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

Author

Listed:
  • Jean Charles Arthur Soloniaina

    (University of Antananarivo, Madagascar)

  • Leong Heng Dauphine Louisette Raharimina

    (University of Antananarivo, Madagascar)

  • Gilbert Rasolomampiandry

    (University of Antananarivo, Madagascar)

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.

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Handle: RePEc:epw:physic:v:8:y:2026:i:2:id:70158
DOI: 10.24018/ejphysics.2026.8.2.70158
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