The method of fundamental solutions for Brinkman flows. Part II. Interior domains

Karageorghis, Andréas; Lesnic, D.; Marin, Liviu

doi:10.1007/s10665-020-10083-2

Cited by 6 publications

(3 citation statements)

References 33 publications

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“…We usually take the number of terms J in the expansion (12) small, e.g., J = 0 or 1, such that the number of unknowns in the vector Θ is 3 or 5, respectively. Since the number of unknowns is small, common practice [20] suggests that this model reduction assists in aleviating the instability of the inverse problem with respect to errors in the measured data (11), and therefore no regularization is usually needed to penalize the least-squares functional (13). The mesh size is m = 20 for the solution of the direct problem that is employed first to numerically simulate the fluid traction data (11) necessary for solving the inverse problem.…”

Section: Parameter Selectionmentioning

confidence: 99%

“…In such a situation, inverse modeling offers a valuable approach to overcome these challenges by utilizing observed effects or indirect measurements to infer the properties, shapes, sizes and locations of submerged obstacles. There are several papers about the identification of obstacles immersed in some different types of fluids such as, potential [5], Stokes [18,3,2], Oseen [15,11], Brinkman [12,13] or Navier-Stokes [1,7]. The studies in [1,7] were mainly theoretical and they dealt with the simpler Dirichlet boundary conditions for which the existence and uniqueness of solution theory is available [23].…”

Section: Introductionmentioning

confidence: 99%

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The identification of obstacles immersed in a steady incompressible viscous fluid

Yuksel,

Lesnic

2024

J Eng Math

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In this paper, the identification of immersed obstacles in a steady incompressible Navier-Stokes viscous fluid flow from fluid traction measurements is investigated. The solution of the direct problem is computed using the finite element method (FEM) implemented in the Freefem++ commercial software package. The solution of the inverse geometric obstacle problem (parameterized by a small set of unknown constants) is accomplished iteratively by minimizing the nonlinear least-squares functional using an adaptive moment estimation algorithm. The numerical results for the identification of an obstacle in a viscous fluid flowing in a channel with open ends, show that when the fluid traction is measured on the top, bottom and inlet boundaries, then the algorithm provides accurate and robust reconstructions of an obstacle parameterized by a small number of parameters in a Fourier trigonometric finite expansion. Stable reconstructions with respect to noise in the measured fluid traction data are also achieved, although for complicated shapes parameterized by larger degrees of freedom nonlinear Tikhonov regularization of the least-squares functional may need to be employed. Multiple-component obstacles may also be identified provided that a good initial guess is provided. In case of limited data being available only at the inlet boundary the pressure gradient provides more information for inversion than the fluid traction.

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Section: Parameter Selectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The identification of obstacles immersed in a steady incompressible viscous fluid

Yuksel,

Lesnic

2024

J Eng Math

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“…Since data describing the direct problem are not available, a direct numerical solver should be called repeatedly in an iterative process to obtain or reconstruct the real state. Karageorghis et al [19,20] solved the inverse problem with respect to Brinkman fluid flows, including obstacles of unknown shapes for the exterior and interior problems. In their papers, they also proved the stability and accuracy of their proposed numerical technique by numerical examples.…”

Section: Introductionmentioning

confidence: 99%

Some Inverse Problems of Two-Dimensional Stokes Flows by the Method of Fundamental Solutions and Kalman Filter

Shao,

Jiang

2023

Mathematics

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Some inverse problems of Stokes flow, including noisy boundary conditions, unknown angular velocity, and dynamic viscous constant identification are studied in this paper. The interpolation equations for those inverse problems are constructed using the method of fundamental solutions (MFS). Based on the noise addition technique, the inverse problems are solved using MFS and a Kalman filter. It is seen from numerical experiments that these approaches and algorithms are valid and have strong robustness and high accuracy in solving inverse Stokes problems.

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Fading regularization method for the stationary Stokes data assimilation problem

Zayeni,

Abda,

Delvare

2025

Computer Methods in Applied Mechanics and Engineering

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The method of fundamental solutions for Brinkman flows. Part II. Interior domains

Abstract: This is a repository copy of The method of fundamental solutions for Brinkman Flows. Part II. Interior domains..

Cited by 6 publications

References 33 publications

The identification of obstacles immersed in a steady incompressible viscous fluid

The identification of obstacles immersed in a steady incompressible viscous fluid

Some Inverse Problems of Two-Dimensional Stokes Flows by the Method of Fundamental Solutions and Kalman Filter

Fading regularization method for the stationary Stokes data assimilation problem

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