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shakhov-model
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Development of Compact Finite Difference Boltzmann Method for Simulating Compressible Rarefied Gas Flow
, M.Sc. Thesis Sharif University of Technology ; Hejranfar, Kazem (Supervisor) ; Fouladi, Nematollah (Co-Supervisor)
Abstract
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...
Numerical Simulation of One-Dimensional Compressible Flow with Real Gas Effects by Solving Boltzmann Equation Using High-Order Accurate Finitedifference Method
, M.Sc. Thesis Sharif University of Technology ; Hejranfar, Kazem (Supervisor)
Abstract
In this study, the Shokov-BGK model of the Boltzmann equation is reformulated and generalized to consider the real gas effects. At first, the formulation is performed to consider an arbitrary specific heats ratio and the correct Prandtl number for polyatomic gases. Here, the resulting equations of the present formulation are numerically solved by applying the high-order finite-difference weighted essentially non-oscillatory (WENO) scheme. The present solution method is tested by computing the one-dimension Reiman problem with different specific heats ratios for a wide range of the Knudsen numbers. The results are compared with the available gas-kinetic results which show good agreement. It...