Development of Chebyshev Collocation Spectral Lattice Boltzmann Method for Solution of LowSpeed Flows

Haji Hassan Pour, Mahya | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45793 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hejranfar, Kazem
  7. Abstract:
  8. In this study, a Chebyshev collocation spectral lattice Boltzmann method (CCSLBM) is developed and assessed for the computation of low speed flows. Both steady and unsteady flows are considered here. The discrete Boltzmann equation (DBE) with the Bhatnagar-Gross-Krook (BGK) approximation based on the pressure distribution function is considered and the space discretization is performed by the Chebyshev collocation spectral method to achieve a highly accurate flow solver. To provide accurate unsteady solutions, the time integration of the temporal term in the LB equation is made by the fourth-order Runge-Kuta scheme. To achieve numerical stability and accuracy, the physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used. An iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows. Note that the CCSLBM applied does not need any numerical dissipation or filtering for the solution to be stable that leads to highly accurate solutions. The CCSLBM is applied in both Cartesian and curvilinear coordinate systems to investigate the performance of the present methodology. Five 2D test cases are simulated in Cartesian coordinates herein that are a regularized cavity, the backward facing step, the Taylor’s vortex problem, the Couette flow and the doubly periodic shear layers.Also, three 2D test cases are simulated in generalized curvilinear coordinates that are a Couette flow with mapping, cylindrical Couette flow and gradual expansion nuzzle. Results obtained for these test cases are in good agreement with the available analytical and numerical results. The solution methodology proposed based on the CCSLBM is also extended to three-dimensions and a 3D regularized cavity is simulated and the corresponding results are presented and validated. Indications are that the CCSLBM developed and applied herein is robust, efficient and accurate for computing 2D/3D low speed flows. Note also that high accuracy solutions obtained by applying the CCSLBM can be used as benchmark solutions for the assessment of other LBM-based flow solvers
  9. Keywords:
  10. Lattice Boltzmann Method ; Chebyshev Collocation Spectral Method ; Low Speed Flows

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