應用非結構性網格之通用平行化三維DSMC程式(PDSC) 的研究與發展

Abstract

本論文發展並驗證一通用平行化之三維直接模擬蒙地卡羅程式(PDSC)於非結構性四面體網格。這個PDSC程式有幾個重要的特色：以動態區域切割之平行化處理、結合變時步方法於可調適網格、可有效率處理稀少氣體之權值守恆法(conservative weighting scheme)以及處理高速流之化學反應等等。此程式利用多層式圖形切割技術，在模擬的過程中根據每顆處理器的負載做動態區域切割。此外，利用DSMC的初步結果，三維非結構可調適網格(h-refined)法以及簡易的網格品質控制可以用來增加DSMC的準確性。變時步法則利用通過界面的流量(質量、動量以及能量)守恆之觀念，在避免犧牲結果準確性的前提下，同時減少模擬分子數目以及到達穩態的疊代次數。確保動量及能量在每次碰撞後均能守恆的權值守恆法(CWS)可以用來有效的模擬具有稀少氣體的流場。這個方法被證實可以大量減少模擬分子的數目及計算時間。分離(Dissociation)、結合(Recombination)以及交換(Exchange)的化學反應亦被結合在PDSC中來處理有化學作用的流場。最後利用發展完全的PDSC模擬數個複雜、具有挑戰性的流場來顯示它優越的計算能力。計算結果與實驗結果或前人的模擬結果進行比較，驗證程式的正確性。 本論文的結構簡述如下：第一章描述此研究之背景、動機以及目的。第二章為DSMC法之簡介及目前PDSC軟體結構內容之概要描述。第三章介紹結合變時步法之非結構性可調適四面體網格。第四章為利用動態區域切割之平行化DSMC程式。第五章介紹權值守恆法以及其處理稀少氣體流場之優點。第六章為化學反應於高速流以及利用單一網格之驗證。第七章為利用PDSC模擬幾個具有挑戰性的應用及結果。第八章為此研究的重要發現，以及對未來發展的建議。

A general-purpose parallel three-dimensional direct simulation Monte Carlo code (PDSC) using unstructured tetrahedral mesh is developed and validated in this thesis. Important features of this PDSC include parallel processing with dynamic domain decomposition, combination of variable time-step scheme with solution-based adaptive mesh refinement, conservative weighting scheme for treating trace species and chemical reaction functions for hypersonic air flows. A multi-level graph-partitioning technique is employed to adaptively decompose the computational domain according to the workload distribution among processors during runtime, which can alleviate the unbalancing loading before it becomes a problem. A three-dimensional h-refined unstructured adaptive mesh with simple mesh quality control, based on a preliminary DSMC simulation, is used to obtain suitable mesh resolution to increase the accuracy of the DSMC solution. A variable time-step method using the concept of fluxes (mass, momentum and energy) conservation across the cell interface is implemented to reduce the number of simulated particles and the number of iterations of transient period to reach steady state, without sacrificing the solution accuracy. A conservative weighting scheme, ensuring exact momentum and near exact energy conservation during each particle collision, is incorporated into the PDSC to efficiently treat flows with trace species. This method is validated and shows it can greatly reduce both the number of particles and computational time. Chemical reaction module, including dissociation, recombination and exchange reactions, is incorporated into the PDSC for treating reactive flows. It is verified by comparing probability, degree of dissociation and mole fractions of a single 2-D cell with theoretical data. Completed PDSC is then applied to compute several complicated, challenging flow problems to demonstrate its superior computational capability. The results are also validated with experimental data or previous simulation data wherever available. Organization of this thesis is briefly described as follows. Chapter 1 describes the background, motivation and objectives of the current study. Chapter 2 describes the general DSMC method and overview of the current implementation of the PDSC. Chapter 3 introduces the variable time-step scheme in combination with solution-based adaptive mesh refinement on unstructured tetrahedral mesh. Chapter 4 describes the parallel implementation and performance of the DSMC method using dynamic domain decomposition. Chapter 5 describes the conservative weighting scheme and its superiority in treating flows having trace species. Chapter 6 describes the chemical reaction functions for treating hypersonic air flows along with its validation using single-cell simulation. Chapter 7 describes the results of simulating several challenging flow problems using the PDSC. Chapter 8 concludes and summarizes the important findings of the current study, along with recommended future studies.