A Characteristic-Based Spectral Element Method for Moving-Domain Problems

Abstract

In this paper, we present a characteristic-based numerical procedure for simulating incompressible flows in domains with moving boundaries. Our approach utilizes an operator-integration-factor splitting technique to help produce an efficient and stable numerical scheme. Using the spectral element method and an arbitrary Lagrangian–Eulerian formulation, we investigate flows where the convective acceleration effects are non-negligible. Several examples, ranging from laminar to turbulent flows, are considered. Comparisons with a standard, semi-implicit time-stepping procedure illustrate the improved performance of our scheme.

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Acknowledgements

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, under Contract DE-AC02-06CH11357. The research also used resources of the Argonne Leadership Computing Facility, which is supported by the U.S. Department iof Energy, Office of Science, under Contract DE-AC02-06CH11357.

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Correspondence to Saumil Patel.

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Patel, S., Fischer, P., Min, M. et al. A Characteristic-Based Spectral Element Method for Moving-Domain Problems. J Sci Comput 79, 564–592 (2019). https://doi.org/10.1007/s10915-018-0876-6

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Keywords

  • Spectral element method
  • Arbitrary Lagrangian–Eulerian methods
  • Operator- integration-factor splitting
  • Characteristics
  • Navier–Stokes equations
  • In-cylinder engine flows