Parallel multigrid method for solving inverse problems

Al-Mahdawi, H.K.; Sidikova, A. I.; Alkattan, Hussein; Abotaleb, Mostafa; Kadi, Ammar; El-kenawy, El-Sayed M.

doi:10.1016/j.mex.2022.101887

Cited by 9 publications

(2 citation statements)

References 22 publications

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“…It’s pretty impressive. Regarding multigrid approaches, more information is provided by Hackbush 42 , 43 . To address the fluid flow problem, which is described in the subsequent sections, we used the multigrid technique.…”

Section: Numerical Procedures and Convergence Testmentioning

confidence: 99%

Multigrid simulations of non-Newtonian fluid flow and heat transfer in a ventilated square cavity with mixed convection and baffles

Rehman,

Mahmood,

Majeed

et al. 2024

Sci Rep

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The impact of baffles on a convective heat transfer of a non-Newtonian fluid is experimentally studied within a square cavity. The non-Newtonian fluid is pumped into the cavity through the inlet and subsequently departs from the cavity via the outlet. Given the inherent non-linearity of the model, a numerical technique has been selected as the method for obtaining the outcomes. Primarily, the governing equations within the two-dimensional domain have been discretized using the finite element method. For approximating velocity and pressure, we have employed the reliable $${\mathbb{P}}_{2}$$ P 2 –$${\mathbb{P}}_{1}$$ P 1 finite element pair, while for temperature, we have opted for the quadratic basis. To enhance convergence speed and accuracy, we employ the powerful multigrid approach. This study investigates how key parameters like Richardson number (Ri), Reynolds number (Re), and baffle gap $${{\text{b}}}_{{\text{g}}}$$ b g influence heat transfer within a cavity comprising a non-Newtonian fluid. The baffle gap ($${b}_{g}$$ b g ) has been systematically altered within the range of 0.2–0.6, and for this research, three distinct power law indices have been selected namely: 0.5, 1.0, and 1.5. The primary outcomes of the investigation are illustrated through velocity profiles, streamlines, and isotherm visualizations. Furthermore, the study includes the computation of the $${Nu}_{avg}$$ Nu avg (average Nusselt number) across a range of parameter values. As the Richardson number (Ri) increases, $${Nu}_{avg}$$ Nu avg also rises, indicating that an increase in Ri results in augmented average heat transfer. Making the space between the baffles wider makes heat flow more intense. This, in turn, heats up more fluid within the cavity.

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Section: Numerical Procedures and Convergence Testmentioning

confidence: 99%

Multigrid simulations of non-Newtonian fluid flow and heat transfer in a ventilated square cavity with mixed convection and baffles

Rehman,

Mahmood,

Majeed

et al. 2024

Sci Rep

View full text Add to dashboard Cite

show abstract

“…The multigrid method has been a dynamic approach for solving forward problems of partial differential equations [22][23][24][25]. More recently, this method has been utilized to address inverse problems in various fields such as heat transfer [26,27], optical imaging [28][29][30][31], biomedical science [32][33][34], fluids in porous media [35], and economics [36,37].…”

Section: Introductionmentioning

confidence: 99%

Combination of Multigrid with Constraint Data for Inverse Problem of Nonlinear Diffusion Equation

Liu

Ouyang

Guo³

et al. 2023

Mathematics

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This paper delves into a rapid and accurate numerical solution for the inverse problem of the nonlinear diffusion equation in the context of multiphase porous media flow. For the realization of this, the combination of the multigrid method with constraint data is utilized and investigated. Additionally, to address the ill-posedness of the inverse problem, the Tikhonov regularization is incorporated. Numerical results demonstrate the computational performance of this method. The proposed combination strategy displays remarkable capabilities in reducing noise, avoiding local minima, and accelerating convergence. Moreover, this combination method performs better than any one method used alone.

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Enhanced heat transfer in vented square enclosures with block structures: Exploring iso-perimetric shapes and multigrid approach for mixed convection of nano-fluids

Rehman,

Mahmood,

Majeed

et al. 2024

Case Studies in Thermal Engineering

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Parallel multigrid method for solving inverse problems

Cited by 9 publications

References 22 publications

Multigrid simulations of non-Newtonian fluid flow and heat transfer in a ventilated square cavity with mixed convection and baffles

Multigrid simulations of non-Newtonian fluid flow and heat transfer in a ventilated square cavity with mixed convection and baffles

Combination of Multigrid with Constraint Data for Inverse Problem of Nonlinear Diffusion Equation

Enhanced heat transfer in vented square enclosures with block structures: Exploring iso-perimetric shapes and multigrid approach for mixed convection of nano-fluids

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