A Cartesian Cut-Cell Solver for Compressible Flows

DOI: 10.1007/978-3-642-17770-5_27


A Cartesian cut-cell solver is presented to simulate two- and three-dimensional viscous, compressible flows on arbitrarily
refined graded meshes. The finite-volume method uses cut cells at the boundaries rendering the method strictly conservative
and is flexible in terms of shape and size of embedded boundaries. A linear least-squares method is used to reconstruct the
cell center gradients in irregular regions of the mesh such that the surface flux can be formulated. The accuracy of the method
is demonstrated for the three-dimensional laminar flow past a sphere.

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Available from: Matthias Meinke, Aug 19, 2014
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    ABSTRACT: We propose a novel high resolution conservative advection scheme that is suitable for thin, embedded moving solid structures. The scheme works by coupling together a high order flux-based method with a conservative semi-Lagrangian solver that is similar in spirit to that of Lentine et al. [26], but modified to treat the cut cells and partial volumes that arise near a thin solid structure. The conservative semi-Lagrangian scheme is unconditionally stable, and so unlike previous methods no cell merging is required to compensate for the small cell volumes that arise. Furthermore, as the semi-Lagrangian scheme works via tracing characteristic curves, no special treatment is required either to enforce non-penetration through thin, moving solid structures, or to populate swept or uncovered degrees of freedom. For the flux-based solver, we use finite-difference ENO with Lax–Friedrich’s diffusion (although any flux-based scheme works), and in doing so we found that a modification to the diffusion calculation leads to improved stability in its third order accurate variant. We integrate this novel hybrid advection scheme into a semi-implicit compressible flow solver, and modify the implicit pressure solver to work with cells of variable size. In addition, we propose an improvement to the semi-implicit compressible flow solver via a new method for computing a post-advected pressure. Finally, this hybrid conservative advection scheme is integrated into a semi-implicit fluid–structure solver, and a number of one-dimensional and two-dimensional examples are considered—in particular, showing that we can handle thin solid structures moving through the grid in a fully conservative manner, preventing fluid from leaking from one side of the structure to the other and without the need for cell merging or other special treatment of cut cells and partial volumes.
    Journal of Computational Physics 07/2013; 245:160–204. DOI:10.1016/ · 2.43 Impact Factor