Evaluation of Interpolation Scheme Alternatives and Variation of the Number of Slave Cells in a Cut-Cell Methodology

Luis Henríquez-Vargas, Francisco Angel, Lawrence Lackey and Pablo Donoso-García
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Luis Henríquez-Vargas: Departamento de Ingeniería Química, Universidad de Santiago de Chile, Santiago 9170022, Chile
Francisco Angel: Departamento de Ingeniería Química, Universidad de Santiago de Chile, Santiago 9170022, Chile
Lawrence Lackey: Departamento de Ingeniería Química, Universidad de Santiago de Chile, Santiago 9170022, Chile
Pablo Donoso-García: Departamento de Ingeniería Química, Universidad de Santiago de Chile, Santiago 9170022, Chile

Mathematics, 2022, vol. 10, issue 6, 1-30

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.

Keywords: interpolation scheme; cut cell; immersed solid; Navier–Stokes; numerical solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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