Abstract
The present work determines numerical solutions applied to flow problems in a cut-cell framework, introducing and evaluating two interpolation alternatives for the treatment of the convective terms and the effect of the variation of the number of slave cells generated near the solid interfaces. Using the upwind, QUICK and WAHYD (TVD) schemes, three benchmark cases were studied in the laminar regime, namely, flow between concentric cylindrical walls, flow in an inclined channel and flow around a cylinder. The numerical results obtained were favorable for the proposed interpolation methodology that prevents velocity over/under-estimations on the finite control volume faces, observing a tendency to produce smaller errors and mid-to-high computational efficiencies when coupled with a smaller number of slave cells generated at the boundaries. Although the magnitude of the errors found were small, improvements are of more significance for quantities that depend on gradient estimations at surfaces.
Highlights
IntroductionWithin the framework of CFD, the use of structured grids to represent complex geometries is a convenient approach to overcome computational accuracy problems and complex grid-generation processes presented in unstructured and/or boundary-conforming grids [1–3]
The number of slave cells generated increases with the κ value resulting in an apparent enlargement of the solid body dimensions accompanied by an erosion of the smoothness of its interfacial surface
This interpretation is bounded to the treatment given to the generated slave cells but, a higher number of slave cells around the body representation are likely to introduce more errors to the numerical solution
Summary
Within the framework of CFD, the use of structured grids to represent complex geometries is a convenient approach to overcome computational accuracy problems and complex grid-generation processes presented in unstructured and/or boundary-conforming grids [1–3]. Berger et al [4] cite among the strengths of Cartesian embedded-boundary grid schemes their accuracy, rapid turnaround time and level of automation. The lowest order method is the Voxel method, in which the boundary is represented in a staircase fashion [3]. Higher order methods comprise the immersed boundary and cut-cell methods, among others. In the former, the influence of solid boundaries is modeled by the introduction of additional terms and/or velocity interpolations to force the no-slip internal boundary condition. For a discussion on the classification of immersed boundary methods, the reader is referred to Mittal [1]
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