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Pré-Publication, Document De Travail Année : 2021

A conservative finite volume cut-cell method on an adaptive Cartesian tree grid for moving rigid bodies in incompressible flows

Résumé

We present here a conservative finite volume cut-cell method for moving rigid bodies immersed in incompressible flows, implemented in the open-source software Basilisk. The method is constructed starting from a uniform Cartesian grid, in which we embed a discrete representation of a rigid body that intersects underlying cells to form irregular fluid control volumes, or cut-cells. In each cell, we then discretize the Navier-Stokes equations using a fractional-step projection method and insure that at each time step, the finite volume discretization scheme remains spatially second-order and conservative in cut-cells by carefully computing gradients normal to the embedded boundaries, even in degenerated cases. To avoid stability issues due to the well-documented problem of small cut-cells, we use a simple and efficient flux redistribution technique to extend the range of influence of small cut-cells to their neighboring cells. We also provide a time history to emerged cells through a field value reconstruction in the direction normal to the embedded boundaries. In case of freely moving particles, we simply use an explicit weak fluid-solid coupling strategy. Finally, we robustly extend our conservative finite volume cut-cell method for moving boundaries to adaptive Cartesian tree grids by constructing specific restriction and prolongation operators between two consecutive levels of a tree grid in the vicinity of a cut-cell. We successfully test the method on a series of validation test cases ranging from fixed, moving with a prescribed motion to freely moving 2D cylinders and spheres for a wide range of Reynolds (0 ≤ Re ≤ 1000) and Galileo numbers (0 ≤ Ga ≤ 250). While the method is accurate, conservative, robust and efficient, we show that a low-amplitude pressure noise is generated when using mesh adaptation in the limit case of very high Reynolds numbers.
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Dates et versions

hal-03948786 , version 1 (20-01-2023)

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  • HAL Id : hal-03948786 , version 1

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Arthur R. Ghigo, Stéphane Popinet, Anthony Wachs. A conservative finite volume cut-cell method on an adaptive Cartesian tree grid for moving rigid bodies in incompressible flows. 2021. ⟨hal-03948786⟩
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