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Development of Characteristic Boundary Conditions with Artificial Compressibility Method by Compact Finite-Difference Discretization

Parseh, Kaveh | 2017

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 51061 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hejranfar, Kazem
  7. Abstract:
  8. In the present study, the preconditioned incompressible Navier‐Stokes equations with the artificial compressibility (AC) method formulated in the generalized curvilinear coordinates are numerically solved by using a high‐order compact finite‐difference scheme for accurately and efficiently computing the incompressible flows. A fourth‐order compact finite‐difference scheme is utilized to discretize the spatial derivative terms of the resulting system of equations and the time integration is carried out based on the dual time‐stepping method. The capability of the proposed solution methodology for computing the steady and unsteady incompressible viscous flows in a wide range of Reynolds numbers including the creeping flows is investigated through the simulation of different benchmark problems and the results obtained are compared with the existing analytical, numerical, and experimental data. Then, the characteristic boundary conditions (CBCs) are applied and assessed for the solution of incompressible inviscid flows. For this aim, the two-dimensional incompressible Euler equations based on the AC method are considered and the CBCs are formulated in the generalized curvilinear coordinates and implemented on both the far-field and wall boundaries. Then, the preconditioned characteristic boundary conditions (PCBCs) based on the AC method are formulated in the generalized curvilinear coordinates and implemented at the artificial boundaries for the solution of two- and three-dimensional incompressible viscous flows. The compatibility equations and the corresponding characteristic variables (or the Riemann invariants) are mathematically derived and applied as suitable boundary conditions (BCs) in the high-order accurate incompressible flow solver. Note that the value of the AC parameter in the flow field and also at the far-field boundary is automatically calculated based on the local flow conditions to enhance the robustness and performance of the solution algorithm. The accuracy and performance of the PCBCs applied are evaluated through the simulation of different benchmark problems in comparison with the simplified BCs and non-PCBCs. A sensitivity analysis is also performed to evaluate the effects of different numerical parameters on the accuracy and performance of the solution algorithm. The developed solver is fully parallelized using the Concurrency Runtime standard and Parallel Patterns Library (PPL) and its performance on a multi-core CPU is also analyzed. The present study indicates that the PCBCs considerably improve the convergence rate of the solution of incompressible flows compared to the other two types of the BCs and the computational costs are significantly decreased
  9. Keywords:
  10. Incompressible Flow ; Artificial Compressibity Method ; Precondition Characteristic Boundary Conditions (PCBC) ; Generalized Curvilinear Coordinates ; High-Order Compact Finite Difference Method

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