DSMC Method Based on 2D Adaptive Cartesian Mesh and Its Application

Abstract: As exploratory space extend continuously, the flight height of vehicles rise and the real gas phenomena have significant impact on flow parameters. For such flow, the Navier-Stokes equations yield poor approximations to the physics of gas dynamics, and the governing equation is the Boltzmann equation. Because of the nonlinear of this equation, attempts to solve it numerically have met with less success. To circumvent the difficulty of a direct solution of this equation, the direct simulation Monte Carlo (DSMC) method was proposed by Bird in 1963. It has become a very popular methodology for the rarefied gas flows. The purpose of this thesis is to study DSMC method on adaptive Cartesian mesh for hypersonic rarefied gas flows and to develop highly automated and efficient DSMC program which is suitable for any complex 2D geometry.Firstly, necessary basic molecular gas dynamics theory is studied for the direct simulation of rarefied gas flows. We discuss the velocity distribution functions. Binary elastic collision is analyzed detailedly and the expression of post collision velocities is deduced. Intermolecular potential and different collision model is discussed.Secondly, we studied quadtree structure for the generation of Cartesian mesh. To provide enhanced flowfiled solution, Cartesian refinement technique is analyzed detailedly.Then, the implementation of DSMC method on Cartesian mesh is investigated. An effective searching method which we called‘positional coordinate deciding’, is presented to reduce the computational time. Some material problems are discussed in implementation of DSMC method.Afterwards, we analyzed the Cartesian mesh adaptation parameters and criteria for better resolve the flow features in the flow field. For saving the running time, we studied some techniques for optimization in DSMC method on Cartesian mesh. One technique is varying the ratio of real molecules to simulated molecules, and the other is varying local time-step method.At last, we studied parallel algorithm of DSMC method on Cartesian mesh using MPI standard library on PC-CLUSTER. By using the characteristic of Cartesian mesh, we presented a new domain decomposition method called‘chain partitioning’. The method maintains dynamic load balance and guarantees the lowest communication between each processor. A complete parallel code of DSMC method on adaptive Cartesian mesh is developed…
Key words: DSMC method; Cartesian mesh; adaptive; parallel; rarefied gas dynamics

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