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A discontinuous Galerkin immersed boundary solver for compressible flows: Adaptive local time stepping for artificial viscosity based shock‐capturing on cut cells

Geisenhofer, Markus and Kummer, Florian and Müller, Björn (2019):
A discontinuous Galerkin immersed boundary solver for compressible flows: Adaptive local time stepping for artificial viscosity based shock‐capturing on cut cells.
In: International Journal for Numerical Methods in Fluids, Wiley-Blackwell, pp. 448-472, 91, ISSN 0271-2091,
DOI: 10.1002/fld.4761,
[Online-Edition: https://doi.org/10.1002/fld.4761],
[Article]

Abstract

We present a higher order cut cell immersed boundary method (IBM) for the simulation of high Mach number flows. As a novelty on a cut cell grid, we evaluate an adaptive local time stepping (LTS) scheme in combination with an artificial viscosity based shock‐capturing approach. The cut cell grid is optimized by a non‐intrusive cell‐agglomeration strategy in order to avoid problems with small or ill‐shaped cut cells. Our approach is based on a discontinuous Galerkin discretization of the compressible Euler equations, where the immersed boundary is implicitly defined by the zero iso‐contour of a level set function. In flow configurations with high Mach numbers, a numerical shock‐capturing mechanism is crucial in order to prevent unphysical oscillations of the polynomial approximation in the vicinity of shocks. We achieve this by means of a viscous smoothing where the artificial viscosity follows from a modal decay sensor that has been adapted to the IBM. The problem of the severe time step restriction caused by the additional second order diffusive term and small non‐agglomerated cut cells is addressed by using an adaptive LTS algorithm. The robustness, stability, and accuracy of our approach is verified for several common test cases. Moreover, the results show that our approach lowers the computational costs drastically, especially for unsteady IBM problems with complex geometries.

Item Type: Article
Erschienen: 2019
Creators: Geisenhofer, Markus and Kummer, Florian and Müller, Björn
Title: A discontinuous Galerkin immersed boundary solver for compressible flows: Adaptive local time stepping for artificial viscosity based shock‐capturing on cut cells
Language: English
Abstract:

We present a higher order cut cell immersed boundary method (IBM) for the simulation of high Mach number flows. As a novelty on a cut cell grid, we evaluate an adaptive local time stepping (LTS) scheme in combination with an artificial viscosity based shock‐capturing approach. The cut cell grid is optimized by a non‐intrusive cell‐agglomeration strategy in order to avoid problems with small or ill‐shaped cut cells. Our approach is based on a discontinuous Galerkin discretization of the compressible Euler equations, where the immersed boundary is implicitly defined by the zero iso‐contour of a level set function. In flow configurations with high Mach numbers, a numerical shock‐capturing mechanism is crucial in order to prevent unphysical oscillations of the polynomial approximation in the vicinity of shocks. We achieve this by means of a viscous smoothing where the artificial viscosity follows from a modal decay sensor that has been adapted to the IBM. The problem of the severe time step restriction caused by the additional second order diffusive term and small non‐agglomerated cut cells is addressed by using an adaptive LTS algorithm. The robustness, stability, and accuracy of our approach is verified for several common test cases. Moreover, the results show that our approach lowers the computational costs drastically, especially for unsteady IBM problems with complex geometries.

Journal or Publication Title: International Journal for Numerical Methods in Fluids
Volume: 91
Publisher: Wiley-Blackwell
Uncontrolled Keywords: BoSSS
Divisions: 16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
Exzellenzinitiative
Exzellenzinitiative > Graduate Schools
Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE)
Zentrale Einrichtungen
Zentrale Einrichtungen > University IT-Service and Computing Centre (HRZ)
Zentrale Einrichtungen > University IT-Service and Computing Centre (HRZ) > Hochleistungsrechner
Date Deposited: 18 Oct 2019 07:22
DOI: 10.1002/fld.4761
Official URL: https://doi.org/10.1002/fld.4761
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