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Unsteady preconditioned characteristic boundary conditions for direct numerical simulation of incompressible flows

Parseh, K ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.2514/1.J058279
  3. Publisher: American Institute of Aeronautics and Astronautics Inc , 2020
  4. Abstract:
  5. The unsteady preconditioned characteristic boundary conditions (UPCBCs) based on the artificial compressibility (AC) method are formulated and applied at artificial boundaries for the direct numerical simulation (DNS) of incompressible flows. The compatibility equations including the unsteady terms are mathematically derived in the generalized curvilinear coordinates and then incorporated as boundary conditions (BCs) in a high-order accurate incompressible flowsolver. The spatial derivative terms of the systemof equations are discretized using the fourth-order compact finite difference (FD) scheme, consistent with the high-order accuracy required for the DNS. The time integration is carried out using an implicit dual time-stepping method, and the robustness and performance of the numerical algorithm are enhanced by applying the preconditioning technique and calculating the automated AC parameter based on the local flow conditions. At first, the steady viscous incompressible flow for a two-dimensional plane jet is computed to assess the accuracy and performance of the solution method by applying the UPCBCs in comparison with the simplified BCs. Then, the simulation of the unsteady incompressible viscous flow around a twodimensional NACA0012 airfoil at the Reynolds number 800 and the angle of attack 20° is performed, and it is indicated that the computational cost of the solution is considerably decreased by implementing the UPCBCs at the artificial far-field boundary compared with the simplified BCs, which is remarkably valuable for the DNSs. Finally, the computation of the transition to unsteady for the incompressible flow around a three-dimensional NACA0012 wing at the sameconditions of the two-dimensional case is successfully performed, and the results obtained are comparedwith those of previous studies that exhibit good agreement. Indications are that the present solution method by applying the UPCBCs at the artificial far-field boundary can be effectively used for the DNSs of the incompressible flows. © 2019 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved
  6. Keywords:
  7. Angle of attack ; Boundary conditions ; Direct numerical simulation ; Numerical methods ; Numerical models ; Reynolds number ; Artificial compressibility ; Characteristic boundary conditions ; Compact finite differences ; Dual time stepping method ; Generalized curvilinear coordinates ; Preconditioning techniques ; Unsteady incompressible viscous flow ; Viscous incompressible flows ; Incompressible flow
  8. Source: AIAA Journal ; Volume 58, Issue 4 , 2020 , Pages 1476-1489
  9. URL: https://arc.aiaa.org/doi/10.2514/1.J058279