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Numerical Simulation of Compressible Viscous Flows Using Central Difference Finite Volume Lattice Boltzmann Method

Katal, Ali | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45596 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hejranfar, Kazem
  7. Abstract:
  8. In this study, 2-D compressible viscous and inviscid flows are simulated by using a finite volume Lattice Boltzmann method. Two different models, namely, the Qu model and Watari model are employed for compressible flows simulations. The first model includes 13 discrete velocity vectors and 2 energy levels in which the Maxwellian function is replaced with a simple function for describing the distribution function that is suitable for inviscid flow simulations. The second model is a thermal multi-velocity model with isotropic tensors up to seventh rank that is suitable for compressible viscous and inviscid flow simulations with arbitrary specific heats ratio. In both the models, lattice velocities are constant in the whole domain. The numerical solution of the Boltzmann transport equation is performed by a second-order central difference finite volume in which the values of distribution function on each cell face are determined by averaging from their values at the two control points located on the center of two neighboring cells. Suitable numerical dissipation that includes second- and fourth-order dissipation terms are used to stabilize the solution, especially when computing problems with high gradients of the flow variables like shocks. The treatment of implementing inviscid and viscous boundary conditions is also explained. Several 2D problems are simulated by the present solution methodology. The test cases for the inviscid computations are isentropic vortex, shock tube, a channel with circular bump, a circular cylinder and the NACA0012 airfoil. For the viscous computations, the test cases are flat plate, a compression corner and a circular cylinder. The present results 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 and the accuracy and performance of the solution algorithm are examined
  9. Keywords:
  10. Lattice Boltzmann Method ; Incompressible Viscous Flow ; Central Difference Finite Volume Method

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