Resolution of Navier-Stokes Equations with a Fractional Laplacian using the Uzawa-Conjugate Gradient Method

Jean Charles Arthur Soloniaina, Leong Heng Dauphine Louisette Raharimina and Gilbert Rasolomampiandry
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Jean Charles Arthur Soloniaina: University of Antananarivo, Madagascar
Leong Heng Dauphine Louisette Raharimina: University of Antananarivo, Madagascar
Gilbert Rasolomampiandry: University of Antananarivo, Madagascar

European Journal of Applied Physics, 2026, vol. 8, issue 2, 13-23

Abstract: The objective of this study was to solve the Navier-Stokes equations with a fractional Laplacian using the finite element method by combining the Uzawa method with the conjugate gradient method. This approach was applied to a rectangular field with an obstacle in the shape of a model car. As part of the Uzawa method, the pressure calculation was carried out using an iterative method: pk+1 = pk + α∇.uk. This approach raises the problem of optimizing the determination of the optimal value of α. For this purpose, the conjugate gradient method was used to improve the speed of convergence when calculating parameter α.

Keywords: Conjugate gradient method; finite element method; Fractional Laplacian; Navier-Stokes (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:epw:physic:v:8:y:2026:i:2:id:70158

DOI: 10.24018/ejphysics.2026.8.2.70158

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