Flora

Florahttps://flora.purejs.icu/index.htmlA garden of connected notes.Acknowledgements · List of Symbols · Abbreviations 致谢 · 符号表 · 缩写https://flora.purejs.icu/cfd-0001.htmlhttps://flora.purejs.icu/cfd-0001.html本书致谢、全部符号的中文名称与缩写对照表。Introduction 第1章引言https://flora.purejs.icu/cfd-0002.htmlhttps://flora.purejs.icu/cfd-0002.htmlCFD的历史沿革、数值方法与网格技术的发展脉络，以及本书的结构安排。Governing Equations 第2章控制方程https://flora.purejs.icu/cfd-0003.htmlhttps://flora.purejs.icu/cfd-0003.html流体流动的数学描述与守恒定律，Navier-Stokes方程的完整形式及其简化。Principles of Solution of the Governing Equations 第3章控制方程求解原理https://flora.purejs.icu/cfd-0004.htmlhttps://flora.purejs.icu/cfd-0004.html空间与时间离散ï¼显式与隐式格式ï¼湍流建模与边界条件概述。Structured Finite Volume Schemes 第4章结构网格有限体积格式https://flora.purejs.icu/cfd-0005.htmlhttps://flora.purejs.icu/cfd-0005.html控制体几何量、单元中心与单元顶点格式ï¼以及通用离散方法学。Unstructured Finite Volume Schemes 第5章非结构网格有限体积格式https://flora.purejs.icu/cfd-0006.htmlhttps://flora.purejs.icu/cfd-0006.html非结构控制体的几何量ï¼单元中心与中位对偶单元顶点格式。Temporal Discretisation 第6章时间离散https://flora.purejs.icu/cfd-0007.htmlhttps://flora.purejs.icu/cfd-0007.html显式多步格式、隐式算子的矩阵形式与通量雅可比的求值。Turbulence Modelling 第7章湍流建模https://flora.purejs.icu/cfd-0008.htmlhttps://flora.purejs.icu/cfd-0008.html湍流的基本方程：平均方法、涡黏性假设与雷诺应力输运。Boundary Conditions 第8章边界条件https://flora.purejs.icu/cfd-0009.htmlhttps://flora.purejs.icu/cfd-0009.html虚单元概念,固壁、远场、入流/出流边界的数值处理。Acceleration Techniques 第9章加速技术https://flora.purejs.icu/cfd-000A.htmlhttps://flora.purejs.icu/cfd-000A.html局部时间步长、焓阻尼、残差光顺等定常解加速方法。Lax, P.D.: Weak Solutions of Nonlinear Hyperbolic Equations and their Numerical Computation. Comm. Pure and Applied Mathematics, 7 (1954), pp. 159-193.https://flora.purejs.icu/cfd-r2-1.htmlhttps://flora.purejs.icu/cfd-r2-1.htmlLax 1954年的经典论文，提出非线性双曲型方程的弱解概念，是含激波等间断流动数值计算理论的奠基性工作。Thomas, P.D.; Lombard, C.K.: Geometric Conservation Law and Its Application to Flow Computations on Moving Grids. AIAA Journal, 17 (1979), pp. 1030-1037.https://flora.purejs.icu/cfd-r2-10.htmlhttps://flora.purejs.icu/cfd-r2-10.htmlThomas与Lombard提出几何守恒定律（GCL）的原始文献。Lesoinne, M.; Farhat, C.: Geometric Conservation Laws for Flow Problems with Moving Boundaries and Deformable Meshes and their Impact on Aeroelastic Computations. AIAA Paper 95-1709, 1995; also in Comp. Meth. Appl. Mech. Eng., 134 (1996), pp. 71-90.https://flora.purejs.icu/cfd-r2-11.htmlhttps://flora.purejs.icu/cfd-r2-11.htmlLesoinne与Farhat针对动边界与变形网格的几何守恒定律及其对气动弹性计算影响的工作。Guillard, H.; Farhat, C.: On the Significance of the GCL for Flow Computations on Moving Meshes. AIAA Paper 99-0793, 1999.https://flora.purejs.icu/cfd-r2-12.htmlhttps://flora.purejs.icu/cfd-r2-12.htmlGuillard与Farhat讨论GCL对移动网格流动计算重要性的AIAA会议论文。Zierep, J.: Vorlesungen über theoretische Gasdynamik (Lectures on Theoretical Gas Dynamics). G. Braun Verlag, Karlsruhe, 1963.https://flora.purejs.icu/cfd-r2-13.htmlhttps://flora.purejs.icu/cfd-r2-13.htmlZierep的德文气体动力学讲义，完全气体各热力学关系式的出处。Liepmann, H.W.; Roshko, A.: Elements of Gas Dynamics. John Wiley & Sons, New York, 1957.https://flora.purejs.icu/cfd-r2-14.htmlhttps://flora.purejs.icu/cfd-r2-14.htmlLiepmann与Roshko的经典教材《Elements of Gas Dynamics》，完全气体假设的参考来源。Srinivasan S.; Weilmuenster, K.J: Simplified Curve Fits for the Thermodynamic Properties of Equilibrium Air. NASA RP-1181, 1987.https://flora.purejs.icu/cfd-r2-15.htmlhttps://flora.purejs.icu/cfd-r2-15.htmlSrinivasan与Weilmuenster为平衡空气热力学性质给出的简化曲线拟合（NASA参考出版物）。Schmatz, M.A.: Hypersonic Three-Dimensional Navier-Stokes Calculations for Equilibrium Gas. AIAA Paper 89-2183, 1989.https://flora.purejs.icu/cfd-r2-16.htmlhttps://flora.purejs.icu/cfd-r2-16.htmlSchmatz关于平衡气体三维纳维–斯托克斯计算的高超声速AIAA会议论文。Mundt, Ch.; Keraus, R.; Fischer, J.: New, Accurate, Vectorized Approximations of State Surfaces for the Thermodynamic and Transport Properties of Equilibrium Air. ZFW, 15 (1991), Springer Verlag, pp. 179-184.https://flora.purejs.icu/cfd-r2-17.htmlhttps://flora.purejs.icu/cfd-r2-17.htmlMundt等人提出平衡空气热力学与输运性质状态面的新型高精度向量化逼近。Bussing, T.R.A; Murman, E.M.: Finite-Volume Method for the Calculation of Compressible Chemically Reacting Flows. AIAA Journal, 26 (1988), pp. 1070-1078.https://flora.purejs.icu/cfd-r2-18.htmlhttps://flora.purejs.icu/cfd-r2-18.htmlBussing与Murman将有限体积方法用于可压化学反应流动计算的代表工作。Molvik, G.A.; Merkle, C.L.: A Set of Strongly Coupled, Upwind Algorithms for Computing Flows in Chemical Non-equilibrium. AIAA Paper 89-0199, 1989.https://flora.purejs.icu/cfd-r2-19.htmlhttps://flora.purejs.icu/cfd-r2-19.htmlMolvik与Merkle针对化学非平衡流动提出的强耦合迎风算法。Aris, R.: Vectors, Tensors and the Basic Equations of Fluid Mechanics. Dover Publ. Inc., New York, 1989.https://flora.purejs.icu/cfd-r2-2.htmlhttps://flora.purejs.icu/cfd-r2-2.htmlR. Aris关于张量与流体力学基本方程的经典教材，本章单位张量、应力张量等张量记号的参考来源。Slomski, J.F.; Anderson, J.D.; Gorski, J.J.: Effectiveness of Multigrid in Accelerating Convergence of Multidimensional Flows in Chemical Nonequilibrium. AIAA Paper 90-1575, 1990.https://flora.purejs.icu/cfd-r2-20.htmlhttps://flora.purejs.icu/cfd-r2-20.htmlSlomski等人研究多重网格在加速化学非平衡多维流动收敛中的效果。Shuen, J.S.; Liou, M.S.; van Leer, B.: Inviscid Flux-Splitting Algorithms for Real Gases with Non-equilibrium Chemistry. J. Computational Physics 90 (1990), pp. 371-395.https://flora.purejs.icu/cfd-r2-21.htmlhttps://flora.purejs.icu/cfd-r2-21.htmlShuen、Liou与van Leer针对非平衡化学真实气体的无粘通量分裂算法，组分温度迭代公式的出处之一。Li, C.P.: Computational Aspects of Chemically Reacting Flows. AIAA Paper 91-1574, 1991.https://flora.purejs.icu/cfd-r2-22.htmlhttps://flora.purejs.icu/cfd-r2-22.htmlC. P. Li关于化学反应流动计算方法的AIAA会议论文。Shuen, J.-S.; Chen, K.-H.; Choi, Y.: A Coupled Implicit Method for Chemical Non-equilibrium Flows at All Speeds. J. Computational Physics, 106 (1993), pp. 306-318.https://flora.purejs.icu/cfd-r2-23.htmlhttps://flora.purejs.icu/cfd-r2-23.htmlShuen等人提出的适用于全速度范围化学非平衡流动的耦合隐式方法。Yu, S.-T.; Chang, S.-C.; Jorgenson, P.C.E.; Park, S.-J.; Lai, M.-C.: Basic Equations of Chemically Reactive Flow for Computational Fluid Dynamics. AIAA Paper 98-1051, 1998.https://flora.purejs.icu/cfd-r2-24.htmlhttps://flora.purejs.icu/cfd-r2-24.htmlYu等人给出CFD用化学反应流基本方程（含通量Jacobian矩阵及其特征值）的AIAA会议论文。Bakhtar, F.; Tochai, M.T.M.: An Investigation of Two-Dimensional Flows of Nucleating and Wet Steam by the Time-Marching Method. Int. J. Heat and Fluid Flow 2 (1980), pp. 5-18.https://flora.purejs.icu/cfd-r2-25.htmlhttps://flora.purejs.icu/cfd-r2-25.htmlBakhtar与Tochai用时间推进法研究成核与湿蒸汽二维流动的早期工作。Young, J.B.; Snoeck, J.: Aerothermodynamics of Low Pressure Steam Turbines and Condensers. Eds. Moore, M.J.; Sieverding, C.H.; Springer Verlag, N.Y., 1987, pp. 87-133.https://flora.purejs.icu/cfd-r2-26.htmlhttps://flora.purejs.icu/cfd-r2-26.htmlYoung与Snoeck撰写的低压汽轮机与凝汽器气动热力学书章（Moore与Sieverding主编）。Bakhtar, F.; So, K.S.: A Study of Nucleating Flow of Steam in a Cascade of Supersonic Blading by the Time-Marching Method. Int. J. Heat and Fluid Flow 12 (1991), pp. 54-62.https://flora.purejs.icu/cfd-r2-27.htmlhttps://flora.purejs.icu/cfd-r2-27.htmlBakhtar与So用时间推进法研究超声速叶栅中的成核蒸汽流动。Young, J.B.: Two-Dimensional Non-Equilibrium Wet-Steam Calculations for Nozzles and Turbine Cascades. Trans. ASME, J. Turbomachinery, 114 (1992), pp. 569-579.https://flora.purejs.icu/cfd-r2-28.htmlhttps://flora.purejs.icu/cfd-r2-28.htmlYoung关于喷管与涡轮叶栅二维非平衡湿蒸汽计算的论文。White, A.J.; Young, J.B.: Time-Marching Method for the Prediction of Two-Dimensional, Unsteady Flows of Condensing Steam. AIAA J. Propulsion and Power, 9 (1993), pp. 579-587.https://flora.purejs.icu/cfd-r2-29.htmlhttps://flora.purejs.icu/cfd-r2-29.htmlWhite与Young提出预测二维非定常凝结蒸汽流动的时间推进方法。Schlichting, H.: Boundary Layer Theory. 7th edition, McGraw-Hill, New York, 1979.https://flora.purejs.icu/cfd-r2-3.htmlhttps://flora.purejs.icu/cfd-r2-3.htmlSchlichting《边界层理论》第七版，边界层理论的权威教科书。Liberson, A.; Kosolapov, Y.; Rieger, N.; Hesler, S.: Calculation of 3-D Condensing Flows in Nozzles and Turbine Stages. EPRI Nucleation Workshop, Rochester, N.Y., October 24-26, 1995.https://flora.purejs.icu/cfd-r2-30.htmlhttps://flora.purejs.icu/cfd-r2-30.htmlLiberson等人在EPRI成核研讨会上报告的喷管与汽轮机级内三维凝结流动计算。Bakhtar, F.; Mahpeykar, M.R.; Abbas, K.K.: An Investigation of Nucleating Flows of Steam in a Cascade of Turbine Blading - Theoretical Treatment. Transaction of the ASME 117 (1995), pp. 138-144.https://flora.purejs.icu/cfd-r2-31.htmlhttps://flora.purejs.icu/cfd-r2-31.htmlBakhtar等人对汽轮机叶栅成核蒸汽流动的理论处理。White, A.J.; Young, J.B.; Walters, P.T.: Experimental Validation of Condensing Flow Theory for a Stationary Cascade of Steam Turbine Blades. Phil. Trans. R. Soc., London, A 354 (1996), pp. 59-88.https://flora.purejs.icu/cfd-r2-32.htmlhttps://flora.purejs.icu/cfd-r2-32.htmlWhite、Young与Walters对汽轮机静止叶栅凝结流动理论的实验验证。Steger, J.L.: Implicit Finite Difference Simulation of Flows About Two-Dimensional Arbitrary Geometries. AIAA Journal, 17 (1978), pp. 679-686.https://flora.purejs.icu/cfd-r2-33.htmlhttps://flora.purejs.icu/cfd-r2-33.htmlSteger关于二维任意外形绕流隐式有限差分模拟的论文，薄剪切层近似的参考来源之一。Pulliam, T.H.; Steger, J.L.: Implicit Finite Difference Simulations of Three-Dimensional Compressible Flows. AIAA Journal, 18 (1980), pp. 159-167.https://flora.purejs.icu/cfd-r2-34.htmlhttps://flora.purejs.icu/cfd-r2-34.htmlPulliam与Steger关于三维可压缩流动隐式有限差分模拟的论文，薄剪切层近似的参考来源之一。Patankar, S.V.; Spalding, D.B.: A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows. Int. J. Heat Mass Transfer, 15 (1972), pp. 1787-1806.https://flora.purejs.icu/cfd-r2-35.htmlhttps://flora.purejs.icu/cfd-r2-35.htmlPatankar与Spalding关于三维抛物型流动中传热、传质与动量传递计算方法的经典论文。Aslan, A.R.; Grundmann, R.: Computation of Three-Dimensional Subsonic Flows in Ducts Using the PNS Approach. ZFW, 14 (1990), Springer Verlag, pp. 373-380.https://flora.purejs.icu/cfd-r2-36.htmlhttps://flora.purejs.icu/cfd-r2-36.htmlAslan与Grundmann用PNS方法计算管道内三维亚声速流动的论文。Kirtley, K.R.; Lakshminarayana, B.: A Multiple Pass Space-Marching Method for Three-Dimensional Incompressible Viscous Flow. ZFW, 16 (1992), Springer Verlag, pp. 49-59.https://flora.purejs.icu/cfd-r2-37.htmlhttps://flora.purejs.icu/cfd-r2-37.htmlKirtley与Lakshminarayana针对三维不可压黏性流动的多遍空间推进方法。Hollenbäck, D.M.; Blom, G.A.: Application of a Parabolized Navier-Stokes Code to an HSCT Configuration and Comparison to Wind Tunnel Test Data. AIAA Paper 93-3537, 1993.https://flora.purejs.icu/cfd-r2-38.htmlhttps://flora.purejs.icu/cfd-r2-38.htmlHollenbäck与Blom将抛物化纳维–斯托克斯代码应用于HSCT构型并与风洞试验数据比较。Krishnan, R.R.; Eidson, T.M.: An Efficient, Parallel Space-Marching Euler Solver for HSCT Research. AIAA Paper 95-1749, 1995.https://flora.purejs.icu/cfd-r2-39.htmlhttps://flora.purejs.icu/cfd-r2-39.htmlKrishnan与Eidson为HSCT研究开发的高效并行空间推进Euler求解器。White, F.M.: Viscous Fluid Flow. McGraw-Hill, New York, 1991.https://flora.purejs.icu/cfd-r2-4.htmlhttps://flora.purejs.icu/cfd-r2-4.htmlF. M. White《Viscous Fluid Flow》，黏性流动理论的常用教科书。Nakahashi, K.; Saitoh, E.: Space-Marching Method on Unstructured grid for Supersonic Flows with Embedded Subsonic Regions. AIAA Paper 96-0418, 1996.https://flora.purejs.icu/cfd-r2-40.htmlhttps://flora.purejs.icu/cfd-r2-40.htmlNakahashi与Saitoh在非结构网格上处理含亚声速嵌入区的超声速流动空间推进方法。Yamaleev, N.K.; Ballmann, J.: Space-Marching Method for Calculating Steady Supersonic Flows on a Grid Adapted to the Solution. J. Computational Physics, 146 (1998), pp. 436-463.https://flora.purejs.icu/cfd-r2-41.htmlhttps://flora.purejs.icu/cfd-r2-41.htmlYamaleev与Ballmann在解自适应网格上计算定常超声速流动的空间推进方法。Stokes, G.G.: On the Theories of Internal Friction of Fluids in Motion. Trans. Cambridge Phil. Soc., 8 (1845), pp. 287-305.https://flora.purejs.icu/cfd-r2-5.htmlhttps://flora.purejs.icu/cfd-r2-5.htmlStokes 1845年的原始论文，提出了关于第二黏性系数的著名假设（Stokes假设）。Gad-el-Hak, M.: Questions in Fluid Mechanics: Stokes' Hypothesis for a Newtonian, Isotropic Fluid. J. of Fluids Engineering, 117 (1995), pp. 3-5.https://flora.purejs.icu/cfd-r2-6.htmlhttps://flora.purejs.icu/cfd-r2-6.htmlGad-el-Hak关于牛顿各向同性流体中Stokes假设适用性的讨论。Vinokur, M.: Conservation Equations of Gas Dynamics in Curvilinear Coordinate Systems. J. Computational Physics, 14 (1974), pp. 105-125.https://flora.purejs.icu/cfd-r2-7.htmlhttps://flora.purejs.icu/cfd-r2-7.htmlVinokur关于曲线坐标系下气体动力学守恒方程形式的论文，与经Gauss定理导出微分形式有关。Hirsch, C.: Numerical Computation of Internal and External Flows. Vols. 1 and 2, John Wiley and Sons, 1988.https://flora.purejs.icu/cfd-r2-8.htmlhttps://flora.purejs.icu/cfd-r2-8.htmlHirsch两卷本CFD权威教材，涵盖内流与外流的数值计算；旋转参考系等内容可参见该书。Pulliam, T.H.; Steger, J.L.: Recent Improvements in Efficiency, Accuracy, and Convergence for Implicit Approximate Factorization Algorithms. AIAA Paper 85-0360, 1985.https://flora.purejs.icu/cfd-r2-9.htmlhttps://flora.purejs.icu/cfd-r2-9.htmlPulliam与Steger关于隐式近似分解算法改进的AIAA会议论文，此处用于网格相对固定坐标系运动的处理。计算流体力学：Computational Fluid Dynamicshttps://flora.purejs.icu/cfd.htmlhttps://flora.purejs.icu/cfd.htmlJiri Blazek《Computational Fluid Dynamics: Principles and Applications》第二版段落级双语翻译,翻译进行中。前言与导言https://flora.purejs.icu/eos-0001.htmlhttps://flora.purejs.icu/eos-0001.htmlRoger Angell的前言与E. B. White为1979年版所写的导言。第一章英语用法的基本规则https://flora.purejs.icu/eos-0002.htmlhttps://flora.purejs.icu/eos-0002.html十一条基本用法规则：所有格、逗号、插入语、从句、代词格与主谓一致等。第二章写作的基本原理https://flora.purejs.icu/eos-0003.htmlhttps://flora.purejs.icu/eos-0003.html十二条关于组篇与风格的原理：段落、主动语态、简洁、并列结构与强调等。第三章格式的若干问题https://flora.purejs.icu/eos-0004.htmlhttps://flora.purejs.icu/eos-0004.html口语、感叹号、标题、连字符、数字、括号、引文等格式细节。第四章常被误用的词与短语（A–F）https://flora.purejs.icu/eos-0005.htmlhttps://flora.purejs.icu/eos-0005.html从Aggravate到Fortuitous的常见误用词条。第四章常被误用的词与短语（G–O）https://flora.purejs.icu/eos-0006.htmlhttps://flora.purejs.icu/eos-0006.html从Get到-oriented的常见误用词条。第四章常被误用的词与短语（P–Z）https://flora.purejs.icu/eos-0007.htmlhttps://flora.purejs.icu/eos-0007.html从Partially到Would的常见误用词条。第五章风格的探索https://flora.purejs.icu/eos-0008.htmlhttps://flora.purejs.icu/eos-0008.html关于风格本质的讨论，以及二十一条写作提醒。后记与术语表https://flora.purejs.icu/eos-0009.htmlhttps://flora.purejs.icu/eos-0009.htmlCharles Osgood的后记，以及Robert DiYanni编写的语法术语表。英语写作：The Elements of Stylehttps://flora.purejs.icu/eos.htmlhttps://flora.purejs.icu/eos.htmlStrunk与White的英语写作指南第四版中文翻译。Flora：用Grove构建可执行文档https://flora.purejs.icu/index.htmlhttps://flora.purejs.icu/index.html从内容树、数学计算与文学编程三个方向认识Grove。术语表：文档、文学编程与数学https://flora.purejs.icu/glossary.htmlhttps://flora.purejs.icu/glossary.html集中解释全站共用的术语，并链接到展开讨论的页面。用.plant写作：元数据、命令与Schemehttps://flora.purejs.icu/grove-0001.htmlhttps://flora.purejs.icu/grove-0001.html认识页面元数据、自动段落、at-exp命令和源码展示。组合tree：subtree与transcludehttps://flora.purejs.icu/grove-0002.htmlhttps://flora.purejs.icu/grove-0002.html把一段内容保留在原处、单独寻址，并在其他位置重复使用。构建阶段与缓存：读取、分析、渲染https://flora.purejs.icu/grove-0003.htmlhttps://flora.purejs.icu/grove-0003.html说明Grove构建的阶段分工，以及内容IR的复用、依赖登记与失效。Grove文档：写作模型与tree组合https://flora.purejs.icu/grove.htmlhttps://flora.purejs.icu/grove.html认识.plant页面、结构化内容、稳定地址与嵌入。尝试使用Grovehttps://flora.purejs.icu/journal-0001.htmlhttps://flora.purejs.icu/journal-0001.html从计算、排版与计划三个平台设想Grove，以及同像性带来的能力。文学编程：片段、计划与实例https://flora.purejs.icu/lp-0001.htmlhttps://flora.purejs.icu/lp-0001.html用累计器学习完整定义的保存、程序装配、状态隔离和同源输出。文章中的可执行Scheme定义https://flora.purejs.icu/lp-0002.htmlhttps://flora.purejs.icu/lp-0002.html使用program展示真实Scheme定义，使用核验表达式说明结果与复用行为。算术解释器与简化器https://flora.purejs.icu/lp-0003.htmlhttps://flora.purejs.icu/lp-0003.html定义表达式语义，组合重写规则，并检查结果保持、幂等性与预期异常。从文章模块导入程序定义https://flora.purejs.icu/lp-0004.htmlhttps://flora.purejs.icu/lp-0004.html从文学化文章导入真实binding，让文档与可复用程序保持同源。文本片段与源码生成https://flora.purejs.icu/lp-0005.htmlhttps://flora.purejs.icu/lp-0005.html用命名代码片段组织解释，组合为Scheme源码，再独立执行导出的程序。文学编程库：接口与构建约定https://flora.purejs.icu/lp-0006.htmlhttps://flora.purejs.icu/lp-0006.html说明LP模块职责、身份、源码范围、模块准备、缓存与支持边界。Scheme元循环解释器https://flora.purejs.icu/lp-0007.htmlhttps://flora.purejs.icu/lp-0007.html按求值、环境和核验组织Scheme子集的解释，并装配成可执行程序。Scheme解释器的闭包与环境https://flora.purejs.icu/lp-0008.htmlhttps://flora.purejs.icu/lp-0008.html提供可跨文章导入的语法片段，不在声明时执行解释器定义。Scheme元循环解释器的自解释与核验https://flora.purejs.icu/lp-0009.htmlhttps://flora.purejs.icu/lp-0009.html比较宿主Scheme、元循环解释器与解释器中的解释器，并导出可独立核验的源码。Scheme解释器的多文件工程https://flora.purejs.icu/lp-000A.htmlhttps://flora.purejs.icu/lp-000A.html用同一份片段组装独立Guile模块，明确导入、初始化顺序与核验入口。文学编程：文章、程序与核验https://flora.purejs.icu/lp.htmlhttps://flora.purejs.icu/lp.html探索代码与解释如何共用来源，并按主题阅读可执行案例。数学表示：Formula、Semantic与Notationhttps://flora.purejs.icu/math-0001.htmlhttps://flora.purejs.icu/math-0001.html一段数学源码如何成为可计算的对象，再成为MathML。构造并执行数学计算https://flora.purejs.icu/math-0002.htmlhttps://flora.purejs.icu/math-0002.html从Semantic输入到多pass报告：精确计算、化简、结果复用。符号推导：求导、搜索与核验https://flora.purejs.icu/math-0003.htmlhttps://flora.purejs.icu/math-0003.html把计算写成可重放的规则链，而不只展示答案。从向量场计算Cartesian算子https://flora.purejs.icu/math-0004.htmlhttps://flora.purejs.icu/math-0004.html声明有序坐标系，计算具体场的grad、div、curl和Laplacian。向量表示：分量与显式偏导https://flora.purejs.icu/math-0005.htmlhttps://flora.purejs.icu/math-0005.html构造具体向量，区分偏导项与执行偏导，并查看来源和前提。Cartesian算子的计算追踪https://flora.purejs.icu/math-0006.htmlhttps://flora.purejs.icu/math-0006.html从具体分量开始，查看多pass计算和推导核验。多项式积分与Poisson方程https://flora.purejs.icu/math-0007.htmlhttps://flora.purejs.icu/math-0007.html观察Semantic IR如何经过专用稀疏多项式IR，再回到数学值。多变量函数与正则性https://flora.purejs.icu/math-0008.htmlhttps://flora.purejs.icu/math-0008.html当函数未知时保留符号导数；用有限前提描述可执行范围。用miniKanren查询数学规则https://flora.purejs.icu/math-0009.htmlhttps://flora.purejs.icu/math-0009.html把规则目录当作关系查询，输出真正参与计算的规则说明。查询没有入向引用的treehttps://flora.purejs.icu/math-000A.htmlhttps://flora.purejs.icu/math-000A.html在Flora项目中定义关系谓词，并查询没有被链接或transclude的文章。关系查询参考：DSL与项目谓词https://flora.purejs.icu/math-000B.htmlhttps://flora.purejs.icu/math-000B.html汇总miniKanren查询语法、规则目录与项目自定义谓词。Grove数学语言：表示、计算与核验https://flora.purejs.icu/math.htmlhttps://flora.purejs.icu/math.html用Formula、Semantic和Notation组织可计算的数学内容。