of incompressible Navier-Stokes flow problems - Archive ouverte HAL Access content directly
Journal Articles Applied Numerical Mathematics Year : 2022

An efficient extended block Arnoldi algorithm for feedback stabilization of incompressible Navier-Stokes flow problems

M.A. Hamadi
  • Function : Author
A. Ratnani
  • Function : Author

Abstract

Navier-Stokes equations are well known in modeling of an incompressible Newtonian fluid, such as air or water. This system of equations is very complex due to the non-linearity term that characterizes it. After the linearization and the discretization parts, we get a descriptor system of index-2 described by a set of differential algebraic equations (DAEs). The two main parts we develop through this paper are focused firstly on constructing an efficient algorithm based on a projection technique onto an extended block Krylov subspace, that appropriately allows us to construct a reduced system of the original DAE system. Secondly, we solve a Linear Quadratic Regulator (LQR) problem based on a Riccati feedback approach. This approach uses numerical solutions of large-scale algebraic Riccati equations. To this end, we use the extended Krylov subspace method that allows us to project the initial large matrix problem onto a low order one that is solved by some direct methods. These numerical solutions are used to obtain a feedback matrix that will be used to stabilize the original system. We conclude by providing some numerical results to confirm the performance of our proposed method compared to other known methods.

Dates and versions

hal-04413486 , version 1 (23-01-2024)

Identifiers

Cite

M.A. Hamadi, A. Ratnani, Khalide Jbilou. An efficient extended block Arnoldi algorithm for feedback stabilization of incompressible Navier-Stokes flow problems. Applied Numerical Mathematics, 2022, 174, pp.142-162. ⟨10.1016/j.apnum.2022.01.011⟩. ⟨hal-04413486⟩
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