Solution of Compressible Flow Using Finite Volume Lattice Boltzmann Method on Unstructured Meshes

Karbalaei baba, Ali Reza | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 42817 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hejranfar, Kazem
  7. Abstract:
  8. In this study, the solution of compressible flows is performed using finite volume lattice Boltzmann method (FVLBM). A model associated with 13 discrete velocity vectors and 2 energy levels is used and the Boltzmann transport equation is solved using a cell-centered finite volume on structured meshes. The values of distribution functions on each cell faceare determined by averaging from their values at the two control points located on the center of two neighboring cells. The fourth-order Runge-Kutta time-stepping scheme is applied to discretize temporal derivative term. The second- and fourth-order numerical dissipation termsareadded to the algorithm to stabilize the solution when solving problems with high gradients of the flow variables like shocks. The treatment of implementing different types of boundary conditions for the proposed method is given. Here, the solution procedure is also extended to unstructured meshes. Different test cases are solved using the present solution procedure to examine the accuracy and validity of the results obtained. The problems studied are isentropic vortex, 2D shock tube, shock-vortex interaction and 2D channel with circular bump. The results obtained by FVLBM are compared with those obtained by solving the Euler equations with the same numerical method and also with the exact solutions and the available numerical results
  9. Keywords:
  10. Lattice Boltzmann Method ; Finite Volume Method ; Unstructured Grid ; Compressible Flow

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