Parallel Direct Simulation Monte Carlo (DSMC) Methods for Modeling Rarefied Reactive and Non-reactive Hypersonic Flow
|關鍵字:||直接模擬蒙地卡羅法(DSMC);化學反應;碰撞能量總和模型(TCE);繪形處理器(GPU);剪切網格;可變時步;瞬態可調適次網格;direct simulation Monte Carlo (DSMC);chemical reaction;total collision energy (TCE);graphic processor unit (GPU);cut-cell;variable time-step;transient adaptive sub-cell|
第二部份：本研究運用單圖形處理器(Graphics Processor Unit, GPU)加速具剪切Cartesian 網格平行二維直接模擬蒙地卡羅法。並利用可變時步法(variable time-step scheme, VTS)與瞬態調適次網格法(transient adaptive sub-cell method, TAS)法在不影響模擬精度下減少模擬所需時間。於論文中以二維極音速流通過斜面與圓柱等案例作為驗證並詳細探討VTS和TAS方法對計算精度和計算效率的影響。模擬結果顯示使用單個GPU相比於單核Intel的CPU處理能力，根據在模擬中使用的問題和GPU的類型的大小，其計算時間將可提升13倍至35倍；同時也顯示，結合VTS與TAS方法，將大量減少模擬計算時間約10倍。
Rarefied gas dynamics has become an increasingly important research topic in the modern science and technology. It is generally very difficult to directly solve the Boltzmann equation that governs rarefied gas dynamics. The direct simulation Monte Carlo (DSMC) method, a particle-based and statistical-based method proposed by Bird for several decades, solves the Boltzmann equation via direct simulation of particle collision kinetics. Extensive verification and validation efforts have led to its greater acceptance for solving the Boltzmann equation, whereas the increase in computer speed has been the main factor behind its greater applicability. Thus, parallel processing of the DSMC method to reduce the computational time is necessary for an efficient application of the method in its future development. In this thesis, two major categories of parallel processing for the DSMC method are presented. The first is the implementation, validation and application of chemical reaction module for simulating hypersonic reactive flows in a parallel direct simulation Monte Carlo code, named PDSC++, using Object-Oriented programming. The second is the implementation, and validation of the DSMC method using a cut-cell Cartesian grid for treating geometrically complex objects on a single graphics processing unit (GPU), which are described briefly next. The first part of the thesis focuses on the implementation and verification of TCE (total collision energy) model in the PDSC++. Through various benchmark test cases, we have demonstrated successful implementation with excellent agreement with analytical results for typical dissociation, recombination and exchange reactions. These benchmarking test cases, which include reproduction of theoretical rate constants in a single cell, 2D hypersonic flow past a cylinder and 2D-axisymmetric hypersonic flow past a sphere, were performed to validate code implementation. Finally, detailed aerothermodynamics of the flown reentry Apollo 6 Command Module at 105 km was simulated to demonstrate the powerful capability of the PDSC++ in treating realistic hypersonic reacting flow at high altitude. In the second part of the thesis, a parallel two-dimensional direct simulation Monte Carlo (DSMC) method with a cut-cell Cartesian grid for treating geometrically complex objects using a single graphics processing unit (GPU) is proposed and validate. Transient adaptive sub-cell (TAS) and variable time-step (VTS) approaches were implemented to reduce computation time without loss of accuracy. The proposed method was validated using two benchmarks: 2D hypersonic flow of nitrogen over a ramp and 2D hypersonic flow of argon around a cylinder using various free-stream Knudsen numbers. We also detailed the influence of TAS and VTS on computational accuracy and efficiency. Our results demonstrate the efficacy of using TAS in combination with VTS in reducing computation time can be more than 10 times. Compared to the throughput of a single core Intel Xeon 5670 CPU, the proposed approach using a single Nvidia GPU enables 13-35 times of increase in computational speed, which varies according to the size of the problem and type of GPUs used in the simulation. Finally, the transition from regular reflection to Mach reflection for supersonic flow through a channel was simulated to demonstrate the efficacy of the proposed approach in reproducing flow fields in challenging problems. At the end of the thesis, major findings are summarized and recommended directions of future work are outlined.
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