Developing a Compact Finite Difference Method for Solving Fluid - Solid Interaction in Incompressible Flow

Parseh, Kaveh | 2011

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 41677 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hejranfar, Kazem
  7. Abstract:
  8. In this study, fluid-solid interaction (FSI) is simulated computationally by using a high-order accurate numerical method. The two-dimensional incompressible viscous flows are considered in the fluid domain. The primary problem with solutions of the incompressible Navier–Stokes equations is the difficulty of coupling changes in the velocity field with changes in the pressure field while satisfying the continuity equation. Herein, the artificial compressibility method is used to overcome this difficulty. Preconditioning is implemented to reduce the stiffness of the system of equations to increase the convergence rate of the solution. Using preconditioning, physical solutions even at low Reynolds numbers (creeping flows) are provided. A coordinate transformation is used to map non-orthogonal structured grid onto a rectangular grid in both the fluid and structure domains. This procedure allows one to cluster the grid points/lines in the regions of interest. The numerical solution of both fluid flow and elastic structure is performed by using the fourth-order compact finite difference method. The present algorithm uses second-order implicit time integration in both the domains. High-order spectral-type low-pass compact filters are used to regularize the numerical solution in the flow domain and eliminate spurious modes due to unresolved scales, nonlinearities and inaccuracies in applying boundary conditions. Test cases considered herein for validating the numerical results in the flow domain are incompressible flows in a 2-D cavity and a 2-D backward facing step, and also 2-D Taylor vortex problem at different flow conditions. The effects of different numerical parameters such as the preconditioning coefficient, the filtering parameter and also the grid size on the accuracy of and performance of the solution are examined. A clamped beam under an axial stress, shear stress and an oscillating load is modeled to validate the accuracy of the numerical algorithm in the structure domain, Then, a fluid-solid interaction problem is numerically simulated to show the accuracy and capability of the solution algorithm developed. Results obtained for all test cases are in good agreement with the available analytical and numerical results. The study shows that the algorithm presented is robust, efficient and accurate for simulating fluid-solid interaction (FSI) problems
  9. Keywords:
  10. Structure Dynamics ; Fluid-Solid Interaction ; Compact Finite Difference Method ; Incompressible Flow ; Preconditioning

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