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Development of Compact Finite-Difference Lattice Boltzmann Method for Solving Two-Phase Flows

Ezzatneshan, Eslam | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 47152 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hejranfar, Kazem
  7. Abstract:
  8. In the present thesis, a high-order compact finite-difference lattice Boltzmann method (CFDLBM) is proposed and applied for an accurate and efficient numerical simulation of liquid-vapor two-phase flows. At first, the stability of the fourth-order CFDLBM is performed by using the von Neumann stability analysis for the D2Q7 and D2Q9 lattices. The stability analysis indicates that the CFDLBM proposed is stable and thus suitable for the simulation of high Reynolds number flows. The high-order CFDLBM is then developed and applied to accurately compute 2-D and 3-D incompressible flows in the Cartesian coordinates. Herein, the spatial derivatives in the lattice Boltzmann equation are discretized by using the fourth-order compact finite-difference scheme and the discretization of the temporal term is performed with the fourth-order Runge-Kutta scheme. A high-order spectral-type low-pass linear compact filter is used to stabilize the numerical solution. An iterative initialization procedure is also presented and applied to generate consistent initial conditions for the simulation of unsteady flows. The accuracy and efficiency of the proposed solution procedure based on the CFDLBM for the solution of single-phase incompressible flows are examined by comparison with the analytical, numerical and experimental results and also those of the classical LBM. The study shows that the present solution methodology is robust, efficient and accurate for solving steady and unsteady incompressible flow problems even at high Reynolds numbers. The implementation of the high-order CFDLBM is also performed in the generalized curvilinear coordinates to improve the computational efficiency of the solution algorithm to handle 2D and 3D curved geometries with non-uniform grids. All the boundary conditions are implemented based on the solution of the governing equations in the generalized curvilinear coordinates. The accuracy and robustness of the implemented solution algorithm are demonstrated by solving different 2-D and 3-D incompressible flow problems in the generalized curvilinear coordinates. Results obtained for these problems are in good agreement with the existing numerical and experimental results. The study shows that the present solution methodology based on the implementation of the high-order CFDLBM in the generalized curvilinear coordinates is capable of solving steady and unsteady incompressible flows over practical geometries. The proposed high-order CFDLBM is then developed to accurately compute liquid-vapor two-phase flows with high density ratios. Herein, the He-Shan-Doolen type lattice Boltzmann multiphase model is used and the spatial derivatives in the resulting equation are discretized by using the fourth-order compact finite-difference scheme and the discretization of the temporal term is performed with the fourth-order Runge-Kutta scheme to provide an accurate and efficient two-phase flow solver. A nonlinear filter is used to stabilize the numerical solution and remove the numerical oscillations in the interfacial region between the two phases. Three discontinuity-detecting sensors for properly switching between a second-order and a higher-order filter are applied and assessed. It is shown that the filtering technique applied can be conveniently adopted to reduce the numerical oscillations and improve the numerical stability of the CFDLBM implemented. The accuracy and efficiency of the proposed solution procedure based on the CFDLBM are examined by solving different 2D two-phase systems. The study shows that the present solution methodology is robust, efficient and accurate for simulating two-phase liquid-vapor flow problems even at high density ratios
  9. Keywords:
  10. Lattice Boltzmann Method ; Finite Difference Method ; Linear Filters ; Curvilinear Coordinates ; Two Dimensional Flow ; Three Dimentional Flow ; Nonlinear Filter ; Cartesian Coordinates ; Liquid-Vapor Two Phase Flow ; Steady Incompressible Flow ; Unsteady Incompressible Flow

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