On the robust, flexible and consistent implementation of time domain impedance boundary conditions for compressible flow simulations

S. Jaensch, C. Sovardi, W. Polifke

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

The accurate simulation of compressible flows requires the appropriate modeling of the reflection of acoustic waves at the boundaries. In the present study we discuss time domain impedance boundary conditions (TDIBC). The formulation proposed allows to impose a desired reflection coefficient at the inflow and outflow boundaries. Our formulation is an extension of the well known Navier-Stokes characteristic boundary conditions. The frequency dependent reflections at the boundaries are implemented with a state-space model in the time domain. We provide a comprehensive discussion on how such state-space models can be constructed and interpreted. This discussion shows that the state-space description allows a robust and flexible implementation. It allows to consider complex reflection coefficients and account for non-constant CFD time steps in a straight forward manner. Furthermore, we prove analytically and demonstrate numerically that the formulation proposed is consistent, i.e. the formulation ensures that the flow simulation exhibits the reflection coefficient imposed accurately, as long as the waves impinging on the boundary are plane, and it prohibits drift of the mean flow variables. Finally, the boundary conditions are tested successfully for laminar and turbulent flows.

Original languageEnglish
Pages (from-to)145-159
Number of pages15
JournalJournal of Computational Physics
Volume314
DOIs
StatePublished - 1 Jun 2016

Keywords

  • Acoustics
  • Boundary condition
  • Impedance
  • NSCBC
  • Reflection coefficient
  • State-space

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