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Development of Spectral Difference Lattice Boltzmann Method for Solution of Compressible Flows

Ghaffarian, Ali | 2019

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 52958 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hejranfar, Kazem
  7. Abstract:
  8. In this research, the spectral difference lattice Boltzmann method (SDLBM) is developed and applied for an accurate simulation of two-dimensional (2D) inviscid and viscous compressible flows on the structured and unstructured meshes. The compressible form of the discrete Boltzmann-BGK equation is used in which multiple particle speeds have to be employed to correctly model the compressibility in a thermal fluid. Here, the 2D compressible Lattice Boltzmann (LB) model proposed by Watari is used. The spectral difference (SD) method is implemented for the solution of the LB equation in which the particle distribution functions are stored at the solution points while the fluxes are calculated using the values of the particle distribution functions at the flux points. For time accurate solutions, the fourth-order Runge-Kutta scheme is used to discretize the temporal term in the LB equation. The time integration is also efficiently performed by implementing an implicit dual-time stepping method to enhance the solution of the SDLBM for the unsteady problems. At first, the SDLBM is developed for the solution of the inviscid compressible flows on the structured meshes and the stationary isentropic vortex, the shock tube, the shock-vortex interaction and the supersonic flow past a bump are solved to demonstrate the accuracy and robustness of the present solution method. To more assess the accuracy and performance of the SDLBM, the third-order finite volume LBM (FVLBM) is also applied and the results obtained by these two methods are compared with each other. It is demonstrated that the SDLBM is more accurate compressible inviscid flow solver that can be used for evaluating the other compressible LB-based flow solvers. The main benefit of the use of the LB method in simulating compressible flows is that a same formulation is applied to compute the inviscid and viscous portions of the flowfield with slight modifications on the boundary condition implementation and the relaxation time determination. Here, the viscous compressible flow problems including the Couette flow, the shock-vortex interaction, the subsonic flow over a circular cylinderand also the NACA0012 airfoil are also solved on the structured meshes and the present results obtained for these problems are in good agreement with the analytical and experimental results and also with the available high-order accurate numerical solutions of the LB and Navier-Stokes equations. The effects of using curved-edge cells for properly representing curved wall boundaries on the solution of the SDLBM are also studied. Then, the SDLBM is extended on the unstructured meshes to accurately simulate the inviscid and viscous compressible flows over complex geometries. To demonstrate the accuracy and capability of the unstructured SDLBM flow solver, different problems including the inviscid supersonic flow past a bump, the inviscid subsonic flow over the two-element NACA 4412-4415 airfoil, the viscous transonic flow around the NACA 0012 airfoil, the unsteady viscous subsonic flow around the NACA 0012 airfoil and the unsteady viscous subsonic flow past two side-by-side cylinders are computed and the results obtained are in good agreement with the available high-order accurate numerical results and the experimental data. Indications are that the SDLBM implemented on the unstructured meshes is an appropriate LB-based flow solver for accurately simulating compressible flows over complex and practical problems
  9. Keywords:
  10. Spectral Difference Method ; Compressible Inviscid Flow ; Viscous Flow ; Boltzman Equation ; Unstructured Grids ; Lattice Boltzmann Method ; Structured Grid

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