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An Immersed Boundary Method on Cartesian Adaptive Grids for the Simulation of Compressible Flows

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Cartesian CFD Methods for Complex Applications

Part of the book series: SEMA SIMAI Springer Series ((ICIAM2019SSSS,volume 3))

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Abstract

In this article, we present an immersed boundary method (IBM) for the simulation of compressible flows encountered in aerodynamics. The immersed boundary methods allow the mesh not to conform to obstacles, whose influence is taken into account by modifying the governing equations locally (either by a source term within the equation or by imposing the flow variables or fluxes locally, similarly to a boundary condition).

A main feature of the approach we propose is that it relies on structured Cartesian grids in combination with a dedicated HPC Cartesian solver, taking advantage of not only their low memory and CPU time requirements but also the automation of the mesh generation and adaptation. Turbulent flow simulations are performed with Reynolds-Averaged Navier–Stokes equations or with Large-Eddy Simulation approach, in combination with a wall function at high Reynolds number, in order to mitigate the cell count resulting from the isotropic nature of Cartesian cells.

The objective of this paper is to demonstrate the capability of the present immersed boundary method on Cartesian adaptive grids to capture compressible flow features. Results obtained are in good agreement with classical body-fitted approaches but with a significant reduction of the time of the whole process, that is, a day for RANS simulations, including the mesh generation.

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Authors and Affiliations

  1. ONERA, Université Paris Saclay, Châtillon, France

    S. Péron, T. Renaud, C. Benoit & I. Mary

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  1. S. Péron
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  2. T. Renaud
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  3. C. Benoit
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  4. I. Mary
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Correspondence to S. Péron .

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Editors and Affiliations

  1. Department of Aeronautics & Astronautics, University of Southampton, Southampton, UK

    Ralf Deiterding

  2. Associate Laboratory of Computing and Applied Mathematics, National Institute for Space Research (INPE), São José dos Campos, Brazil

    Margarete Oliveira Domingues

  3. Institut de Mathématiques de Marseille (I2M), Aix-Marseille Université, Marseille, France

    Kai Schneider

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Péron, S., Renaud, T., Benoit, C., Mary, I. (2021). An Immersed Boundary Method on Cartesian Adaptive Grids for the Simulation of Compressible Flows. In: Deiterding, R., Domingues, M.O., Schneider, K. (eds) Cartesian CFD Methods for Complex Applications. SEMA SIMAI Springer Series(), vol 3. Springer, Cham. https://doi.org/10.1007/978-3-030-61761-5_4

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