离散时空直接建模思想及其在模拟多尺度输运中的应用

统一气体动理学格式是基于离散空间直接建模的思想构建的多尺度数值格式。本文对统一气体动理学格式近十年的发展进行总结,并对未来的发展方向进行展望。统一气体动理学格式的建模思路突破了传统偏微分方程数值离散求解的制约,回归物理建模的出发点,基于守恒定律在离散时空有限尺度的控制体上进行建模,利用网格界面处的动理学方程时间演化解构建数值通量,从而构造出有限控制体上取决于网格尺度和时间步长的气体动力学控制方程。统一气体动理学格式建模有两个关键点:一是宏观守恒量与微观分布函数耦合演化,二是通过界面处的多尺度时间演化解构建数值通量。统一气体动理学格式是一种多尺度数值格式,根据网格努森数能够准确捕捉从稀薄到连续不同流域的流体物理。从某种意义上说气体动理学格式提供了有效的随不同网格努森数变化的连续性方程,即连续流的纳维-斯托克斯(N-S)方程和稀薄流的波尔兹曼(Boltzmann)是统一气体动理学格式在网格努森数很小和很大情况小逼近的两个极限方程。对于连续流的黏性边界层问题的捕捉,统一动理学格式不要求网格尺度小于粒子平均自由程。统一气体动理学格式成功应用于多尺度气体输运,等离子体输运,中子、光子输运,以及气固离散两相流等领域的数值模拟,在计算精度和计算效率上都体现出明显优势。尤其对于等离子体的输运计算,统一气体动理学格式提供了一个在连续变化尺度上的模拟方法,包括从求解电子、离子的自由输运的Vlasov动理学方程到连续流域内的双流体方程以及磁流体方程。本文总结了统一气体动理学格式的建模思想,数值性质,以及格式在不同领域的应用。 The direct modeling methodology provides a framework for multiscale modeling of transport processes, based on which the unified gas kinetic scheme (UGKS), the discrete unified kinetic scheme (DUGKS), and unified gas kinetic wave-particle (UGKWP) method have been developed over the last decade. The methodology of direct modeling is to construct the numerical governing equations on a discrete control volume by taking into account the contribution of both particle transport and collision process. The two important ingredients of the direct modeling methodology are the coupling evolution of the macroscopic quantities and microscopic distribution function, and the utilization of the local evolution solution in the construction of numerical flux. Based on the direct modeling methodology, we construct a continuous spectrum of governing equations in the whole flow regimes, which automatically recovers the collision-less Boltzmann and Navier-Stokes equations in their corresponding limiting regimes. In this paper, we are going to review the direct modeling methodology, the construction of schemes, and the multiscale and unified preserving properties. We will also review the applications of the schemes in the transport process of gas, plasma, photon, and disperse multiphase flow, and give an outlook of the future developments. © 2020, The Editorial Board of Acta Aerodynamica Sinica. All right reserved

求解非平底一维浅水方程的KFVS格式

以 Boltzmann方程為基礎 ,本文提出了求解非平底淺水方程的 KFVS(Kinetic FluxVector Splitting)格式。因通量計算中考慮了底坡項的作用 ,計算方法和諧 ,即在非平底靜水計算中始終能保持流速為零 ,水位為常數。數值試驗表明 ,無論是計算恒定流還是非恒定流 ,該方法具有健全性和高分辨率等特點. This paper presents a kinetic flux vector splitting (KFVS) scheme for the shallow water equations with source terms. Due to the appropriate implementation of the source term effect in the flux evaluation, the current scheme is a well balanced method. The scheme is accurate and robust for both steady and unsteady flow simulations

三角形网格下求解二维浅水方程的KFVS格式

以Boltzmann方程為基礎,建立了求解二維淺水方程的KFVS(Kinetic Flux Vector Splitting)格式。為保證計算格式的和諧性,通量計算中考慮了底坡源項的作用。在此基礎上,采用特殊的底坡源項處理技術,建立了三角形網格下二階精度的KFVS和諧格式。經典型算例和錢塘江涌潮計算驗證,證明本文提出的方法分辨率高,邊界適應性強,并具有模擬間斷流動的能力。Based on the Boltzman equation, the kinetic flux vector splitting (KFVS) scheme for solving 2-D shallow water equations with triangular mesh is developed. In order to establish a well-balanced scheme, the source term effect is taken into account explicitly in the flux evaluation. On this basis, a special technique for dealing with source term due to bottom topography is adopted and the well-balanced KFVS scheme with triangular mesh possessing second order accuracy is established. The validity of the proposed method is verified by the comparison of calculation result of a traditional typical example with the field observation data of a tidal bore in Qiantang River

氣體動理學格式研究進展

介紹了近年來氣體動理學格式(gas-kinetic scheme,GKS,亦簡稱BGK格式)的主要研究進展,重點是高階精度動理學格式及適合從連續流到稀薄流全流域的統一動理學格式.通過對速度分布函數的高階展開和對初值的高階重構,構造了時間和空間均為三階精度的氣體動理學格式.研究表明,相比于傳統的基于Riemann解的高階格式,新格式不僅考慮了網格單元界面上物理量的高階重構,而且在初始場的演化階段耦合了流體的對流和黏性擴散,也能夠保證解的高階精度.該研究為高精度計算流體力學(computatial fluid dymamics,CFD)格式的建立提供了一條新的途徑.通過分子離散速度空間直接求解Boltzmann模型方程,在每個時間步長內將宏觀量的更新和微觀氣體分布函數的更新緊密地耦合在一起,建立了適合任意Knudsen(kn)數的統一格式,相比于已有的直接離散格式具有更高的求解效率.最后,本文還討論了合理的物理模型對數值方法的重要性.氣體動理學方法的良好性能來自于Boltzmann模型方程對計算網格單元界面上初始間斷的時間演化的準確描述.氣體自由運動與碰撞過程的耦合是十分必要的.通過分析數值激波層內的耗散機制,我們認識到采用Euler方程的精確Riemann解作為現代可壓縮CFD方法的基礎具有根本的缺陷,高馬赫數下的激波失穩現象不可避免.氣體動理學格式為構造數值激波結構提供了一個重要的可供參考的物理機制.Recent progress in the development of the gas-kinetic scheme is reviewed in this article, with emphasis laid on the construction of high-order-accurate gas-kinetic flux function for the Navier-Stokes equations and the unified gas-kinetic scheme for flow simulations in the entire Knudsen number regimes. A third-orderaccurate gas-kinetic scheme is presented through the high-order reconstruction of the initial data and the high-order gas evolution model of the gas distribution function. Different from traditional high-order schemes based on Riemann solution, the new scheme not only takes into account the high-order initial reconstruction at a cell interface, but also follows its time evolution, which ensures a high-order time accurate flux function. This study pioneers a new way to construct high accurate time-space coupling CFD method. The unified gaskinetic scheme for arbitrary Knudsen number is developed by direct solving the Boltzmann model equation in the discrete velocity space, where the update of both macroscopic conservative variables and microscopic gas distribution function takes place simultaneously within a time step. The newly developed method is more efficient than existing DVMs, where the continuum flow limit can be easily obtained in the unified scheme due to its hydrodynamic scale part of the flux function. The importance of using a valid physical evolution model in the construction of a numerical method is also discussed. The good performance of gas-kinetic scheme comes mainly from its capability of capturing a rational gas evolution process from an initial discontinuity using gas-kinetic model. The coupling of particle free transport and collision plays an important role here. Through the analysis of dissipative mechanism inside a numerical shock layer, it is realized that the adoption of exact Riemann solution of the Euler equations as a foundation of modern compressible CFD methods has fundamental flaws, and the shock instability at high Mach number simulation is unavoidable. The gas-kinetic scheme follows a valid physical process in the construction of numerical shock structure

高超声速计算中的气体动理学格式

回顧了高超聲速連續流部分的計算流體力學(CFD)方法,總結了近些年興起的氣體動理學格式。闡述了該格式的構造機制,強調了將物理規律直接用于構造數值方法的思路。結合一些應用實例,例如激波相互作用、激波邊界層相互作用以及邊界層分離等高超聲速問題,說明了這種構造思路給數值模擬帶來的優點。從高超聲速的發展歷程來看,氣體動理學格式的構造過程包含了更基礎的物理規律,而且具有多尺度的特性。這些特性有助于研究復雜的高超聲速問題。介觀或者微觀角度直接構造數值方法的發展趨勢為高超聲速計算工具指出了可能的發展方向。 For hypersonic flow simulation, a review of computation fluid dynamics (CFD) and a summary of gas kinetic scheme are presented in this paper. The mechanism underlying the construction of gas kinetic scheme is clarified by comparing it with the traditional CFD method. The importance of direct modeling and the implementation of the physical laws in a discretized space are emphasized. Through some classical hypersonic applications in recent years, such as the shock/shock interaction, shock wave/boundary layer interaction, and hypersonic boundary layer separation problems, the advantages of the methodology are also demonstrated. As a trend of CFD, the gas kinetic scheme includes more fundamental physical laws in its algorithm construction, and the multiple scale nature makes the kinetic scheme feasible for the hypersonic applications. The principle of direct modeling and the methodology of constructing numerical schemes from mesoscopic or microscopic flow dynamics would benefit the development of reliable flow solvers, especially for the high speed flow. ©, 2014, AAAS Press of Chinese Society of Aeronautics and Astronautics. All right reserved

A New Distributed Admission Control Based on Token Passsing

為了能提供良好的服務品質(QoS)以因應日漸重要的即時性與互動性的網路服務，整合式服務(IntServ)的出現使得頻寬保證服務(Guaranteed Service)的要求得以實現，但為了解決其最大的缺點-可擴性(Scalability)的問題，差異式服務(DiffServ)因而產生。由於差異式服務在網域內部各節點不需維持其上所傳資料流狀態資訊的服務架構(Core Stateless)，得以解決可擴性的問題，加上它亦能提供相當的服務品質，使得這種服務架構成為日後發展的一種主流。但在此服務架構下為求提供更嚴格的服務品質時，以往的允入控制(Admission Control)方法有著嚴重的瑕疵。 使用訊標分散式允入控制法(Distributed Admission Control Based on Token Passing)能達到嚴格要求的頻寬保證，並且有著不錯的效能。而本論文修改其中的方法，提出一個新的訊標分散式允入控制法(A New Distributed Admission Control Based on Token Passing)，改善對於頻寬的利用率，並且使之能更合乎現實網路狀況的環境。More and more applications need real-time and interactive service in the current network. For this reason, InterServ is a prominent architecture to support Qos (Quality of Service) and provide guaranteed service in Internet but it is not scalable. DiffServ is scalable because it does not maintain per-flow states in core router (Core Stateless) but it can not guarantee strict QoS. Admission control methods proposed to support guaranteed service in core stateless network have significant drawback. Distributed Admission Control Based on Token Passing is a good way which can provide guaranteed service. Therefore, modify original method becomes our A New Distributed Admission Control Based on Token Passing is proposed to improve utilization of links' bandwidth and to survive in real networks.摘要 Abstract 目錄 圖目錄 第一章 序論 第一節 研究背景 第二節 研究動機 第三節 研究目的 第四節 論文架構 第二章 文獻探討 第一節 基本的允入控制(Basic Admission Control) 1.1 傳統允入控制 (Traditional Admission Control) 1.2 量測式允入控制(Measurement-Based Admission Control) 第二節 端點式允入控制(Endpoint Admission Control) 2.1 集中式允入控制(Centralized Admission Control) 2.2 分散式允入控制(Distributed Admission Control) 第三章 一個新的訊標分散式允入控制法(A New Distributed Admission Control Based on Token Passing) 第一節 基本架構 第二節 計算公平分享的方法 第三節 支援保證頻寬的服務 第四節 我們提出的訊標分散式允入控制演算法 第五節 特點的探討 第四章 模擬 第一節 簡單的單一Link拓撲 (Simple Single Link Topology) 第二節 模擬結果 第五章 結論與未來方向 第一節 結論 第二節 未來方向 參考文

高階氣體動理學格式在湍流數值模擬中的應用

本文回顧了高階氣體動理學格式在湍流數值模擬中的應用。與傳統的Riemann求解器相比,氣體動理學格式可以提供時空耦合的演化過程,這對發展高精度格式十分重要。因此,基于兩步四階時間離散和高精度WENO重構,發展了具有四階時間精度的氣體動理學格式。該格式有更高的數值精度和穩定性,并且具有更好的處理復雜流動問題的能力。目前,兩步四階格式已經成功地應用到低雷諾數湍流直接數值模擬和高雷諾數工程湍流RANS模擬中,包括低速槽道湍流、超聲速均勻各向同性衰減湍流、二維亞聲速翼型湍流和三維跨聲速翼身湍流等。數值結果表明該格式對湍流直接數值模擬和湍流RANS模擬具有高數值精度和高數值穩定性。下一步將利用高階氣體動理學格式研究更具有挑戰性的可壓縮湍流問題,例如超聲速湍流邊界層和激波邊界相互作用等。 We review the application of high-order gas-kinetic scheme (HGKS) in the numerical simulations of turbulence. HGKS was developed based on the two-stage fourth-order temporal discretization and high-order weighted essentially non-oscillation (WENO) reconstruction. Compared with the classical Riemann solvers, the high-order temporal evolution process, which is extremely helpful in the design of robust, accurate, and efficient higher-order schemes, can be used to construct a spatial-temporal coupled gas-kinetic flux solver. Currently, HGKS has been successfully applied in the direct numerical simulations and Reynolds averaged Navier-Stokes (RANS) simulations of turbulence, including low-speed turbulent channel flows, the decaying supersonic isotropic turbulence, the subsonic NACA0012 airfoil turbulence, and the transonic ARA M100 wing-body turbulence. The numerical results show that HGKS has the high accuracy and outstanding robustness for turbulence simulations. In summary, the HGKS provides a powerful computational tool for studying turbulent flows, especially for compressible turbulence. In the future, more challenging studies will be conducted, including the supersonic turbulent boundary layers and the shock-boundary layer interaction. © 2021, The Editorial Board of Acta Aerodynamica Sinica. All right reserved

类探月返回试验器稀薄气体电离特性分析

探月返回试验器以接近第二宇宙速度再入,绕流气体将发生较为严重的化学反应和电离,传统上发生在连续流区的通信黑障大幅向稀薄区域延伸。本文基于自主开发的稀有组分权重因子方法的DSMC计算平台,采用公开的外形和与探月返回试验器相似的飞行条件,针对第一次再入、第一次跳出和第二次再入的稀薄流域,重点考察类探月返回试验器的稀薄气体电离特性。通过电子数密度预测通信中断发生高度,其结果与飞行试验观测值具有良好的一致性,误差在2 km以内。计算结果还表明,与RAM-C II等细长体的联合电离不同,对于类探月返回试验器的大钝头体再入,主要电离来源是N、O与中性分子或原子碰撞导致的直接电离。 As the lunar exploration capsule reentries with the second cosmic speed, serious chemical reactions and ionization occur in the surrounding atmosphere, and the communication blackout traditionally happened in continuum flows extends widely to the rarefied regime. Based on our own developed DSMC computation platform based on weighting factor scheme for trace species, the rarefied air ionization of lunar exploration type capsule is investigated, including the first reentry, first jump-out as well as second reentry processes in rarefied flow regimes, with an open configuration and simulation flying conditions. The communication blackout starting altitudes are predicted due to the electron number density, and the results behave excellent agreement with the flight observations, with errors smaller than 2 km. The results also reveal that, different from the associative ionization for slender body such as RAM-C II, the main ionization source of the reentry for large blunt body like the lunar exploration type capsule is the direct ionization due to the collision between N, O and neutral molecules or atoms. © 2019, The Editorial Board of Acta Aerodynamica Sinica. All right reserved

用BGK格式计算不可压缩流场

簡要介紹ＢＧＫ方法的基本思想，數值方法及其對不可壓縮流場數值計算的推廣．然后詳細介紹將ＢＧＫ方法應用于平面方框流的結果，將其結果與Ｇｈｉａ的結果進行了詳細的比較．本方法還用來模擬后臺階流動，所得結果與相應的實驗數據進行比較．以上比較表明本方法的有效性，同時也確定在計算不可壓縮流體時參數的正確選擇