Non-Reflecting Boundary Conditions in the context of the Discontinuous Galerkin Finite Element Method

Edmond Shehadi

Research output: ThesisPhD Thesis - Research UT, graduation UT

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Abstract

To assess the efficacy of different non-reflecting boundary conditions (NRBCs) in high-order compressible flow solvers, several NRBCs have been implemented and studied in the context of the discontinuous Galerkin (DG-)finite element method (FEM) discretization. The methods considered are based on buffer zone techniques and boundary-imposed conditions. The boundary-imposed methods are mainly a standard Riemann-extrapolation technique and a novel reconstruction that imposes the Navier-Stokes characteristic boundary condition (NSCBC). The buffer zone strategies considered utilize the sponge layer (SL), the perfectly matched layer (PML), the supersonic layer (SSL) and a novel characteristic matching layer (CML).

The reconstruction, termed as a polynomial-correction (PC), assembles an explicit boundary state, needed by the numerical fluxes (inviscid and viscous) of the DG-FEM, by taking the standard NSCBC methodology into account. The CML uses characteristic theory to enforce a non-reflective behavior over an entire layer, by eliminating or "matching" incoming reflections into the physical domain.

Tests have been done on several problems, ranging from 1D to 3D, using (non-linear) Euler and Navier-Stokes equations, on academic and industrial test-cases. The proposed methods, PC-NSCBC and CML, demonstrate how effective they are when compared to a standard Riemann extrapolation, as well as other NRBCs.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • University of Twente
Supervisors/Advisors
  • Venner, Cornelis H., Supervisor
  • van der Weide, Edwin, Co-Supervisor
Award date13 May 2024
Place of PublicationEnschede
Publisher
Print ISBNs978-90-365-6092-4
Electronic ISBNs978-90-365-6093-1
DOIs
Publication statusPublished - 13 May 2024

Keywords

  • Computational Fluid Dynamic (CFD)
  • perfectly matched layers
  • Navier-Stokes Characteristic Boundary Conditions
  • Discontinuous Galerkin finite element method
  • High-order methods
  • Non-reflecting boundary conditions
  • Navier-Stokes equations
  • Euler equations

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