A second-order pressure-accurate finite-difference scheme for the Stokes problem with rigid non-conforming boundaries

Abdelkader Hammouti; Anaël Lemaître

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arXiv · 1110.1311

A second-order pressure-accurate finite-difference scheme for the Stokes problem with rigid non-conforming boundaries

Abdelkader Hammouti·Anaël Lemaître

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Abstract

We present a finite-difference scheme which solves the Stokes problem in the presence of curvilinear non-conforming interfaces and provides second-order accuracy on physical field (velocity, vorticity) and especially on pressure. The gist of our method is to rely on the Helmholtz decomposition of the Stokes equation: the pressure problem is then written in an integral form devoid of the spurious sources known to be the cause of numerical boundary layer error in most implementations, leading to a discretization which guarantees a strict enforcement of mass conservation. The ghost method is furthermore used to implement the boundary values of pressure and vorticity near curved interfaces.

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Abdelkader Hammouti, Anaël Lemaître. 2011-10-06. A second-order pressure-accurate finite-difference scheme for the Stokes problem with rigid non-conforming boundaries. https://arxiv.org/abs/1110.1311

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