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Development of a Lattice Boltzmann Method in an Arbitrary Lagrangian-Eulerian Framework for Simulating Compressible Flows over Moving Bodies

Hashemi Nasab, Hossein | 2024

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 58262 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hejranfar, Kazem
  7. Abstract:
  8. The objective of this study is to develop and apply an arbitrary Lagrangian-Eulerian unstructured finite-volume lattice-Boltzmann method (ALE-FVLBM) for solving two-dimensional compressible flows around moving bodies. The two-dimensional compressible form of the LB equation, along with the Batangar-Gross-Crook (BGK) approximation for modeling the collision operatore, and the D2Q65 Watari model for modeling the equilibrium distribution function, are considered here. The resulting LB equation is formulated in the ALE framework on an unstructured body-fitted mesh to correctly model the body shape and properly incorporate the mesh movement due to the body motion. The spatial discretization of the resulting system of equations is performed by a second-order cell-centered finite-volume method on arbitrary quadrilateral meshes and an implicit dual-time stepping method is utilized for the time integration. To stabilize the numerical solution, appropriate numerical dissipation terms are added to the formulation. To examine the accuracy and performance of the developed solver, benchmark problems such as the shock tube and the stationary isentropic vortex are simulated. Then, the inviscid and viscous compressible flows around stationary and moving airfoils under different conitions are computed and the accuracy of the results from the present solver is evaluated against the available results. Next, the compressible lattice Boltzmann equation is preconditioned by modifying the Watari multi-speed equilibrium distribution function to improve the performance of the present solver in the simulation of steady and unsteady compressible flows and the equivalent macroscopic governing equations are obtained by applying the Chapman-Enskog procedure to this equation. The accuracy and efficiency of the present preconditioned lattice Boltzmann solver are examined through simulations of compressible flows over stationary and moving airfoils. The investigation shows that the applied preconditioning method to the compressible lattice Boltzmann equation increases the convergence rate of solution for both the steady and unsteady compressible flows, thereby enhancing the efficiency of the present solver
  9. Keywords:
  10. Lattice Boltzmann Method ; Compressible Flow ; Finite Volume Method ; Arbitrary Lagrangian-Eulerian Method ; Preconditioning ; Unstructured Grid

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