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Development of Compact Finite Difference Boltzmann Method for Simulating Compressible Rarefied Gas Flow

Alemi Arani, Ali | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53127 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hejranfar, Kazem; Fouladi, Nematollah
  7. Abstract:
  8. In this work, a high-order accurate gas kinetic scheme based on the compact finite-difference Boltzmann method (CFDBM) is developed and applied for simulating the compressible rarefied gas flows. Here, the Shakhov model of the Boltzmann equation is considered and the spatial derivative term in the resulting equation is discretized by using the fourth-order compact finite-difference method and the time integration is performed by using the third-order TVD Runge-Kutta method. A filtering procedure with three discontinuity-detecting sensors is applied and examined for the stabilization of the solution method especially for the problems involving the discontinuity regions such as the shock. The accuracy and robustness of the present solution method are assessed by computing several well-known problems, such as the shock tube, the normal shock wave, the shock-density wave interaction and isentropic vortex. The present results are compared with the available gas-kinetic and DSMC results for different Knudsen numbers which exhibit good agreement. It is shown that the proposed gas kinetic scheme based on the compact finite-difference Boltzmann method (CFDBM) is capable of accurately computing rarefied gas flows in a wide range of Knudsen numbers from highly rarefied free-molecular flow to near-continuum flow regimes
  9. Keywords:
  10. Filtering ; Compact Finite Difference Method ; Boltzman Equation ; Compressible Rarfied Gas Flow ; Discontinuity-Detecting Sensor ; Shakhov Model

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